Talks of mathematics colloquium of the previous years
Listed by date, speaker, title, abstract.
If slides are available, links to the slides are included.
General Mathematics Colloquium Archive
Colloquium talks of previous years
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2021
24 November - Ian Stewart (Warwick, UK) [Slides]
Title: Synchrony and Phase Relations in Network Dynamics
Abstract: The talk will summarize some of the main ideas in a formal theory of networks of coupled dynamical systems, developed over the past 20 years or so. It is intended for non-specialists, so much of the material will be familiar to experts, but I will include some more recent results. I will also mention applications to neuroscience, synthetic gene circuits, and animal locomotion. By 'network' I mean a directed graph whose nodes represent dynamical systems, and whose arrows represent coupling between those systems. Both nodes and arrows can be assigned 'types': roughly speaking, nodes of the same type have identical internal dynamics, and arrows of the same type represent identical coupling. Each network diagram defines a class of 'admissible' differential equations, which are compatible with the network topology (and types). Two nodes are synchronous, for a specific solution of this equation, if they have the same state at all times. For periodic states, nodes can also be related by a phase shift. Symmetries of the network can create synchrony and phase patterns; however, such patterns can also exist without symmetry. The key concept here is that of a 'balanced coloring' of the nodes: one in which nodes of the same color receive inputs whose colors and types match. I will discuss how balanced colorings determine synchrony and phase patterns, summarise some basic conjectures in the theory that have been partly proved, and describe recent results on networks with the topology of a lattice.
10 November - Alex Cole (UvA)
Title: The Shape of Physics Data
Abstract: Physics data occupies an intriguing middle ground between theoretical control and complexity. On the one hand, physics data is constrained by deep principles like symmetry and causality. On the other hand, symmetries can be obscured by nonlinear dynamics, or qualitatively new behavior can emerge when the number of degrees of freedom is increased. In this talk, I will describe how a common set of computational methods can illuminate physics data across subfields. The guiding principle is that physics data has “shape,” and this shape efficiently organizes information regarding symmetries, dynamics, and organization by scale. To probe this shape, we will use a tool from applied topology called persistent homology. Persistent homology associates a data set with a family of discrete complexes and tracks topological changes (such as the formation of voids) in this family. I will demonstrate how this approach proves useful in three distinct physical settings: phase transitions in condensed matter systems, nonlinear structure formation at cosmological scales, and the “landscape” of string theory vacua.
20 October - Shane Kepley (VU) [Slides]
Title: Combinatorial and numerical methods for studying global dynamics in gene regulatory networks
Abstract: Modeling the dynamics of gene regulatory networks is a central problem in Systems Biology. Using ODE models is a common approach which produces reliable models. However, these models often suffer from a rapid increase in the parameter dimension as additional gene interactions are added to the model. Despite these high dimensional parameters, the dynamics observed in experiments are generally robust and limited to relatively few dynamical phenotypes which suggests these models are overparameterized in a certain sense.
In this talk we introduce recent work which combines combinatorial and numerical techniques aiming to explicitly compute these dynamic phenotypes globally and estimate the extent to which these models are overparameterized. We demonstrate these techniques in several examples and describe how this approach has revealed surprising connections between dynamical systems, algebraic geometry, and order theory.
06 October - Julia Olkhovskaya (VU) [Slides]
Title: Robust algorithms for sequential learning with bandit feedback
Abstract: The framework of contextual bandits can be used to address a broad range of important and challenging decision-making problems such as online advertising and sequential treatment allocation. In the first part of the talk, we will consider an adversarial variant of the linear contextual bandit problem, where the sequence of loss functions associated with each arm is allowed to change without restriction over time. In the second part of the talk, we consider a more complex setting, where the learner interacts with an episodic Markov decision process.
For all mentioned settings, we develop computationally efficient algorithms and provide theoretical guarantees on the performance of those algorithms.
Based on joint work with Gergely Neu.
22 September - Nirvana Coppola (VU) [Slides]
Title: A brief history of reduction types of algebraic curves
Abstract: Algebraic curves over number fields, i.e. curves defined by polynomial equations, are of great interest in number theory and algebraic geometry. Many questions may be asked on this topic. For example, does a given curve have a (rational) point? What is its genus? How does a given curve behave locally?
In this talk, we will focus on the local behaviour of algebraic curves, and more precisely on their reduction types. We will see how finding an answer to this question is increasingly difficult, depending on the genus, and what is known for low-genus curves. Finally, we will show a recent result on the (stable) reduction types of a certain family of genus 3 curves - the Ciani curves, based on joint work with I. Bouw, S. Kunzweiler, P. Kılıçer, E. Lorenzo-García and A. Somoza.
08 September - Gabriele Benedetti (VU) [Slides]
Title: From Hamiltonian Mechanics to Symplectic Geometry
Abstract: Born from the principle of conservation of energy at the beginning of
the 19th century, Hamiltonian mechanics still gives a successful
description of conservative systems in contemporary physics. In recent
years, Hamiltonian mechanics has also brought mathematicians to the
study of a new type of geometry in phase space characterized by many
unexpected features and intriguing open questions. In this talk we will
focus on some of these features and questions which are connected to
seemingly unrelated topics such as the uncertainty principle, Fibonacci
numbers and the volume of convex bodies.17 May – Martijn Kool (UU)
Title: The Geometry of Magnificent Four
Abstract: Solid partitions are piles of boxes in the corner of a 4-dimensional room. Their enumeration is a mystery since MacMahon proposed an incorrect formula around 1916. Motivated by super-Yang-Mills theory on (complex) 4-dimensional affine space, Nekrasov recently assigned a measure to solid partitions and proposed a conjectural formula for their weighted enumeration.
We give a geometric definition of this measure using Hilbert scheme of points on 4-dimensional affine space. Although this Hilbert scheme is very singular and has "higher obstructions", we can use recent work of Oh-Thomas to localise our invariants and prove Nekrasov's conjecture. This is a non-technical talk based on joint work with J. V. Rennemo.
21 April – Tere M-Seara (UPC) [Slides]
Title: Chaos and oscillatory motions in the planar three body problem.
Abstract: The planar three body problem models the motion of three bodies under the Newtonian gravitational force. In 1922 Chazy classified the possible final motions of the three bodies, that is, the behaviours the bodies may have when time tends to infinity. One of them are what is known as oscillatory motions, that is, solutions of the three body problem such that the positions of the bodies is unbounded but comes back infinitely many times to a bounded region of the configuration space. At the time of Chazy, all types of final motions were known, except the oscillatory ones. We prove that, if all three masses are not equal, such motions exist. In fact, we prove the existence of chaotic behaviour on the motion of the bodies. The oscillatory orbits are one of the consequences of the existence of this chaotic behaviour.
07 April – Jose Mujica (VU Amsterdam) [Slides]
Title: Slow Manifolds, Invariant Manifolds and their interactions: a tale of slow-fast dynamical systems
Abstract: Slow-fast dynamical system arise in several applications. They describe phenomena in which system variables evolve in different timescales. Since Fenichel’s seminal work in the late 70’s, a method known as Geometric Singular Perturbation Theory (GSPT) has proven to be successful in the study of slow-fast systems. One of the main ideas of GSPT is to exploit the timescale separation in order to construct trajectories as a concatenation of slow and fast segments, obtained as solutions of subsystems describing the limiting slow and fast motion, respectively. This was one gets understanding of the geometry of so-called slow manifolds, along which the flow behaves considerably slow with respect to the rest of the dynamics; togethter with classical invariant manifolds, slow manifolds organize the phase space globally and locally.
In this talk we discuss some of the ideas of GSPT and describe the dynamics of a family of slow-fast systems with one fast and two slow variables. The focus is on a bifurcation that occurs in the slow dynamics known as a folded saddle-node of type II. This scenario provides a crash between classical dynamical systems and slow-fast systems, in the sense that there is an interaction of a slow manifold with a global invariant manifold. This has consequences for the local and global dynamics of the system. In particular we discuss the organization of recurrent dynamics in the form of oscillatory patterns known as mixed-mode oscillations, and the homoclinic scenarios nearby. The way we approach this is via the numerical approximation of these manifolds in a boundary-value-problem setup with the software AUTO, and track the manifolds when system parameters are varied.
17 March – Vanja Nikolic (RU) [Slides]
Title: The mathematics behind nonlinear sound waves
Abstract: Sound waves with sufficiently large amplitudes are known to exhibit nonlinear behavior. The nonlinearity will be apparent sooner in high-frequency waves because these effects accumulate over the distance measured in wavelengths. This makes ultrasonic waves inherently nonlinear. Their many applications range from non-invasive surgery to non-destructive material testing and motivate the mathematical investigation into nonlinear acoustics. In this talk, we will give an overview of research questions and some recent results in the analysis and numerics of partial differential equations that model the propagation of such nonlinear waves.
03 March – Thomas Rot (VU Amsterdam) [Slides]
Title: Most ropes have an even number of ends.
Abstract: Compact one-dimensional manifolds can be classified: They are finite unions of circles and intervals. A simple consequence of this classification is that the number of boundary components of a compact one-dimensional manifold is even. This innocent looking observation has far reaching consequences. It allows you to determine quickly if you can escape a maze, can prove the fundamental theorem of algebra, and much more. I will discuss some classical consequences that I particularly enjoy. I will end my talk with discussion of recent work, joint with Federica Pasquotto, on degree theory for orbifolds, In this setting ropes might have an odd number of ends, but we can still say something. No prior knowledge of (differential) topology will be assumed.
17 February – Chris Bick (VU Amsterdam) [Slides]
Title: Coupled Oscillator Networks: Structure, Interactions, and Dynamics
Abstract: The collective dynamics of coupled oscillatory processes govern many aspects crucial to our lives, whether it is the synchronous beating of our heart cells, collective activity of neurons in the brain, or power grid networks that operate in a stable frequency regime. In this talk we discuss how the collective network dynamics are shaped by the network structure (what oscillator is coupled to what other oscillator) and the network interactions (how one oscillator is coupled to another). We discuss in particular how "higher-order" interactions, which have attracted tremendous attention in recent years, give rise to heteroclinic and chaotic dynamics.
03 February – Svetlana Dubinkina (VU Amsterdam) [Slides]
Title: Shadowing approach to data assimilation
Abstract: Data assimilation is broadly used in atmosphere and ocean science to correct error in the state estimation by incorporating information from measurements (e.g. satellites) into the mathematical model. The widely-used variational data assimilation method has a drawback of a drastic increase of the number of local minima of the corresponding cost function as the number of measurements increases. The shadowing approach to data assimilation, which was pioneered by K. Judd and L. Smith in Physica D (2001), aims at estimating the whole trajectory at once. It has no drawback of several local minima. However, it is computationally expensive, requires measurements of the whole trajectory, and has an infinite subspace of solutions.
We propose to decrease the computational cost by projecting the shadowing approach to the unstable subspace that typically has much lower dimension than the phase space. Furthermore, we propose a novel shadowing-based data assimilation method that lifts up the requirement of a fully-observed state. We prove convergence of the method and demonstrate in numerical experiments with Lorenz models that the developed data assimilation method substantially outperforms the variational data assimilation method.
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2020
09 December – Francesca Arici (University of Leiden) [Slides]
Title: A non-commutative approach to the topology of circle and sphere bundles
Abstract: The theory of C*–algebras offers an elegant setting for many problems in mathematics and physics. In view of Gel’fand duality, their study is often referred to as non-commutative topology: general noncommutative C*–algebras are interpreted as non-commutative spaces. Many classical geometric and topological concepts can be translated into operator algebraic terms, leading to the so-called noncommutative geometry (NCG) dictionary. In this talk, I will describe how circle and sphere bundles, central objects in the development of algebraic topology, can be realised in terms of modules over operator algebras.
25 November – Botond Szabo (VU)
Title: On theoretical guarantees for variational Bayes method
Abstract: I will start by giving a brief introduction to Bayesian statistics, talk about its theoretical analysis and introduce variational methods to make the computations feasible. Variational Bayes is very popular and frequently used in practice, however, so far it was considered as a black box procedure. Theoretical results started to emerge only in the last 1-2 years, but we still have a rather limited fundamental understanding about the limitations and guarantees of this procedure. In the end of the talk I will provide theoretical and empirical guarantees for variational Bayes in context of the popular high-dimensional linear and logistic regression models.
Based on a joint work with Kolyan Ray and Gabriel Clara.
28 October – Eni Muska (UvA), Zoom meeting [Slides]
Reference: Amico, M. and Van Keilegom, I. (2018) Cure models in survival analysis. Annual Review of Statistics and Its Application, 5(1).
Title: Statistical methods for survival data: accounting for cured patients
Abstract: Survival analysis is a branch of statistics that analyzes time-to-event data, where the variable of interest is the time it takes for a certain event to happen. It helps us answer questions like: -What percentage of cancer patients will survive more than 4 years? or -Which factors affect the survival time of cancer patients? Even though the main motivation comes from the medical setting, survival analysis is used in a variety of fields as any event of interest can be considered. In this talk, I will introduce the basics of survival analysis and some issues related to conventional methods that are still subject of ongoing research. In particular, I will focus on cure rate models which offer an alternative modelling approach that accounts for the presence of 'cure' (the possibility that the event never happens). Cure models can provide additional insights with respect to the traditional methods and are of particular interest in studies of some cancer types for which advances in medical treatments have led to increased chances of long-term-survival.
07 October – Martijn Caspers (VU Amsterdam), Zoom meeting [Slides]
Title: Perturbations of commutators
Abstract: The commutator [x,y] = xy-yx is of central importance in mathematics and physics. In mathematics the commutator of two self-adjoint matrices is 0 if and only if the matrices admit a complete set of common eigenvectors. In physics - more precisely in quantum mechanics - this translates to the famous Heisenberg uncertainty principle: two observables can be measured simultaneously if and only if the observables commute. In a qualitative way the commutator actually tells how good two observables can be measured simultaneously.
The mathematical physicists M.G. Krein posed in 1964 the question whether the norm of a commutator can be estimated after it is perturbed (for instance by noise or a chance of variables, to be made precise in the talk). We provide a solution to Krein's problem that is moreover sharp. The proof relies - surprisingly - almost entirely on harmonic analysis. The solution has important consequences, for instance for the existence of non-commutative Taylor series.
23 September – Paulo Serra (VU Amsterdam), Zoom meeting [Slides]
Title: Short tour through Mathematical Statistics
Abstract: In this talk I will be taking you through some fundamental ideas in Mathematical Statistics. I will use the regression model to illustrate those ideas, as well as some common approaches to inference, and I will make a connection with some concrete problems that I am currently working on. I will close by presenting some recent ork. Technical aspects will be kept to a minimum so that everyone can follow.
09 September – Joost Berkhout (VU Amsterdam), Zoom meeting [Slides]
Title: Production Scheduling in an Industry 4.0 Era
Abstract: In this talk, a modern industrial plant is considered that produces a large variety of composite biomaterials. Incoming orders are processed in real-time and slotted into a production schedule to meet the required delivery deadline. The scheduling problem is complicated because of numerous constraints, chief among them the limited storage capacity for intermediate or finished products and avoiding contamination between product runs. To tackle this scheduling problem, an algorithm is presented that combines a state-of-the-art model-based evolutionary algorithm (called Gene-pool Optimal Mixing Evolutionary Algorithm) with a mixed integer linear programming. Results from numerical experiments will be presented to demonstrate the effectiveness of the algorithm.
17 June – Wioletta Ruszel (UUtrecht), Zoom meeting
Title: Emergence of interfaces from sandpile models
Abstract: Interfaces separating two phases (e.g. water and ice) are created in phase coexistence situations such as at 0 degree Celsius. Random interface models (in continuum space) are the Gaussian free field or fractional Gaussian fields. In this talk we would like to explain how Gaussian interface models emerge from divisible sandpiles. A divisible sandpile models is defined as follows: Given a graph, assign a (real-valued) hight s(x) to each vertex of G. A positive value s(x)>0 is interpreted as mass and a negative one as a hole. At every time step do the following: If the mass s(x)>1, then keep mass 1 and redistribute the excess among the neighbours. Under some conditions, the sandpile configuration will stabilise, meaning that all the heights will be lower or equal to 1. The odometer function u(x) collects the amount of mass emitted from x during stabilisation. It turns out that, depending on the initial configuration and redistribution rule, the odometer interface (u(x))_(x in G) will scale to a Gaussian field. The results presented in this talk are in collaboration with A. Cipriani (TU Delft), L. Chiarini (TU Delft/IMPA), J. de Graaff (TU Delft), R. Hazra (ISI Kolkata) and M. Jara (IMPA).
08 April – Johannes Schmidt-Hieber (University of Twente), Zoom Meeting
Title: Towards a statistical foundation of deep learning
Abstract: Recently a lot of progress has been made in the theoretical understanding of deep learning. One of the very promising directions is the statistical approach, which interprets deep learning as a statistical method and builds on existing techniques in mathematical statistics to derive theoretical error bounds. The talk surveys this field and describes future challenges.
26 February – Nicolas Garcia Trillos (Assistant Professor, University of Wisconsin-Madison)
Title: From clustering with graph cuts to isoperimetric inequalities: quantitative convergence rates of Cheeger cuts on data clouds
Abstract: Graph cuts have been studied for decades in the mathematics and computer science communities, and in modern applications in machine learning have been used to formulate optimization problems for data clustering. A canonical example with historical motivation is the so called Cheeger cut problem. This problem is on the one hand intuitively motivated, but on the other, is highly non-convex with a pessimistic NP hard label stamped on it (at least in a worst case scenario setting). Despite this, in the past decade or so, several algorithmic improvements made the minimization of Cheeger cuts more feasible, and at the same time there was a renewed interest in studying statistical properties of Cheeger cuts. New analytical ideas have provided new tools to attack problems that were elusive using classical approaches from statistics and statistical learning theory. Despite the advances, several questions remain unanswered. The purpose of this talk is to present some of these theoretical developments, with emphasis on new results where, for the first time, high probability converge rates of Cheeger cuts of proximity graphs over data clouds are deduced. These quantitative convergence rates are obtained by building bridges between the original clustering problem and another field within the mathematical analysis community that has seen enormous advancements in the past few years: quantitative isoperimetric inequalities. This connection serves as a metaphor for how the mathematical analyst may be able to contribute to answer theoretical questions in machine learning, and how one may be able to deduce statistical properties of solutions to learning optimization problems that have a continuum counterpart.
12 February – Daniele Avitabile (VU), 16:00-17:00 in MathLab (NU-09A46)
Title: This is not a bump
Abstract: This talk discusses patterns in a well-known spatially-extended, deterministic network of synaptically-coupled spiking neurons, which supports coherent structures commonly referred to as “bump” and “wandering bump”, respectively. Patterns of this type are observable in a variety of cortical recordings, and determining their existence and stability properties is a key question in mathematical neuroscience. Cortical bumps have been studied intensively in neural fields (that is, coarse-grained models), but a dynamical system treatment for the case of spiking networks is more elusive. I will present a novel approach to analyse these coherent structures in spiking networks, leading to the following conclusions: The model under consideration does not support a stationary, localised, heterogeneous steady state, therefore the coherent structure referred to as “bump" is not a bump in the usual sense. In a wide region of parameter space, the model supports countably many coexisting travelling waves. These waves are linearly unstable, have a spatially localised profile, and a vanishingly small speed. I will show numerical evidence that the structures known as “bump” and “wandering bump” are a peculiar form of spatio-temporal chaos, and their existence is underpinned by the bifurcation structure of the travelling waves mentioned above.
29 January – Flavien Léger, Room WN-S664, 16:00-17:00
Title: The Schrödinger bridge problem
Abstract: The Schrödinger bridge problem (SBP) nowadays plays a vital role in the physics, mathematics, engineering, information geometry and machine learning communities. It was first introduced by Schrödinger in 1931 and is closely related to, but different from the famous Schrödinger equation. The SBP searches for the minimal kinetic energy density path for drift-diffusion processes with fixed initial and final distributions. In physics, the SBP is related to the Schrödinger equation via Nelson’s stochastic mechanics. For numerical purposes, the SBP can be seen as an entropic regularisation of optimal transport; its numerical solvers include the Sinkhorn algorithm and Fisher information regularisation method. In information geometry and machine learning, the SBP has been studied as a statistical divergence function. In modelling, the SBP minimising path, via Hopf–Cole transformation, shares similar structures with Nash equilibria in mean field games.
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2019
18 December – Senja Barthel (VU), Room WN-P631, 16:00-17:00
Title: Shapes in Chemistry
Abstract: Many properties in chemistry are related to shapes. These shapes can be found in the bond-network of a molecule, or be the shapes of electronic densities, the pore shapes of nanoporous materials, the shapes of configuration landscapes whose minimal energy paths give catalytic pathways, etc. Chemist often have a good intuition on how to think about shape and its impact, but often lack the language and tools to translate and quantify their intuition. In this talk, I exemplify the wide range of modelling of chemical intuitions by translating them into mathematical concepts that lead to computable quantities: We will see how to distinguish and classify surfaces formed from carbons that mimic triply periodic minimal surfaces. We also see how pure mathematical questions are motivated by applications, for example in spatial graph theory.
03 December – Hiroki Takahasi (Keio University, Yokohama, Japan), Room WN-M655, 16:00-17:00
Title: Peculiar asymptotic behaviors of arithmetic mean of digits in the backward continued fraction expansion
Abstract: Khinchine proved that the arithmetic mean of digits in the regular continued fraction expansion of typical irrational numbers diverges to infinity. On the other hand, the asymptotic behavior of the arithmetic mean of digits in the backward continued fraction expansion is counter-intuitive. After introducing results of Aaronson, Aaronson and Nakada on typical behaviors, I will talk about a recent joint work with Johannes Jaerisch (Nagoya University) on the Hausdorff dimension of exceptional sets. Although our main tool is ergodic theory and thermodynamic formalism for dynamical systems, no prior knowledge in this field is assumed in this talk.
20 November – Alessandro Zocca (VU), Room WN-M655, 16.00-17.00
Title: Rare Events in Stochastic Networks: Theory and Applications to Power Systems
Abstract: I will give an overview of my current research, which aims to develop new mathematical tools to analyze complex networks and their performance in the presence of uncertainty. In this talk, I will focus in particular on rare events analysis and large deviations techniques, which in many instances are crucial to correctly assess the network performance and the risk of failures. The main application area for the purpose of this talk will be power systems with high penetration of renewables. More specifically, I will present some novel insights into the interplay between renewable energy sources and power grid reliability: rare stochastic fluctuations of the power injections, amplified by correlations and network effects, can cause failures and possibly blackouts. I will discuss various solutions we devised to mitigate their impact and non-local propagation, using mathematical methods ranging from applied probability to optimization, including new ad-hoc MCMC methods for rare events and novel clustering techniques
06 November – Harry van Zanten (VU), Room WN-M655, 16:00-17:00
Title: Performance of distributed methods for high-dimensional statistical problems
Abstract: For several reasons, computer scientists and statisticians are increasingly using distributed methods to handle and analyse data. In its basic form, the idea is simply to split up the data and distribute it among multiple local servers or cores. Computations can then be done locally, parallel to each other. Typically the local machines transmit the outcomes of their computations to a central server which aggregates the local results into a global one. In the literature various methods were proposed for distributed computational methods with seemingly good practical performance, but with limited theoretical underpinning. In our work we investigate several existing distributed methods in a standard, nonparametric “benchmark” model and compare their theoretical performance. For instance, in the case of Bayesian methods, we compare posterior contraction rates and coverage probabilities of credible sets. This analysis shows that some of the methods that have been proposed have better performance than others. Next we ask what is fundamentally possible in the distributed setting. To make this precise we add certain communication restrictions and prove minimax lower bounds for distributed procedures under such restrictions. Moreover, we exhibit distributed procedure attaining the bounds. Finally, we address the issue of adaptive distributed estimation. Based on joint work with Botond Szabo (Leiden).
09 October – Joris Bierkens (VU), Room M-664, 16:00-17:00
Title: Monte Carlo in Continuous Time
Abstract: Markov Chain Monte Carlo (MCMC) is an essential computational tool in quantitative fields such as Bayesian statistics, statistical physics and machine learning. The goal of MCMC is to perform computations with respect to a probability distribution of interest, which is often only implicitly specified in terms of an unnormalized density and which furthermore often cannot be approached by numeric integration techniques due to a curse of dimensionality. In recent years piecewise deterministic Markov processes (PDMPs) have emerged as a promising alternative to classical MCMC algorithms. One of the attractive features of this approach is the possibility of `exact subsampling' of the data. In this talk PDMP based algorithms will be introduced and recent progress in our understanding of the underlying processes will be presented.
25 September – Álvaro del Pino Gomez (UU), Room WN-M664, 16:00-17:00
Title: A control-theoretic version of convex integration
Abstract: Convex integration is a powerful technique for solving partial differential relations. It was developed by M. Gromov, based on the earlier work of J. Nash on the C^1 isometric embedding problem. One dimensional convex integration was developed independently within the Control Theory community, where it is better known as the Filippov relaxation theorem. The latter can be thought as a first order version of the Chow-Rashevskii theorem on the controllability of bracket-generating motion systems. In this talk I will explain all these ideas starting from the very basics and using a historical perspective. At the very end I will explain how one may define a scheme that generalises convex integration by using ideas from the Chow-Rashevskii theorem. This is work in progress joint with F.J. Martínez-Aguinaga.
11 September – Augusto Gerolin (VU), Room WN-M655, 16:00-17:00
Title: Optimal Transport Theory: from Monge to Scientific Computing
Abstract: In the last 20 years, the theory of Optimal Transportation (OT) has emerged as a fertile field of inquiry, and a diverse tool for exploring applications within and beyond mathematics, in such diverse fields as economics, meteorology, geometry, statistics, fluid mechanics, design problems and engineering. More recently, due to unexpected connections, as for instance with Data Sciences and Quantum Chemistry, computational aspects of OT has receive substantial attention of both theorists and practitioners. The plan of the talk is to give a gentle introduction of theoretical and computational aspects of Optimal Transport Theory, from the classical Monge problem to more recent developments in the field. The talk have few prerequisites and no contraindications - therefore Ph.D. and/or advanced master students are highly encouraged to attend the seminar.
01 May – Magdalena Kedziorek (UU), Room WN-S623, 16:00-17:00
Title: How to understand rational G-cohomology theories?
Abstract: One of the themes of algebraic topology aims at capturing geometry of objects with symmetries by finding algebraic invariants which take this symmetries into account. One class of such invariants are rational G-cohomology theories. By extracting essential structural information from rational G-cohomology theories we are able to provide a much easier, algebraic description of them in many cases. Such a description is called ``an algebraic model’’. The ultimate aim is to do it for any compact Lie group G. In this talk I will give a gentle introduction to rational G-cohomology theories and present algebraic models for several groups G. This is joint work with David Barnes and John Greenlees.
17 April – Fahimeh Moktari (VU), Room WN-S623, 16:00-17:00
Title: Algebraic structure study of vector fields near the triple-zero bifurcation point.
Abstract: In this talk, a practical method is described for computing the classical normal form of vector fields near the bifurcation point. Some necessary formulas are derived and applied to the anharmonic oscillator, the Bogdanov-Takens bifurcation, the 3D nilpotent problem, and elastic pipe conveying fluid, to demonstrate the applicability of the theoretical resultsThen, a review will be given of the developments in the last decade concerning the classification of unique normal forms in 3D nilpotent problems.This work generalizes the work on the Bogdanov-Takens bifurcation and its unique normal form, which took off with the papers of Baider and Sanders (1991-92). Here the application of the Jacobson-Morozov theorem led to a systematic approach to computing the unique normal form in a number of cases. Some of the subcases of the 2D double-zero bifurcation analysis are still open.One can imagine that the complications of analyzing the 3D triple-zero bifurcation are rather challenging. Nevertheless, progress has been made in the last decade and it is time to list what has been done and what still needs to be done.We apply the Jacobson–Morozov theorem to embed this class of three dimensional vector fields into an sl_2-triple. Three irreducible families are produced this way.The first task is to find the structure constants of these families. In this talk, we also show how the Clebsch-Gordan formula is employed to find explicit formulas for the structure constants. We demonstrate that these families can generate some Lie sub-algebras with respect to the triple-zero bifurcation point, thereby creating smaller subproblems that can be studied independently in their own right (like the Hamiltonian case in the 2D analysis).Further, we discuss possible generalizations toward a general n-dimensional theory.
20 March – Bernard Geurts (UTwente), Room WN-P647, 16:00-17:00
Title: Mathematics for Turbulence
Abstract: Turbulent flow arises in a wide variety of natural and technological situations. While the full richness of turbulence is appreciated qualitatively, a quantitatively accurate prediction is often outside the scope of numerical computations. As an alternative, filtered flow descriptions, such as large-eddy simulation (LES), have been proposed and studied intensively, promising a combination of accuracy and computational feasibility. A brief review of mathematical cornerstones for LES is given. Many heuristic closure models for small-scale turbulence have been put forward to represent dynamic small scale effects on the large-scale characteristics of a flow. While these models are often effective in reducing the dynamic complexity of the LES approach, accuracy limitations of LES are a matter of ongoing discussion.In this presentation, mathematical regularization for turbulence, pioneered already by Leray in the 1930s, is explored. Following the regularization approach for the nonlinear convective terms, the closure model is uniquely connected to the underlying regularization principle, thereby by-passing heuristic closure modeling that is characteristic of the filtering approach to LES. A number of regularization models will be reviewed and their performance in turbulence will be discussed. It will be shown that regularization methods can be accurate at strongly reduced computational costs.
06 March – Ronald Meester (VU Amsterdam), Room WN-P647, 16:00-17:00
Title: The DNA Database Controversy 2.0
Abstract: What is the evidential value of a unique match of a DNA profile in database? Although the probabilistic analysis of this problem is in principle not difficult, it was the subject of a heated debate in the literature around 15 years ago, to which today's speaker also contributed. Very recently, to my surprise, the debate was re-opened by the publication of a paper by Wixted, Christenfeld and Rouder, in which a new element to the discussion was introduced. In this lecture I will first review the problem, together with the principal solution. Then I will explain what has recently been proposed as a new element in the analysis, and also explain why this new ingredient does not add anything, and only obscures the picture. The fact that not everybody agrees with us will be illustrated by some interesting quotes from the recent literature, which might be a nice subject for discussion during the drinks in the Basket afterwards. If you thought that mathematics could not be polemic you should certainly come and listen. (Joint work with Klaas Slooten.)
20 February – Nick Lindemulder (TU Delft), Room WN-S607, 16:00-17:00
Title: A randomized difference norm for vector-valued fractional Sobelev spaces
Abstract: Sobolev spaces of Banach space-valued distributions and variants with fractional smoothness play an important role in the $L_{p}$-approach to evolution equations. In this talk we discuss several (equivalent) ways how to define a suitable scale of fractional Sobolev spaces. In particular, we discuss the well known Fourier analytic definition by means of the Bessel potential operator and the less well known classical characterization of the latter by means of differences due to Strichartz from the scalar-valued setting. The main aim is to discuss extensions of the classical scalar-valued setting to the Banach space-valued setting, where the concept of randomization comes into play.06 February – Sophia B. Coban (CWI), 16:00-17:00
Title: Things your radiologist would not tell you about
Abstract: Computed tomography is the perfect example of a large-scale, mildly ill-conditioned inverse problem, and one that is highly important to accurately solve in many real world applications. In today's talk, I will be introducing the basics of computed tomography, in particular X-ray CT; discuss some of the building blocks and novel trends of image reconstruction, and finish with the state-of-the-art methods developed within the Computational Imaging group at Centrum Wiskunde & Informatica.
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2018
12 December – Floske Spieksma (LU), Room WN-P663, 16:00-17:00
Title: Alternative formula for the Deviation Matrix
Abstract: In Markov process theory, the deviation matrix measures the total deviation over time of the marginal distributions from stationarity. As such, it plays a central role in the determination of average optimal policies in Markov decision processes. In finite state space, the deviation matrix is minus the generalised inverse of the generator or rate matrix of a continuous time Markov process. However, the generalised inverse is not simply computable. In countable space, if it exists at all, it may even not be unique. The importance of the deviation matrix is not restricted to Markov process theory, but e.g. it plays an important role in network robustness of undirected graphs. This motivates the study of alternative computations methods. In my talk I will discuss this, as well as some applications.
28 November – Max Welling (UvA), Room WN-M639, 16:00-17:00
Title: Combining Deep Learning with External and Expert Knowledge
Abstract: Deep learning is a typical 'black box’ technique: create lots of labeled examples between input and output and train a general purpose map between the two. This works great when you can create a very large annotated dataset but has it limitations when the dataset is not so large, or poorly annotated. In the latter case we should try to inject our inductive biases or expert knowledge into the model. We will discuss two new directions to achieve this. 1) extend the translational equivariance of traditional convolutional neural networks to larger groups of symmetries, such as rotations and reflections, and 2) to incorporate bits and pieces of the (known) generative process of the data into the NN. We will illustrate both examples in the medical imaging domain: using group convolutions to improve performance in pathology slide analysis and using generative knowledge to speed up MRI reconstruction. Reversely, or more generally, one could ask the question, how can deep learning integrate with rich data sources such as knowledge graphs. A successful integration could lead to improved high level reasoning and systems that have a deeper understanding of the world they operate in. We will discuss a method called graph convolutions which allows us to embed rational data into a semantic space from which reasoning becomes easier.
14 November – Stéphanie van der Pas (LU), Room WN-S623, 16:00-17:00
Title: Posterior concentration for Bayesian regression trees and their ensembles
Abstract: Since their inception in the 1980's, regression trees have been one of the more widely used nonparametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to terminal nodes of recursive partitioning. Trees are powerful, yet susceptible to overfitting. Strategies against overfitting have traditionally relied on pruning greedily grown trees. The Bayesian framework offers an alternative remedy against overfitting through priors. Roughly speaking, a good prior charges smaller trees where overfitting does not occur. In this paper, we take a step towards understanding why/when do Bayesian trees and their ensembles not overfit. We study the speed at which the posterior concentrates around the true smooth regression function. We propose a spike-and-tree variant of the popular Bayesian CART prior and establish new theoretical results showing that regression trees (and their ensembles) (a) are capable of recovering smooth regression surfaces, achieving optimal rates up to a log factor, (b) can adapt to the unknown level of smoothness and (c) can perform effective dimension reduction. These results provide a piece of missing theoretical evidence explaining why Bayesian trees (and additive variants thereof) have worked so well in practice.
31 October – Magnus Botnan (VU), Room WN-P633, 16:00-17:00
Title: From Clustering to Quiver Representations
Abstract: Clustering analysis is a statistical method for uncovering structure in large and complicated data. In this talk I will show how the desire for a parameter-free, stable, and density sensitive hierarchical clustering method inspired research in the field of representation theory of quivers.
17 October – Viresh Patel (UvA), Room WN-F123, 16:00-17:00
Title: Quasi Ramsey problems
Abstract: Ramsey theory is currently one of the most active areas of research in combinatorics. The seminal question in the area, raised by Ramsey in 1930 can be formulated as follows: how large does n have to be to guarantee that in any room with n people we can find a set S of k people such that either every pair in S is acquainted or every pair in S is not acquainted. It is not immediately clear that such an n exists, although it is not hard to show. On the other hand the known bounds for n as a function of k are quite poor. I will discuss the Ramsey problem as well as variants of it. In particular I will discuss a relaxation of the problem above for which we are able to give quite precise bounds. This is based on joint work with Janos Pach, Ross Kang, Eoin Long and Guus Regts.03 October – Ben Moonen (RU Nijmegen), Room WN-S655, 16:00-17:00
Title: Curves, Jacobians and CM points
Abstract: I will tell a story of two moduli spaces: the moduli space M_g of curves of genus g, and the moduli space A_g of abelian varieties of dimension g. To a curve C of genus g (or if you prefer: a compact Riemann surface of genus g) we can associate its Jacobian J(C), an abelian variety of dimension g. This gives a map t: M_g --> A_g that is known to be injective. As I will explain in my talk, though M_g and A_g have been studied extensively and much is known about them, there are many basic questions to which we don't know the answer. I will illustrate this by discussing a conjecture of Coleman about curves whose Jacobian is of CM-type (which, informally, means that it is 'maximally symmetrical'). Along the way I will review some important developments of the last three decades, notably the André-Oort conjecture, which has now been proved using a rather spectacular variety of techniques.
19 September – Jan Bouwe van den Berg (VU), Room WN-S623, 16:00-17:00
Title: Computer-assisted theorems in dynamics
Abstract: In nonlinear analysis we often simulate dynamics on a computer, or calculate a numerical solution to a partial differential equation. This gives very detailed, stimulating information. However, it would be even better if we can be sure that what we see on the screen genuinely represents a solution of the problem. In particular, rigorous validation of the computations would allow such objects to be used as ingredients of theorems. In this talk we explore an approach based on a Newton-Kantorovich type argument in a suitable neighborhood of a numerically computed candidate. This method has been applied successfully for various problems in ordinary differential equations, delay differential equations and partial differential equations. We will illustrate the general setup using an example stemming from the Navier-Stokes equations in two dimensions. The latter is joint work in progress with Maxime Breden, Jean-Philippe Lessard and Lennaert van Veen.
13 June – Paola Gori-Giorgi (VU), Room WN-M143, 16:00-17:00
Title: Multi-marginal Optimal Transport and Density Functional Theory: A mathematical setting for physical ideas
Abstract: Electronic structure calculations are at the very heart of predictive computational materials science, chemistry and biochemistry. Their goal is to solve, in a reliable and computationally affordable way, the many-electron problem, a complex combination of quantum-mechanical and many-body effects. The most widely used approach, which achieves a reasonable compromise between accuracy and computational cost, is Kohn-Sham (KS) density-functional theory (DFT). Although exact in principle, practical implementations of KS-DFT must heavily rely on approximations for the so-called exchange-correlation (XC) functional. Empirical approximations (e.g., fitted on several data sets) are successful in normal cases, but typically lack predictive power for systems outside the training set. For this reason, exact mathematical conditions and rigorous guiding principles to build the XC functional have always played a key role in the field. In the recent years, it has been shown that there is a special semiclassical limit of the XC functional, relevant for the most challenging cases in KS DFT, which can be reformulated as a multi-marginal optimal transport problem, linking two rather distant research fields. In this talk I will review this reformulation, providing an overview of the key results from the optimal transport community, and discussing some of the open questions and conjectures that still need a rigorous proof.
30 May – Michiel Bertsch (University of Rome Tor Vergata), Room WN-M143, 16:00-17:00
Title: Mathematical modelling of Alzheimer's disease
Abstract: Up to now there is no effective cure for Alzheimer's disease (AD). One of the major reasons is its complexity. Although the biomedical knowledge about AD is rapidly increasing, there is not yet a clear picture available about the major causes and the evolution of the disease. In such circumstances, can mathematical modelling be useful at all? In the colloquium I propose a modelling approach which, in a certain sense, is characterized by flexibility. I present a "toy model", which deliberately takes into account only a very limited amount of aspects of the disease (in this case the role of beta-amyloid and the existence of different time scales). The toy model seems to be flexible enough to include other aspects (such as the role of the tau protein) or novel biomedical insight. Surprisingly, the toy model itself suggests the possible importance of a very specific biomedical process, which is also discussed in the biomedical literature.BA
16 May – Viresh Patel (UvA), Room WN-M143, 16:00-17:00
Title: Quasi Ramsey problems
Abstract: Ramsey theory is currently one of the most active areas of research in combinatorics. The seminal question in the area, raised by Ramsey in 1930 can be formulated as follows: how large does n have to be to guarantee that in any room with n people we can find a set S of k people such that either every pair in S is acquainted or every pair in S is not acquainted. It is not immediately clear that such an n exists, although it is not hard to show. On the other hand the known bounds for n as a function of k are quite poor. I will discuss the Ramsey problem as well as variants of it. In particular I will discuss a relaxation of the problem above for which we are able to give quite precise bounds. This is based on joint work with Janos Pach, Ross Kang, Eoin Long and Guus Regts.
02 May – Joris Mooij (UvA), Room WN-M143, 16:00-17:00
Title: Joint Causal Inference from Observational and Experimental Data
Abstract: The standard method to discover causal relations is by using experimentation. Over the last decades, alternative methods have been proposed: constraint-based causal discovery methods can sometimes infer causal relations from certain statistical patterns in purely observational data. We introduce Joint Causal Inference (JCI), a novel constraint-based approach to causal discovery from multiple data sets that elegantly unifies both approaches. Compared with existing constraint-based approaches for causal discovery from multiple data sets, JCI offers several advantages: it deals with several different types of interventions in a unified fashion, it can learn intervention targets, it systematically pools data across different datasets which improves the statistical power of independence tests, and most importantly, it improves on the accuracy and identifiability of the predicted causal relations.
18 April – Sjoerd Verduyn Lunel (UU), Room WN-M143, 16:00-17:00
Title: Transfer operators, Hausdorff dimension and the spectral theory of positive operators
Abstract: In this talk we present a new approach to compute the Hausdorff dimension of conformally self-similar invariant sets using an elementary direct spectral analysis of a transfer operator associated with the problem. We start from scratch, introduce the notion of transfer operator and combine ideas from the theory of positive operators and from the theory of trace class operators and their determinants. Our approach is illustrated with examples from dynamical systems and number theory via Diophantine approximations.
21 March – Peter Grunwald (CWI, Leiden), Room WN-M143, 16:00-17:00
Title: Safe Testing
Abstract: A large fraction (some claim > 1/2) of published research in top journals in applied sciences such as medicine and psychology is irreproduceable. In light of this 'replicability crisis', standard p-value based hypothesis testing has come under intense scrutiny. One of its many problems is the following: if our test result is promising but nonconclusive (say, p = 0.07) we cannot simply decide to gather a few more data points. While this practice is ubiquitous in science, it invalidates p-values and error guarantees. Here we propose an alternative hypothesis testing methodology based on supermartingales - it has both a gambling and a data compression interpretation. This method allows us to consider additional data and freely combine results from different tests by multiplication (which would be a mortal sin for p-values!), and avoids many other pitfalls of traditional testing as well. If the null hypothesis is simple (a singleton), it also has a Bayesian interpretation, and essentially coincides with a proposal by Vovk (1993). We work out the case of composite null hypotheses, which allows us to formulate safe, nonasymptotic versions of the most popular tests such as the t-test and the chi square tests. Safe tests for composite H0 are not always Bayesian, but rather based on the 'reverse information projection', an elegant concept with roots in information theory rather than statistics.
07 March – Nelly Litvak, Room WN-M143, 16:00-17:00
Title: Power-law hypothesis for PageRank
Abstract: PageRank is a well-known algorithm, which has been proposed by Google for ranking pages in the World-Wide Web. PageRank can be interpreted as a stationary distribution of a random walk of a user that hops from one web page to another. Beyond the web search, PageRank has many applications in network of different kinds, for example, discovering communities in social networks, or finding endangered species in ecological networks. Most of these real-life networks have so-called power-law degree distribution: if a network is represented as a graph, then the fraction of vertices with degree k is approximately proportional to a negative power of k. Moreover, many empirical studies confirm that PageRank also has a power law distribution, with the same negative power as in-degree. In this talk I will discuss to which extend we can formalize this empirical observations analytically. Formally, we will model networks as random graphs and investigate the limiting behavior of PageRank as the graph size goes to infinity. I will present results for some specific random graph models, and very recent general limiting results for a large class of random graphs. This talk is based on joint works with Remco van der Hofstand and Alessandro Garavaglia (Eindhoven University of Technology) and Mariana Olvera-Cravioto (Univerity of California at Berkley).
21 February – Gijs Heuts (UU), Room WN-M143, 16:00-17:00
Title: Lie algebras and periodicity in homotopy theory
Abstract: Homotopy theory is the study of continuous deformations of spaces. The general problem of classifying such deformations is notoriously hard. However, if one is only interested in rational invariants of spaces then there are good algebraic tools available: Quillen constructed for every space a Lie algebra from which such invariants can be calculated, whereas Sullivan built a commutative algebra (much like the algebra of differential forms on a manifold) that retains essentially the same information. I will discuss a modern viewpoint of homotopy theory called the "chromatic perspective": much like a ray of white light is broken into different colours through a prism, a space can be decomposed into pieces corresponding to various "frequencies". The rational invariants correspond to one of these pieces. It turns out that Lie algebras may also be used to give models for the others.
07 February – Damaris Schindler (UU), Room WN-M143, 16:00-17:00
Title: Systems of quadratic forms
Abstract: In this talk we discuss some aspects concerning the arithmetic of systems of quadratic forms. Our focus will be on the local-global principle for the existence of rational or integral solutions and we will discuss some failures of this principle.
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2017
13 December – Jaap Storm (VU), Room P-647, 16:00-16:15
Title: Stability of stochastic systems
Abstract: Stochastic dynamical systems are widely used nowadays in modeling real life phenomena, especially Markov processes. The applications are numerous and include the modelling of the dynamics of financial processes, populations, traffic networks and communication networks. The analysis of these models allows us to predict behavior of these systems and also allows for control on the dynamics, however for a lot of the analysis one typically uses the ergodic properties of the Markov process. For the Markov process to be ergodic we require the Markov process to be stable. Stability of Markovian systems will be the topic of my talk and during the talk I hope to give some intuition to what we mean by stability and how we can prove it.
13 December – Wouter Hetebrij (VU), Room P-647, 16:20-16:35
Title: The parameterization method for center manifolds
Abstract: For a hyperbolic fixed point of a dynamical system, we can topologically conjugate the dynamics with the linearization of the dynamical system. Furthermore, under some mild conditions, there exists a smooth parameterization of the (un)stable manifold which conjugates the dynamical system to a linear system on the (un)stable manifold and describes the manifold. However, for center manifolds, we can only describe the center manifold as a graph over the center subspace. In my talk, I will give a short introduction to (un)stable and center manifolds, as well as the parameterization method. Also, I will sketch how we can generalize the parameterization method to center manifolds.
13 December – Joey van Langen (VU), Room P-647, 16:45-17:00
Title: The modular method for Diophantine equations
Abstract: In 1994 Andrew Wiles proved the famous problem known as Fermat's Last Theorem. In the years that followed number theorists have used the same ideas to solve more general Diophantine equations, such as the generalized Fermat equation, i.e. x^p + y^q = z^r , for p, q and r not necessarily the same. This general method became known as the modular method and has since been used to solve many different Diophantine equations. In this talk I want to give a broad overview of the modular method, describing the different fields of mathematics it uses and the links between them. Fermat's Last Theorem will feature as an 'easy' example in this overview. If time allows I will also highlight the areas of current research involving the modular method, including my own research.
29 November – Rikkert Hindriks (VU), Room P-647, 16:00-17:00
Title: Propagation of spontaneous hemodynamic fluctuations in the human brain
Abstract: In the absence of explicit cognitive tasks, the brain consumes about 20% of the body's energy budget, even though its weight is only 2% of the total body weight. Since perceptual and cognitive processing only add a tiny fraction to this energy consumption, this poses the question what the brain is doing during the resting-state. Functional magnetic resonance imaging (fMRI) has brought about a paradigm shift in our thinking about brain function, by demonstrating that, during the resting-state, brain activity is organized into the same functional networks as those engaged during a variety of cognitive and perceptual tasks. Although resting-state networks provide a framework to understand functional segregation, it is unclear how information is integrated across networks. I this talk I will discuss preliminary results that suggest that resting-state networks do not behave independently, but occur in reproducible temporal progressions that reflect propagating waves of neural activity. I will also discuss several methodological issues that come up in the analysis.
15 November – Eddie Nijholt (VU), Room P-647, 16:00-17:00
Title: Transversality in Dynamical Systems with Generalised Symmetry
Abstract: In bifurcation theory, an important role is played by the spectrum of the linearised system. For example, a steady state bifurcation is ruled out by the implicit function theorem, unless the linearisation has a non-trivial kernel. Likewise, a Hopf bifurcation is associated with a pair of complex eigenvalues crossing the imaginary axis. When the dynamical system has a symmetry, i.e., commutes with the linear action of a compact Lie-group, spaces such as the kernel and center subspace become invariant under this action. Consequently, they may be written as the direct sum of so-called irreducible subrepresentations. These spaces are characterised by the property that they do not contain any non-trivial invariant spaces, and they come in three types: real, complex and quaternionic. A classical result from equivariant dynamics says that in the case of compact Lie-group symmetry, a one-parameter bifurcation occurs generically along one irreducible subrepresentation of real type. We generalise this result to the case where the linear action is given by a monoid (i.e a group without inverses), without any further assumptions such as finiteness or compactness. More-precisely, we describe the generic structure of the generalised kernel in the case of a k-parameter monoid-equivariant bifurcation, and likewise for the center subspace (for any natural number k). This question arose from the study of network dynamical systems, where more exotic types of symmetry occur naturally.
09 November – Hein Putter (Leiden UMC), Room HG-15A37, 13:30-14:30
Title: Non-parametric estimation of transition probabilities in non-Markov multi-state models: the landmark Aalen-Johansen estimator
Abstract: The topic non-parametric estimation of transition probabilities in non-Markov multi-state models has seen a remarkable surge of activity recently. Two recent papers have used the idea of subsampling in this context. The first paper, by de Uña Álvarez and Meira-Machado, uses a procedure based on (differences between) Kaplan–Meier estimators derived from a subset of the data consisting of all subjects observed to be in the given state at the given time. The second, by Titman, derived estimators of transition probabilities that are consistent in general non-Markov multi-state models. Here, we show that the same idea of subsampling, used in both these papers, combined with the Aalen–Johansen estimate of the state occupation probabilities derived from that subset, can also be used to obtain a relatively simple and intuitive procedure which we term landmark Aalen–Johansen. We show that the landmark Aalen–Johansen estimator yields a consistent estimator of the transition probabilities in general non-Markov multi-state models under the same conditions as needed for consistency of the Aalen–Johansen estimator of the state occupation probabilities. Simulation studies show that the landmark Aalen–Johansen estimator has good small sample properties and is slightly more efficient than the other estimators.
01 November – Henk Don (RU), Room P-647, 16:00-17:00
Title: Bounding the length of synchronizing words.
Abstract: In 1964, Cerny conjectured that every n-state synchronizing deterministic finite automaton (DFA) has a synchronizing word of length at most (n-1)^2. In this talk I will explain this conjecture and discuss upper and lower bounds for the length of the shortest synchronizing word. If we randomize the input word, we can still ask if a DFA synchronizes and how long the corresponding random word will be. For this setting I will give bounds on the expected length of the random synchronizing word. Based on joint works with Michiel de Bondt, Vladimir Gusev and Hans Zantema.
18 October – Assia Mahboubi (Inria and U Nantes), Room P-647, 16:00-17:00
Title: Machine-checked proofs
Abstract: Proof assistants belong to the large collection of tools available today for "doing mathematics with a computer". These systems allow their users to check with the highest degree of certainty the validity of the proofs they have carefully described to the machine. Formalized mathematics refers to the digitized mathematical data (definitions, theorems, and proofs) amenable to computer processing, and checking. Formalized mathematics provides a very high correctness guarantee, and can be used to verify proofs based on large-scale
computations. But it can also lead to the discovery of new constructions and proofs, and helps to organize mathematical knowledge with the help of a computer. In this talk, we will give a glimpse of the variety of research areas and methodologies involved in the area of machine-checked proofs, from the meta-mathematical properties of the underlying logical language, to the design and features of the proof assistant. We will try to illustrate what formalizing mathematics looks like on the concrete example of the formal verification of a
computer-algebra based proof of the irrationality of ζ(3). The latter example is a joint work with Frédéric Chyzak (Inria) and Thomas Sibut-Pinote (Microsoft Research).04 October – Wadim Zudilin (RU), Room P-647, 16:00-17:00
Title: Variations on One over Pi
Abstract: The number \pi=3.1415926\dots is recognised as the bestselling mathematical constant of all the time. One hundred years ago, well before the era of the computer, the Indian prodigy Srinivasa Ramanujan found a remarkable list of formulae for 1/\pi, which can be used to compute the quantity to several thousand places. Today, Ramanujan's equations are still in use. The last few decades have witnessed an exploding development of new methods and generalisations of these formulae, bringing together topics from analysis, combinatorics, algebraic geometry, differential equations and number theory. At the same time, we lack understanding about the structure of such generalisations. In my talk, I will surf on the waves of the story of 1/\pi.
20 September – Rob van der Mei and Martin van Buuren (VU), Room P-647, 16:00-16:30
Title: Applied Mathematics in Practice: How to Save Lives with Maths?
Abstract: In this talk, we will talk about (1) stochastic models for how to reduce emergency response times by smart proactive relocations of ambulance vehicles, and (2) how these models work in real-life.
17 May – Elenna Dugundji, Room P-647, 16:00-17:00
Title: Social and spatial interactions in transportation mode choice.
Abstract: To what extent are consumers influenced in their choice of mode of transport by their neighbors’ choices? Or the choices made by peers in their social circle? These are important questions to understand for both policy makers and private sector parties interested in promoting particular modes of transport, but they have only recently attracted attention of transportation researchers. We discuss a socio-dynamic variant of a classic approach to predictions in this context, from both theoretical and empirical points of view, including an application to mobility in Amsterdam.03 May – Bernard Zweers, Room P-647, 16:00-16:15
Title: Minimizing the cost for inland container transportation
Abstract: A real-life operational planning problem for a logistic service provider is considered. A number of containers have to be shipped from multiple deep sea terminals to a single inland terminal. On may choose the day of transportation and the mode: truck or barge. The goal is to find an assignment for the containers that minimizes the total costs without visiting too many terminals with one barge. For this purpose an integer linear program is formulated that can solve practical instances in reasonable time.
03 May – Jan-David Salchow, Room P-647, 16:20-16:35
Title: Function spaces on manifolds
Abstract: The foundation for existence and regularity of solution spaces of PDE is the theory of function spaces. While historically most interest was directed towards PDE on subspaces of R^n, there is a growing demand for function spaces on Riemannian manifolds. In my talk
I will report on recent progress in the theory of Sobolev spaces on manifolds.03 May – Chris Groothedde, Room P-647, 16:40-16:55
Title: Instability in Dynamical Systems with Delayed Feedback
Abstract: Many mathematical models describe systems with feedback loops. When this feedback is not instantaneous the behaviour and analysis of such a system becomes much more complex. In this talk we will look at equilibrium solutions of such Delay Dynamical systems and the instability that occurs near equilibrium solutions. The set of unstable solutions originating in an equilibrium can be described as a manifold: the Unstable manifold. In particular I will explain some of the basic functional analytic setup behind the study of Delay Dynamical Systems and their Equilibria and how to describe and visualise the Unstable Manifolds.19 April – Mark Veraar (TUD), Room P-647, 16:00-17:00
Title: Fourier multiplier theory: old and new results
Abstract: Using Fourier multiplier theory one can prove the L^p-boundedness of many singular integrals. The first Fourier multipliers theorem has been proved by Marcinkiewicz in 1939. His main motivation was the application to elliptic PDEs. Since his work there have been many results on multiplier theory, among which the results of Mihlin and H\"ormander. During the last 20 years, multiplier theory was extensively studied in the weighted setting and in the vector-valued setting. The weighted setting is motivated by complex and geometric analysis and has led to several famous results. The vector-valued setting is important in the operator theoretic approach to PDE. In the talk I will present a survey of some of the recent results and their applications.05 April – Sandjai Bhulai (VU), Room P-647, 16:00-17:00
Title: Value Function Discovery In Markov Decision Processes.
Abstract: In this talk, we introduce a novel method for discovery of value functions for Markov Decision Processes (MDPs). This method is based on ideas from the evolutionary algorithm field. Its key feature is that it discovers descriptions of value functions that are algebraic in nature. This feature is unique, because the descriptions include the model parameters of the MDP. The algebraic expression can be used in several scenarios, e.g., conversion to a policy, control of systems with time-varying parameters. We illustrate its application on an example MDP.22 March – Bart de Smit (RUL), Room P-647, 16:00-17:00
Title: On the abelian coverings of curves over finite fields
Abstract: The main result of this talk identifies when two curves over finite fields have equivalent categories of (possibly ramified) abelian coverings. We will also sketch where this result fits in the wider context of number theoretic analogs of Kac's famous question: "Can you hear the shape of a drum?".08 March – Daan Crommelin (UvA and CWI), Room P-647, 16:00-17:00
Title: Stochastic models for multiscale dynamical systems
Abstract: Modeling and simulation of multiscale dynamical systems such as the climate system is challenging due to the wide range of spatiotemporal scales that need to be taken into account. A promising avenue to tackle this multiscale challenge is to use stochastic methods to represent dynamical processes at the small/fast scales. The feedback from microscopic (small-scale) processes is represented by a network of Markov processes conditioned on macroscopic model variables. I will discuss some of the work from this research direction. A systematic derivation of appropriate stochastic processes from first principles is often difficult, and statistical inference from suitable datasets can provide an interesting alternative.22 February – Jens Rademacher (Bremen), Room P-647, 16:00-17:00
Title: Nonlinear waves: gems in evolution equations
Abstract: While the overall dynamics of an evolution equation can be complicated and even inaccessible to an analysis, there are often subsystems that allow for more. A prominent case are nonlinear waves in parabolic partial differential equations with an extended spatial direction. The simplest such solutions have constant shape up to translation. Examples are solitons, excitation waves and periodic patterns. The identification of such objects is not only much easier than the task to understand the dynamics of the overall problem. These nonlinear waves often form building blocks for more complex behaviour, and, last but not least, often shape the phenomena that are of most interest in applications. In this talk some prominent examples will be present, combined with a brief introduction to analytic tools for existence and stability analysis.
08 February – Richard J. Boucherie (Twente), Room P-647, 16:00-17:00
Title: Operations research solutions to improve the quality of healthcare
Abstract: Healthcare expenditures are increasing in many countries. Delivering adequate quality of healthcare requires efficient utilization of resources. Operations Research allows us to maintain or increase the current quality of healthcare for a growing number of patients without increasing the required work force. In this talk, I will describe a series of mathematical results obtained in the Center for Healthcare Operations Improvement and Research of the University of Twente, and I will indicate how these results were implemented in Dutch hospitals.
Efficient planning of operating theatres will reduce the wasted hours of staff, balancing the number of patients in wards will reduce peaks and therefore increases the efficiency of nursing care, efficient rostering of staff allows for more work to be done by the same number of people. While employing operations research techniques seems to be dedicated to improving efficiency, at the same time improved efficiency leads to increased job satisfaction as experienced workload is often dominated by those moments at which the work pressure is very high, and it also improves patient safety since errors due to peak work load will be avoided.