Upcoming talks:
Inaugural lecture:
Date: Wednesday, April 26th
Time: 15:45
Place: Aula (main building)
Speakers: Assia Mahboubi
Title: tba
Aula opens at 15:30 (the cortège leaves at 15:40 from the Forumzaal).
Previous talks:
Extra dynamics seminar:
Date: Monday, January 23rd
Time: 16:00-16:45
Place: NU-09A46 (Mathlab)
Speakers: Antonio Ponno (University of Padova) and Matteo Gallone (SISSA, Trieste)
Title: The Fermi-Pasta-Ulam-Tzingou problem: the pre-thermal perspective
Abstract: In 1955, Fermi, Pasta, Ulam and Tzingou were interested in understanding the route to thermalization of an isolated physical system with a large number of degrees of freedom, a process that is governed by non-linearities in the governing equations. They decided to investigate it using the first numerical simulation in history -- of a conservative chain of interacting oscillators. The outcome of their experiment was quite astonishing: instead of a slow driving to a so-called "thermal equilibrium", they observed recurrent behavior. Since then, different approaches were able to unveil and explain features of their observations (which we now think of as the prototypical “pre-thermal scenario”). In this talk we will overview some cornerstone results on the analysis of the problem, and present some recent advances, including work of the two of us in collaboration with Bob Rink. If time permits, we also discuss some results on pre-thermalization (that is, dynamics resembling that of the Fermi-Pasta-Ulam-Tsingou system) for Quantum Mechanical models.
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Extra AI talk
Time : November 23, 16:00-16:30
Location : Math Lab: 9A-46
Speaker : Pavle Milošević (University of Belgrade)
Title : Artificial Intelligence for Managing Workplace Safety
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Extra AI and optimization techniques Seminar
Time: November 16, 15:00-15:50
Location: Math Lab: 9A-46
Speaker: Sándor Miklós Szilágyi (Budapest University)
Title: The possibility to use artificial intelligence and optimization techniques to enhance protein folding prediction
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Extra dynamics seminar: Monday Nov 21st 2022; 13:30-14:14; Room NU-09A46.
Speaker: Mattia Sensi from INRIA
Title: “A geometric singular perturbation approach to epidemic compartmental models”
Abstract: We study fast-slow versions of the SIR, SIRS and SIRWS epidemiological models [1], and of the SIRS epidemiological model on homogeneous graphs [2], obtained through the application of the moment closure method. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways.
Our main purpose is to show that the fast-slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT).
In particular, without using Lyapunov’s method, we are able to not only analyze the stability of the endemic equilibria of the SIR and SIRS models, but also to show that in the remaining models limit cycles arise.
We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model and the SIRS on homogeneous graphs, for which we provide a detailed description of their dynamics by combining analytic and numerical techniques. In particular, for the latter we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
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"Lowlands Double Feature"
Speaker: *Clara Stegehuis (Twente)*
Title: *Network structures and processes: the effect of higher-order structures*
When: Nov 9, 2022, 15-16h
Location in person: MathSeminar room 09A46
Location via Zoom: please contact Chris Bick for details.
Abstract: What is the effect of local structures on network processes? And how do we find these local structures? In this talk, we will investigate the difference in the behavior of network processes when specific local structures are planted in the network. For the process of bond percolation, we derive analytical approximations for large percolation probabilities and the critical percolation value. Interestingly, they show that the influence of these planted structures is small, and that differences in behavior that were found in previous works can be almost completely attributed to differences in degree sequences rather than differences in structures. We then investigate the properties of such local structures, and show that local structures often appear at very specific locations in a network.
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4.10.2022: Extra geometry talk
Time: 3:30pm
Venue: Room 09A46
Speaker: Valerio Assenza (Heidelberg)
Title: Magnetic Curvature and Existence of Closed Magnetic Geodesic
Abstract: A Magnetic System is the toy model for the motion of a charged particle moving on a Riemannian Manifold endowed with a magnetic field.
Solutions for such systems are called Magnetic Geodesic and preserve the Kinetic Energy. One of the most relevant investigative interest in the theory is to understand the existence and in case the topological nature of Closed Magnetic Geodesics (periodic solutions) in a given level of the energy. I will introduce the Magnetic Curvature, an object which encodes the geometrical properties coming from the Riemannian Curvature structure together with terms of perturbation due to the magnetic interaction. We will see how a positive curved Magnetic System carries a Contractible Closed Magnetic Geodesic for small energies.
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6-8.07.2022: 2022 International Conference on Mathematical Neuroscience - Digital Edition
More information including program and link to Youtube channel
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16.06.2022: extraordinary Dynamics Seminar
Time: 4pm
Venue: Mathlab 09A46
Speaker: Sören von der Gracht (U Hamburg),
Title: Amplification in general feedforward networks
Abstract: We investigate bifurcations in feedforward coupled cell networks. Feedforward structure can be defined in multiple ways: It is characterized by the absence of feedback, a partial order on the cells, the structure of the adjecancy matrices, as well as the algebraic properties of the input maps. We exploit the interplay of these definitions to study generic one-parameter steady state bifurcations for such networks. Branching solutions can be determined by an algorithm that only utilizes the network structure. Similar to previous results on feedforward chains, we observe amplifications of the growth rates of steady state branches induced by the feedforward structure. Branching solutions and their asymptotics are described in terms of Taylor coefficients of the internal dynamics. Contrary to the earlier results, as the interaction scenarios can be more complicated in general feedforward networks, different branching patterns and different amplifications can occur for different regions in the space of Taylor coefficients.
Drinks afterwards.
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24. May 2022: Extra Geometry and Topology Seminar
Time: 3pm
Venue: Mathlab 09A46
Speaker: Johanna Bimmermann, Heidelberg University
Title: On the Hofer-Zehnder capacity of magnetic surfaces via pseudo-holomorphic curves
Abstract: The Hofer-Zehnder capacity is a symplectic invariant that roughly speaking measures the symplectic size of a manifold in terms of the possible Hamiltonian dynamics. In general this quantity is hard to compute and only known in few cases. In this talk I will present a computation of its value for the tangent bundle over surfaces with a certain twisted symplectic form. The main tools will come from theory of pseudo holomorphic curves and the existence of a Hamiltonian circle action.
Drinks and pizza afterwards.
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13. May 2022: Extra Dynamics Seminar
Time: 10:00
Speaker: La Mi (University of Luxembourg)
Title: Polarization of multi-agent gradient flows over manifolds
Venue: Math Seminar Room (09A46) (for zoom attendance please contact Chris Bick)
Abstract: Multi-agent systems are known to exhibit stable emergent behaviors, including polarization, over Rn or highly symmetric nonlinear spaces. In this article, we eschew linearity and symmetry of the underlying spaces, and study the stability of polarized equilibria of multi-agent gradient flows evolving on general hypermanifolds. The agents attract or repel each other according to the partition of the communication graph that is connected but otherwise arbitrary. The manifolds are outfitted with geometric features styled “dimples” and “pimples” that characterize the absence of flatness. The signs of inter-agent couplings together with these geometric features give rise to stable polarization under various sufficient conditions.
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02. May 2022: Pip Goodman (MPIM Bonn) will give a Number Theory Seminar on "Restrictions on endomorphism algebras".
Time: 16:00 - 17:00 pm (with more discussion time afterwards)
Room: NU-09A46 (i.e. NU-building, 9th floor, lecture room adjacent to the main/coffee room)
Zoom link on request (Contact Nirvana Coppola)
Drinks will follow at the restaurant "de Boele".
Title: Restrictions on endomorphism algebras
Abstract: Given a hyperelliptic curve y^2=f(x) defined over a number field, can one find easy conditions on f to determine whether its Jacobian is absolutely simple or not? Or, even better, obtain information on the structure of its (geometric) endomorphism ring?
Zarhin has shown that in many cases when the Galois group of f is "large" (insoluble, two-transitive, ...) the possibilities for the endomorphism ring are heavily restricted. In this talk, we will see that many restrictions persist when the Galois group of f is merely cyclic of large prime order. In fact, for certain base fields, we are able to give a finite explicit list.
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09. March 2022: Modelling visual illusion using neurobiological networks.
Room NU-09A46 and hybrid (ask Daniele Avitabile for the link), 14:45-15:45
Speaker: Emre Baspinar
Title: Wilson-Cowan type models for visual illusions.
Abstract: In this two part talk, we will discuss the reproduction of visual perception phenomena, specifically visual illusions, by means of Wilson-Cowan-type models of neuronal dynamics.
In a first part of this talk, we show that the celebrated Wilson-Cowan equations can reproduce a number of brightness and orientation-dependent illusions, and that the latter type of illusions require that the neuronal dynamics equations to consider explicitly the orientation, coherently with the architecture of V1, by means of a suitable lifting procedure. We then present a modification of the Wilson-Cowan equations which makes such model consistent with the efficient representation principle, that is it can be interpreted as the gradient flow of a suitable functional. This shows that this model minimises redundant information, making it capable of replicating more visual illusions than the original Wilson-Cowan formulation.
In a second part of the talk we then focus on a geometric adaptation of the previous models allowing for a reproduction of orientation-dependent Poggendorff-type illusions. The novelty of the model is that it embeds sub-Riemannian diffusion into the neuronal interaction term appearing in the mean field equations, according to the Citti-Sarti-Petitot model of the primary visual cortex.
This is based on joint works with M. Bertalmío, L. Calatroni, V. Franceschi, B. Franceschiello, D. Prandi.
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17. November 2021: Extra Dynamics seminar, room NU-09A46, 16:00-17:00
Speaker: Prof. Konstantin Mischaikow (Rutgers University and Visiting Professor VU)
Title: Global Dynamics of Ordinary Differential Equations: Ramp Systems, Rook Fields, and Connection Matrices
Abstract: Given a nonlinear system of differential equations insights into its dynamics usually come about via numerical simulations. This suggests the following goal:
Given a parameterized system of ordinary differential equations develop an algorithm that identifies the global dynamics over all parameters.
If one uses classical ideas of what it means to identify nonlinear dynamics, e.g. invariant sets, then it is not possible to achieve this goal. With this in mind I will discuss three topics:
1. An alternative framework based on combinatorial topology of what it means to identify global dynamics (connection matrices).
2. I will introduce a rather general class of differential equations for which we are making significant progress towards the goal (ramp systems).
3. I will discuss a means by which we can transition from the analytic setting of differential equations to the combinatorial framework (rook fields).
The focus of the talk will be on providing a perspective of this approach rather than one particular details or results.