BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Vrije Universiteit Amsterdam//NONSGML v1.0//EN NAME:PhD defense L.J.W. van der Aalst METHOD:PUBLISH BEGIN:VEVENT DTSTART:20261117T134500 DTEND:20261117T151500 DTSTAMP:20261117T134500 UID:phd-defense-l-j-w-van-der-aals@8F96275E-9F55-4B3F-A143-836282E12573 CREATED:20260924T235158 LOCATION:Main building VU, 1105, Auditorium, De Boelelaan, 1081 HV, Amsterdam SUMMARY:PhD defense L.J.W. van der Aalst X-ALT-DESC;FMTTYPE=text/html:

Computer-assisted pr oofs for partial differential equations in multiple spatial dimension s

From suspension bridges to fluid flows: solutions can b e proven with the help of computers

Engineers rely hea vily on computer calculations to predict physical behavior. The metho ds from this thesis help to strengthen the mathematical reliability b ehind such simulations. It is in line with a time in which we are inc reasingly dependent on computers.

Physical phenomena s uch as an undulating suspension bridge or a flow of fluid are describ ed by complicated mathematical equations. Computer models can often a pproximate that behavior, but standard simulations never provide one hundred percent mathematical certainty. This is a big gap in science: we see a phenomenon on the screen, but cannot prove it definitively.

My research therefore focuses on the question: how can we use computers so that they provide rigorous evidence for the existence of these kinds of complex phenomena?

Too complex to calc ulate

Physical systems, such as those fluid flows or undulating bridges, are often too complex to calculate directly in re al life, so we capture them in simplified mathematical models. Comput er evidence has long been used to prove all kinds of models. In my re search, I made these models more realistic by calculating in multiple spatial dimensions at the same time, and adapted the methods accordi ngly.

By combining computer power with classical pen-and-paper mathematics, we can show that specific patterns actually exist withi n these theoretical models. This removes the doubt whether an outcome on the screen is, for example, a calculation or rounding error.

DESCRIPTION: Computer-assisted proofs for partial differential equatio ns in multiple spatial dimensions

From suspension bridges to flui d flows: solutions can be proven with the help of computers

Engineers rely heavily on computer calculations to predict physica l behavior. The methods from this thesis help to strengthen the mathe matical reliability behind such simulations. It is in line with a tim e in which we are increasingly dependent on computers.Physic al phenomena such as an undulating suspension bridge or a flow of flu id are described by complicated mathematical equations. Computer mode ls can often approximate that behavior, but standard simulations neve r provide one hundred percent mathematical certainty. This is a big g ap in science: we see a phenomenon on the screen, but cannot prove it definitively.My research therefore focuses on the question: how can we use computers so that they provide rigorous evidence for the exist ence of these kinds of complex phenomena?

Too complex to c alculate

Physical systems, such as those fluid flows or undulating bridges, are often too complex to calculate directly in re al life, so we capture them in simplified mathematical models. Comput er evidence has long been used to prove all kinds of models. In my re search, I made these models more realistic by calculating in multiple spatial dimensions at the same time, and adapted the methods accordi ngly.

By combining computer power with classical pen-and-paper mathematics, we can show that specific patterns actually exist withi n these theoretical models. This removes the doubt whether an outcome on the screen is, for example, a calculation or rounding error. END:VEVENT END:VCALENDAR