# General Mathematics Colloquium

This colloquium takes place every other Wednesday afternoon, 16:00-17:00, in room P-647. For more information, please contact one of the organizers Joost Hulshof and Rob de Jeu.

A database of earlier years' talks can be found here.

...

## Previous talks in 2017:

...

Wed 13 December 2017:  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.

Wed 13 December 2017: 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.

Wed 13 December 2017:  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.

Wed 29 November 2017: 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.

Wed 15 November 2017: 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.

Thu 09 November 2017: 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.

Wed 01 November 2017: 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.

Wed 18 October 2017: 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).

Wed 04 October 2017: 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 $1/\pi$.

Wed 20 September 2017: 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.

Wed 17 Mei 2017: 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.

Wed 03 Mei 2017: 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.

Wed 03 Mei 2017: 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.

Wed 03 Mei 2017: 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.

Wed 19 April 2017: 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

Wed 05 April 2017: 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.

Wed 22 Maart 2017: 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?".

Wed 08 Maart 2017: 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.

Wed 22 Februari 2017: 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.

Wed 08 Februari 2017: 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.