Earlier years' colloquium talks

2010

• Wed. 27 Jan: Colloquium in memory of Israel Gohberg. Room M-129, 15:00-17:00. Click here to see a more detailed program. Main speaker: Albrecht Böttcher (Chemnitz).
  Title: Two projections: from Paul Halmos to Israel Gohberg
  Abstract: The two projections theorem by Paul Halmos provides us with a canonical representation of two selfadjoint projections that can be used to solve several problems in geometry and operator theory in Hilbert space. Singular integral or Toeplitz operators with discontinuous symbols lead to Banach algebras generated by two idempotents which are usually not selfadjoint. Motivated by these applications, Roch, Silbermann, Gohberg, and Krupnik established an invertibility criterion for Banach algebras generated by two idempotents, which is one of the most spectacular achievements in the field since Halmos. The talk gives an introduction to the subject and also embarks on the fascinating history of the topic.  
• Wed. 24 Feb: Speaker: Spencer Bloch (Chicago), Room HG-04A05, 16:00-17:00
  Note: This colloquium is part of a dedicated afternoon on the occasion of Prof. Bloch's Stieltjes-professorship in Spring 2010.
  Title: An algebraic geometer looks at renormalization in physics
  Abstract: Algebraic geometry has some powerful tools to deal with divergent integrals. I will outline one approach in elementary terms and sketch how it can be applied to integrals arising in physics.
• Wed. 10 Mar: Speaker: Marius Crainic (Utrecht), Room M-623, 16:00-17:00
  Title: Stability of leaves
  Abstract: In this talk I will discuss stability phenomena (and criteria) for leaves/orbits of geometric structures.  I will start with the classical cases of vector fields/foliations (and the known "Reeb-Thurston stability'') and group actions on manifolds ("Hirsch-Stowe stability'') and then, depending on the time left, I will explain similar recent results in Poisson geometry (joint work with R.L. Fernandes).  
• Wed. 24 Mar: Speaker: Erik van den Ban (Utrecht) - cancelled 
  We are deeply sad to hear that last weekend Hans Duistermaat passed away.
  We offer our condolences to his family, friends and colleagues.
  This week's general mathematics colloquium is cancelled.  
• Wed. 7 Apr: Speaker: Kirsten Valkenburg (VU), Room M-623, 16:00-17:00
  Title: On nonseparable Erdős type spaces
  Abstract: Erdős space is the subspace of Hilbert space consisting of vectors that have all coordinates rational. For complete Erdős space one takes coordinates in a convergent sequence instead of the rationals. Erdős showed that both are one-dimensional and homeomorphic to their own squares. Therefore, they are important examples in dimension theory. Nevertheless, complete Erdős space has surfaced in complex dynamics, functional analysis and descriptive set theory as well. Note that both spaces are basically the intersection of a countable product of zero-dimensional subsets of the reals and an l^p-space. We investigate Erdős type spaces that are uncountable products of zero-dimensional subsets of the reals in a nonseparable l^p-space. Spaces of this kind that are one-dimensional and topologically complete can be classified as products of complete Erdős space with a countable product of discrete spaces, depending on two cardinal invariants of the Erdős type space. There is a similar classification that links certain one-dimensional Erdős type spaces and products of Erdős space with a countable product of discrete spaces.
• Wed. 21 Apr: Speaker: Markus Heydenreich (VU), Room M-623, 16:00-17:00
  Title: Mean-field behaviour in percolation
  Abstract: Various random spatial models show 'mean-field behaviour' above a certain upper critical dimension d_c. In this talk I shall explain what is meant by mean-field behaviour, and why it holds for percolation on the high-dimensional (Euclidean) lattice. Furthermore, I will discuss why it holds for a percolation model on the hyperbolic disc.
• Wed. 5 May: No colloquium (liberation day)
• Wed. 19 May: Speaker: Bernd Heidergott (VU), Room M-623, 16:00-17:00 
  Title: A Swiss Army knife formula for Markov processes 
  Abstract: Starting point of our presentation will be a simple and easy to prove relation for Markov operators. As we will explain, this  relation is a versatile tool for the analysis of Markov processes. On the one hand, it leads to gradient estimation and Taylor series expansions of stationary Markov processes. On the other hand, it can be made fruitful for numerical approximations. The latter application is of particular interest as it provides a new approach to Markov decision processes (independent of value iteration or policy iteration). Time permitting, we will also address applications to the numerical analysis of general Markov operators.
• Wed. 2 Jun: Speaker: Geert Geeven (VU), Room M-623, 16:00-17:00  
  Title: Computational statistics for the identification of transcription factor gene interactions
  Abstract: Condition-specific and time-dependent transcriptional regulatory networks underlie the coordinated expression of genes involved in all biological processes. Insight into these networks is crucial for the understanding of biological systems under normal and pathological conditions. In this talk I will discuss how statistical models can be used to infer relationships between DNA binding proteins and target genes by analyzing experimental gene expression and DNA sequence data. We developed an algorithm called GEMULA (Gene Expression Modeling Using LASSO) and applied it to real experimental data to identify transcription factors that are crucial regulators of the transcriptional network underlying neuronal outgrowth.
• Wed. 16 Jun: Speaker: Eric Opdam (UvA), Room M-623, 16:00-17:00  
  Title: The local L-function conjecture 
  Abstract: The local Langlands conjecture asserts that the Fourier dual of a real or p-adic reductive group G has a description in terms of algebraic data, so-called Langlands parameters. This would imply that the Shahidi-Langlands local L-functions attached to those representations of G relevant for the Fourier analysis on G are holomorphic in the right half plane. Recently we could prove this property of L-functions in general (joint work with Volker Heiermann).
• Wed. 29 Sept: Speaker: Laurent Stolovitch (Nice), Room F-123, 16:00-17:00  
  Title: On normal forms of vector fields
  Abstract: In this talk, we'll give an overview of recent progress that was made in the study of vector fields (or systems of ODEs) in a neighbourhood of a fixed point. We shall focus on the notion of normal form. The latter is supposed to be a "simple" model to which the vector field can be transformed. We shall show some dynamical and geometric properties that can be deduced in the analytic setting.  
• Wed. 13 Oct: Speaker: Christof Melcher (Aachen), Room F-123, 16:00-17:00  
  Title: Landau-Lifshitz-Gilbert dynamics of magnetic vortices
• Wed. 27 Oct: Speaker: Erik van den Ban (Utrecht), Room F-123, 16:00-17:00  
  Title: Radon transformation on symmetric spaces
  Abstract: The goal of this talk is to give an impression of the theory of Radon transformation on symmetric spaces. We still start with describing the classical Radon transform defined by integration over hyperplanes in Euclidean space. It is natural to view this transform in relation to the group of isometries in Euclidean space. This viewpoint was advocated by S.S.Chern who formulated integral geometry in the context of homogeneous spaces of Lie groups. Later, S. Helgason took up this viewpoint to study several transforms of Radon type in the context of Riemannian symmetric spaces (of which the Poincare disk is the simplest example). For the so-called horospherical transform Helgason established a support theorem, which is closely related to a Paley-Wiener theorem for the Fourier transform for these spaces. Towards the end of the talk I will describe recent work of my PhD student Job Kuit, who obtained an interesting generalization of Helgason's result in the context of pseudo-Riemannian symmetric spaces.
• Wed. 24 Nov: Speaker: Stefan Bauer. Room: M-129, 16:00-17:00
  Title: Four Dimensional Manifolds
  Abstract: The world we live in is four dimensional: There are three space dimensions, complemented by time. Manifolds of dimension three  and four are mathematical models of our universe,considered either as a space at a fixed time or in its a totality, from beginning to end of time. Of course we don't stand a chance to ever know how our universe looks like as a whole. Nevertheless, we may pose the question, which models there are and how to distinguish them. During the past decades, ideas and methods from topology, geometry and physics revealed phenomena unknown of in other dimensions. Indeed, amongst all dimensions, geometry is most bizarre and least understood in dimension four. The talk aims to elucidate some aspects of the puzzle.

2009

• Wed. 16 Dec:  Frits Beukers  (UU), Room C-648, 16:00-17:00
  Title: Monodromy of linear differential equations, the case of Lam\'e's equation
  Abstract: The monodromy group of ordinary linear differential equations in the complex plane is a classical but elusive subject. The case of Fuchsian second order differential equations with three singularities is well-known, they come down to Gauss' hypergeometric functions. However, second order Fuchsian equations with four singular points already present with an almost intractable variety of possibilities. We illustrate this by dealing with a special class of Lam\'e differential equations.
• Wed. 2 Dec: Ernst Wit (RUG), Room M-655, 16:00-17:00
  L_1 sparse, penalized inference, with applications in genomics
  The advent of high-dimensional datasets has presented a challenge to traditional statistical inference. The n>p paradigm turned out to be too restrictive and statisticians seemed to be for a while in high seas. However, they found their (wet) feet again, when they realized the connections between high-dimensional inference on the one hand and model choice and penalized methods on the other. L_1 penalized inference had the additional advantage of also resulting in sparse solutions. We give a background to L_1 penalized inference, consider some extensions to other types of "path estimators" and look at an application of L_1 penalized inference in a genomic network context.
• Wed. 18 Nov:  Jan Sanders (VU) Room M-655, 16:00-17:00.
  Title: Classical Invariant Theory and Automorphic Lie Algebras.
  Abstract: First the concepts of reduction and Automorphic Lia Algebra are introduced. It is then shown that the problem of reduction can be formulated in a uniform way using the classical theory of invariants. It follows that $\mathfrak{sl}_2(\mathbb{C})$ Automorphic Lie Algebras associated to the Platonic groups \(\mathbb{T}, \mathbb{O}, \mathbb{I}\) and $\mathbb{D}_n$ are isomorphic. The proof makes use of Clebsch-Gordan decomposition and transvectants, Molien functions and the trace-form. The result is a crucial step towards the complete classification of $\mathfrak{sl}_2(\mathbb{C})$ Automorphic Lie Algebras associated to finite groups. If time allows, some remarks will be made concerning the McKay correspondence.
• Wed. 11 Nov: Geeke Bruin-Muurling en Irene van Stiphout, promovendi Eindhoven School of Education (ESoE), Zaal P-663, 16:00-17:00. 
  Aansluitingsproblematiek in de doorlopende leerlijn rekenen en algebraïsche vaardigheden
  De onderzoeken van de sprekers richten zich op het zoeken naar diepere oorzaken van de aansluitingsproblemen waar havo/vwo en het hoger onderwijs mee worden geconfronteerd. Tegen deze achtergrond wordt de theoretische basis van het huidige reken- en wiskundeonderwijs besproken. Aan de hand van concrete voorbeelden van lesmateriaal en werk van leerlingen en studenten wordt een gedetailleerd beeld gegeven van waar problemen liggen.
• Wed. 4 Nov: Leen Stougie (VU, CWI), Room M-655, 16:00-17:00
  Metabolic Pathway Analysis: Polyhedral Cones and Extreme Rays 
  Abstract: The mathematical questions in this lecture are raised by the study of metabolic networks in steady state. I will start by sketching this application. The biological problems translate into some problems related to extreme rays of a polyhedral cone {x ∈ R^n | Ax = 0, x ≥ 0}, for some m × n matrix A. These extreme rays correspond one-to-one to the vertices of a bounded poly- hedron (polytope) and as a result the complexity of enumerating the extreme rays of the cone is equivalent to the complexity of enumerating the vertices of a bounded polyhedron, which is a famous and long-standing open question. We will not solve this question but present an intriguing related result: given a coordinate i enumerating all extreme rays r of the cone that have ri > 0 cannot be done with polynomial delay unless P=NP. I will give precise definitions of enumeration complexity. Our second result, using essentially the same reduction, is: given two coordi- nates i and j does there exist an extreme ray r of the cone that has both ri > 0 and rj > 0 is NP-complete. Both results are based on a reduction to the decision problem on the existence of negative cycles in directed graphs and inspired by the work of Khachyian et al. [Khachyian et al. 2008], who proved that enumerating vertices of any (possibly unbounded) polyhedron cannot be achieved with polynomial delay unless P=NP.
• Wed. 21 Oct: Theo de Jong (Univ. Mainz), Room C-648, 16:00-17:00
  The geometric definition of the Lebesgue integral
  Abstract: There exist several possibilities for introducing the Lebesgue integral of a function f: R^n -> R. The most commonly known uses the notion of step functions. Lebesgue's original definition, however, was very geometric: for f \ge 0 one considers the set O(f) = {(x,y)| 0 \leq y < f(x)} and one defines \int f(x)dx as the Lebesgue measure of O(f). In general one has f = f_+ -f_- with f_+,f_ \ge 0 and one defines \int f(x)dx = \int f_+(x)dx - \int f_-(x)dx. In this talk we discuss this geometric definition and show how the main theorems  (Fubini and the Change of Variables Formula), can be proved in an elegant way.
• Wed. 7 Oct: Mark Peletier (TUE), Room S-655, 16:00-17:00
  Energy-driven pattern formation via competing long- and short-range interactions
  Abstract: I will discuss patterns in block copolymer melts. This is a model system that is mathematically tractable, physically meaningful (and experimentally accessible) and representative for a large class of energy-driven pattern-forming systems. Such systems show a remarkable variety of different patterns, of which only a small fraction is well understood. I will describe a number of mathematical results that provide insight into their behaviour.
• Wed. 23 Sept: Jeroen Lamb (Imperial College London), Room S-655, 16:00-17:00
  Tilings of Penrose type
  Abstract: The Penrose tiling is a planar tiling with two rhombic tiles, orginally designed by R. Penrose in the early 1970s to illustrate the fact that local properties of tiles (matching rules) can enforce global aperiodicity.  Penrose demonstrated this by a renormalization argument that involves a substitution rule. Some ten years later, N. De Bruijn showed that Penrose's tiling can also be viewed as the projection of a slice of a 5-dimensional lattice. In this talk we present a
  comprehensive characterisation of all tilings of Rⁿ that, like Penrose's original example, can
  be constructed by De Bruijn's projection method and admit renormalization by substitution rules.
  This is joint work with Edmund Harriss (Leicester).
  
• Wed. 24 June, 16:00-17:00, Room S-655: Marianne Jonker (VU University)
  Statistical Methods for Localizing Disease Genes
  In my talk I will explain two methods for localizing disease genes: case- control association analysis and linkage analysis. In a case-control association study one tries to find genes that cause a disease by comparing the genomes of affected and healthy individuals (cases and controls). In a linkage study family data is considered. Here, the idea is that if a disease runs in a family, a chromosomal region that runs exactly the same way in the family contains the causal gene. Foreknowledge on genetics is not necessary, since I start my talk with a short introduction into genetics.
  
• Wed. 10 June, 16:00-17:00, Room S-655: Dave Visser (VU University)
  Homeomorphism groups of Sierpinski carpets and Erdos space
  Erdos space is the ‘rational’ Hilbert space, that is, the set of square summable infinite sequences of rational numbers. Erdos showed that this space is one-dimensional and since it is homeomorphic to its own square it is an important example in dimension theory. Let M be either a topological manifold, a Hilbert cube manifold or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group H(M,D) which consists of all homeomorphisms of M that map D onto itself. Dijkstra and van Mill give a complete topological classification of H(M,D) by showing that it is homeomorphic to the countable power of the space of rational numbers, if M is a one-dimensional topological manifold, and that it is homeomorphic to Erdos space in all other cases. The last result is obtained by using their topological characterizations of Erdos space. As a natural continuation of these results we shall consider the homeomorphism group H(S,D) of an n-dimensional Sierpinski carpet S with countable dense subset D. We show that under some appropriate conditions on D we have that H(S,D) is homeomorphic to Erdos space if the dimension of S is not equal to 3. Since the proof of this result is technical and long we restrict ourselves to the main ideas in the proof, including the topological characterization of Erdos space that we use.
  
• Wed. 27 May, 16:00-17:00, Room M-143: Marcel de Jeu (Universiteit Leiden)
  Real Paley-Wiener theorems and local spectral radius formulas
  The classical complex Paley-Wiener theorems relate the support of a function on R^n to the growth rate of its Fourier transform on C^n. In the first part of the lecture, we will show how the support can also be related to certain growth rates of the Fourier transform on R^n (as opposed to C^n), and why these so-called real Paley-Wiener theorems are more precise than the complex ones can be. In the second part, we will explain how some of these real Paley-Wiener theorems are manifestations of local spectral radius formulas. This is joint work with Nils Andersen.
  
• Wed. 13 May, 16:00-17:00, Room S-655: Erik Koelink (Radboud Universiteit Nijmegen)
  Tridiagonality!
  One usually tries to diagonalise matrices, operators, etc. We will show that tridiagonalisation can also be very useful. The link between tridiagonal operators and orthogonal polynomials is explained. The example of the Schrodinger equation with the Morse potential on the real line is discussed as a basic example for a tridiagonalisation procedure for differential operators.
  
• Wednesday 29 April, 16:00-17:00, Room S-655: Erik Winands (VU UniversityTUE)
  Cancelled.
  
• Wed. 1 April, 16:00-17:00, Room S-655: Francesco Calogero (University of Rome I "La Sapienza")
  Isochronous dynamical systems and the arrow of time
  A vector-valued time-dependent function is called isochronous if all its components are periodic in time with the same fixed period T. A dynamical system is called isochronous if its generic solution is isochronous: periodic in all its degrees of freedom with a fixed period T independent of the initial data. It will be shown how essentially any (autonomous) dynamical system can be modified into another (also autonomous) dynamical systems which is isochronous with an (arbitrarily !) assigned period T, and which moreover behaves, over time periods very short with respect to T, essentially as the original (unmodified) system---up to a constant time rescaling. This can also be done for a large class of Hamiltonian systems (both the unmodified and the modified one), including the Hamiltonian describing the most general (classical, nonrelativistic) many-body problem (provided it is, overall, translation-invariant). Some implications of this fact for statistical mechanics and thermodynamics will be mentioned, and for the distinction among integrable and nonintegrable dynamical systems (all isochronous systems are integrable, in fact maximally superintegrable). These findings have all been obtained together with F. Leyvraz: some of them are reported in my monograph entitled Isochronous systems (Oxford University Press, February 2008), others are more recent.
  
• Wed. 18 March, 16:00-17:00, Room S-655: Rob van den Berg (VU University)
  Ponds and power laws
  This talk concerns a random spatial growth model with very simple rules but surprisingly rich and complex behaviour. It was introduced around 1980 by reserachers related to the oil (exploitation) industry but soon drew attention from many others, including theoretical physicists and mathematicians. After defining this `invasion percolation' model, I will concentrate on an object called a 'pond', and explain that this object has indeed a natural `hydrologic' interpretation. Although there is no special tuning of a parameter in this model, it turns out that these ponds are, in a sense which will be explained, critical. Such 'self-organized critical behaviour' seems to be quite common in nature, but this is one of the very few 'natural' models where it can be rigorously proved.
  
• Wed. 4 March, 16:00-17:00, Room S-655: Olga Holtz (UC Berkeley/University of Berlin)
  Zonotopal Algebra, Analysis and Combinatorics
  A wealth of geometric and combinatorial properties of a given linear endomorphism X of RN is captured in the study of its associated zonotope Z(X), and, by duality, its associated hyperplane arrangement H(X). This well-known line of study is particularly interesting in case n := rank X << N. We enhance this study to an algebraic level, and associate X with three algebraic structures, referred herein as external, central, and internal. Each algebraic structure is given in terms of a pair of homogeneous polynomial ideals in n variables that are dual to each other: one encodes properties of the arrangement H(X), while the other encodes by duality properties of the zonotope Z(X). The algebraic structures are defined purely in terms of the combinatorial structure of X, but are subsequently proved to be equally obtainable by applying suitable algebro-analytic operations to either of Z(X) or H(X). The theory is universal in the sense that it requires no assumptions on the map X (th e only exception being that the algebro-analytic operations on Z(X) yield sought-for results only in case X is unimodular), and provides new tools that can be used in enumerative combinatorics, graph theory, representation theory, polytope geometry, and approximation theory. Special attention in this talk will be paid to the case when X is the incidence matrix of a graph (and therefore unimodular), when the general theory provides interesting combinatorial information about the graph, refining the statistics recorded by its Tutte polynomial and related generating functions.
  
• Wed. 18 February, 16:00-17:00, Room S-655: Ronald Meester (VU University)
  The evidential value in the DNA database search controversy and the two-stain problem
  Does the evidential strength of a DNA match depend on whether the suspect was identified through database search or through other evidence? In Balding and Donnelly (1995) and elsewhere, it has been argued that the evidential strength is slightly larger in a database search case than in a probable cause case, while Stockmarr (1999) reached the opposite conclusion. Both these approaches use likelihood ratios. By making an excursion to a similar problem, the two-stain problem, we argue in this paper that there are certain fundamental difficulties with the use of a likelihood ratio, which can be avoided by concentrating on the posterior odds. This approach helps resolving the above-mentioned conflict.
  
• Wed. 4 February, 16:00-17:00, Room S-655: Miroslav Kramar (VU University)
  Conley index theory for braids and forcing in fourth order conservative systems
  We study dynamical systems coming from fourth order conservative equations. We combine variational and topological methods to find periodic solutions of the equations. The dynamics of these systems is restricted to energy manifolds which foliate the phase space. Since the solutions lie on three dimensional energy surfaces the orbits can be regarded as braids in the energy surface. The space of braids decomposes into braid classes. We define topological invariants for braids that allow us to prove forcing results for periodic solutions. In order to avoid analytical difficulties of infinite dimensional spaces we use the concept of discretized braid diagrams. To pass from infinite dimensional space to a finite dimensional one, variational techniques are employed.

2008

• Wednesday 10 December, 16:00-17:00, room S2.05: Marco Bijvank (VU)
  Periodic Review Inventory Models with Lost Sales
  The majority of the models available in the literature assume backlogging when customer demand can not be fulfilled immediately with inventory on hand. The main reason for this development is because there is a simple replenishment policy that is proven to be optimal for periodic review inventory models with a fixed lead time and backorders. However, the retail market has become very competitive and customers are not as loyal anymore to a specific brand or store as they used to be. Therefore, it is not reasonable to assume that customers are willing to wait for the next order delivery when a product is out of stock. When there is a positive lead time and excess demand is lost rather than backordered, the optimal policy is extremely complex. During this presentation I consider the performance of several replenishment policies for inventory systems with periodic reviews and lost sales. A heuristic procedure is used to determine near-optimal values for the order moment and order size.
  
• Wednesday 26 November, 16:00-17:00, room S2.05: Wouter Kager (VU)
  Reflected random walks in wedges
  I will review some remarkably elegant properties of reflected random walks in wedges and their scaling limit, reflected Brownian motion. I will focus on properties that can be proved by simple yet beautiful arguments. Finally, I will sketch one direction of ongoing work.
  
• Wednesday 12 November, 16:00-17:00, room C6.48: Arjen Doelman (CWI)
  The Dynamics of Reaction-Diffusion Patterns
  This talk is intended as an overview of the field of pattern formation in reaction-diffusion equations. Since this is a huge subject that includes many phenomena and a multitude of mathematical approaches, a personalized selection will be presented.
  
• Wednesday 29 October, 16:00-17:00, room C6.38: Cor Kraaikamp (TU Delft)
  Arithmetic and metric properties of continued fractions
  What continued fractions are, why one could/should be interested in them, and what the relation is to other parts of mathematics (in particular Diophantine approximation and ergodic theory) will be outlined in this talk. Motivated by this, we will also briefly look at other number theoretic expansions, in particular expansions to non-integer bases &beta >1.
  
• Wednesday 15 October, 16:00-17:00, room S2.01: Tilman Bauer (VU)
  Modular forms in stable homotopy theory
  Homotopy theorists study spaces by means of homology theories. These are algebraic invariants (abelian groups, rings) which, chosen carefully, strike a good balance between being computable on the one side and carrying a lot of information about the original space on the other side. A good test of the expressiveness of a homology theory is which maps from spheres to spheres it can detect. Ordinary singular homology, while very easy to compute, is exceptionally bad at this: it can only detect maps between spheres of the same dimension. On the other hand, stably homotopy is a homology theory that, by definition, detects all the maps between spheres, but it is notoriously hard to compute. Starting with ground-breaking work of Quillen, it has turned out there is a strong connection between a certain class of homology theories ("complex oriented") and one-dimensional formal group schemes. This surprising link to algebraic geometry begs the question whether classical group constructions in algebraic geometry, for example elliptic curves, have a counterpart on the homotopy side. Work of Hopkins, Miller, Mahowald et al., starting in the late 90s, has given an intriguing and beautiful answer to this: not only can a single elliptic curve be realized by a homology theory, but also the whole moduli space of elliptic curves. This leads to an interesting connection between the stable homotopy groups of spheres and the ring of modular forms. I will discuss this construction, show some explicit computations, and briefly touch on applications.
  
• Wednesday 1 October, 16:00-17:00, room C6.38: Jan Bouwe van den Berg (VU)
  Braids in dynamical systems
  Pieces of string or curves in three dimensional space may be knotted or braided. This topological tool can be used to study certain types of dynamical systems. In particular, such an approach leads to forcing theorems in the spirit of the famous "period three implies chaos" for interval maps. Applications to ordinary and partial differential equations will be discussed.
  
• Wednesday 17 September, 16:00-17:00, room S2.01: Richard Gill (University of Leiden)
  Careless statistics costs lives
  The PROPATRIA randomized clinical trial of probiotics treatment in acute pancreatitis ended in drama, recriminations, and intense media interest, when it turned out that there had been many more deaths in the treatment group than in the control group. Yet the trial had been apparently carefully designed using state-of-the-art statistical methodology, including interim analysis and early-stopping rules. How could the researchers not have noticed that things were going wrong? I will explain the beautiful mathematics behind the Snapinn early-stopping protocol used by the researchers, and explain how a basic design error in the statistical package SPSS, well-known (to professionals) for years but still uncorrected, contributed to the occurrence of maybe 5 unnecessary deaths in this most carefully planned and executed clinical trial. In brief technical terms: you cannot compute a one-sided p-value without specifying the direction of the alternative. SPSS looks at the data and then chooses the direction which gives the most exciting result. My findings lead to several recommendations for the future conduct of randomized clinical trials; the most important being that the monitoring and safety committee should always be advised by a professional statistician who is not blinded to the identity of the treatment and the control groups.
  
• Wednesday 25 June, 16:00-17:00, room S2.01: Fetsje Bijma (VU University Amsterdam)
  Mathematical models for magnetoencephalographic brain signals
  Magnetoencephalographic signals are measurements of the magnetic field generated by neural activity in the (human) brain. In this talk I will discuss some mathematical topics that occur during the analysis of these data: the so-called forward model, regarding the calculation of the predicted measurements based on known activity in the brain, and different models for the covariance of the background/error signal. Furthermore the question of how to compare the different covariance models in an adequate way is addressed.
  
  
• Wednesday 11 June, 16:00-17:00, room S2.01: Frank den Hollander (Leiden University en Eurandom)
  Metastability under stochastic dynamics
  A physical, chemical or biological system driven by a noisy microscopic dynamics may explore different regions of its state space on different time scales, i.e., for certain values of the interaction parameters the dynamics may move fast within regions but slow between regions. The macroscopic phenomenon associated with this separation is called metastability.
  In this talk we consider one such system, namely, particles hopping on a lattice subject to on-site repulsion and off-site attraction. This system serves as a model for condensation of a supersaturated gas. We explain what has been achieved in past years and what are the key challenges for the future.
  
  
• Wednesday 14 May, 16:00-17:00, room S2.01: Marcel Oliver (Jacobs University, Bremen)
  
  
• Wednesday 23 April, 16:00-17:00, room N3.43: Chris Rogers (University of Cambridge)
  Contracting for optimal investment with risk control
  The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions for the solution to this problem.
  The second theme of the paper is to discuss how one would actually manage (not just measure) risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal then proposes a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation package that induces the agent to select the principal's optimal choice.
  
  
• Wednesday 16 April, 16:00-17:00, room S2.01: Udayan Darji (University of Louisville)
  Two notions of small sets and their applications
  In this talk we discuss two notions of small sets, one topological and one analytic. We discuss how these basic notions of smallness can be exploited in various areas of mathematics by giving some applications in infinite group theory and topological dynamics. In particular, we discuss applications to the highly transitive subgroups of the permutation group on the integers and the persistence of adding machines in a generic topological dynamical system on a manifold.
  
  
• Wednesday 2 April, 16:00-17:00, room S2.01: Hansjörg Geiges (University of Cologne)
  A contact geometric proof of the Whitney-Graustein theorem
  I shall give a very gentle introduction to some basic concepts of contact geometry, notably concerning knots in contact 3-manifolds. This will be used to give a contact geometric proof of the Whitney-Graustein theorem in planar geometry: immersions of the circle in the 2-plane are classified, up to regular homotopy, by their rotation number.
  
  
• Wednesday 19 March, 16:00-17:00, room S2.05: Marek Fila (Comenius University, Bratislava)
  Reaction versus diffusion: blow-up induced and inhibited by diffusivity
  We review results on the relation of the dynamics of a system of ordinary differential equations to the dynamics of the corresponding reaction-diffusion system when diffusion is added. We are mainly interested in the influence of diffusion on the global existence of solutions. We present examples of systems where diffusion induces or inhibits blow-up.
  
  
• Wednesday 27 February, 16:00-17:00, room S2.05: Don Zagier (Bonn)
  Mock theta functions and their applications
  In 1920 Ramanujan introduced a class of functions that he called "mock theta functions". They had properties similar to those of classical modular forms but did not belong to any known class. The mystery was finally solved in 2002 in the thesis of Sander Zwegers. We will discuss his theory and its generalizations and applications.
  
  
• Wednesday 20 February, 16:00-17:00, room S2.03: Dietrich Notbohm (VU University Amsterdam)
  Lie group theory from the homotopy point of view
  Compact Lie groups have a very rich structure. They can be considered as analytic objects (Lie 's original point of view), as objects of Differential Geometry (homogeneous spaces), Differential Topology (manifolds), Combinatorics (root systems), Algebra (group structure, Lie algebra, representations of Weyl groups) and of Homotopy Theory (topological spaces, H-spaces). We will look at them from the homotopy theoretic point of view and show how all the information about a compact Lie group can be encoded in purely homotopy theoretic terms. This development culminated in the notion of p-compact groups, developed by Dwyer and Wilkerson. p-compact groups provide a class of very interesting topological spaces, which "behave" completely like compact Lie groups.
  
  
• Wednesday 6 February, 16:00-17:00, room S2.03: Juan Luis Vázquez (Universidad Autónoma de Madrid)
  Asymptotics of diffusion equations via entropies and functional inequalities
  The large time behaviour of diffusion processes is a main topic in partial differential equations and probability. We consider classes of nonlinear diffusion equations and prove nonlinear central limit theorems using either scaling groups or entropies. The latter go back to L. Boltzmann. In the more specific technical setting, we show how the entropy/ entropy-entropy dissipation method alows to obtain the fine detail of the large time behaviour of renormalized fast diffusion flows. Rates of convergence are obtained through spectral gap estimates of associated linearization which take the form of Hardy Poincare functional inequalities. The method has potential application in many different equations and problems.

2007

• Wednesday 28 November, 16:00-17:00, room S2.03: Harry van Zanten (VU University Amsterdam)
  Representations of fractional Brownian motion and related processes
  Fractional Brownian motion (fBm) is the simplest stochastic process exhibiting self-similarity and long-range dependence properties. It arises in scaling limits of models having these propererties (for instance in telecommunication) and is also frequently considered directly as a building block for models in e.g. queuing theory or finance. A less attractive feature of the fBm is that it does not belong to one of the particularly "nice" classes of processes: it is not a Markov process and it is not a semimartingale. It is therefore desirable to have representation results expressing the fBm somehow in terms of better understood objects. After introducing some basic notions from stochastic process theory we will focus in this talk on series representations for the fBm. We will discuss how these can be found using some classical Sturm-Liouville-type theory. It will turn out that this approach is in fact applicable to the whole class of Gaussian processes with stationary increments.
  
  
• Wednesday 14 November, 16:00-17:00, room S2.03: Jaap van der Vegt (Twente University)
  A posteriori error analysis for the Maxwell equations
  The efficient numerical solution of the Maxwell equations, which describe the behavior electromagnetic waves, is complicated due to the limited regularity of the solution, such as near sharp and non-convex corners and at material interfaces. Resolving these local structures requires solution adaptive finite element techniques, which either locally refine the computational mesh or adjust the polynomial order. For the control of the adaptation process detailed knowledge about the error distribution is necessary which can be provided by a posteriori error analysis. Compared to elliptic partial differential equations, the a posteriori error analysis of the Maxwell equations is considerably more complicated due to lack of regularity and the fact that the bilinear form is in general not coercive. After a brief introduction to finite element methods for the Maxwell equations several techniques for a posteriori error estimation will be discussed in this presentation. Special attention will be given to the efficiency and reliability of the error estimates and their relation to the true error. In particular, implicit a posteriori error estimates are quite accurate and results for several test problems, including the application of a posteriori error estimates in an adaptive algorithm, will be discussed.
  
  
• Wednesday 31 October, 16:00-17:00, room S2.03: Peter Lancaster (University of Calgary)
  Matrices, Polynomials, and Conditioning
  I will introduce problems known as "conditioning" in the context of numerical linear algebra. This is closely connected with the coincidence or near-coincidence of eigenvalues or polynomial zeros. Conditioning will then be considered in the unifying context of matrix polynomials, and recent results on their pseudospectra. In particular, the role played by the new notion of "fault-lines" for pseudospectra will be discussed.
  
  
• Wednesday 17 October, 16:00-17:00, room S2.03: Hans Duistermaat (Utrecht University)
  QRT and elliptic surfaces
  
  
• Wednesday 3 October, 16:00-17:00, room S2.03: Rob de Jeu (VU University Amsterdam)
  K-groups and zeta-functions
  K-groups are groups with a somewhat complicated definition, but they are related to explicit arithmetic in many ways. For example, the structure of K_2 of the rationals is strongly related to quadratic reciprocity. In a different direction, the values of the Riemann zeta function at 2,4,6,... can be expressed in terms of Bernoulli numbers and factors pi, whereas those at 3,5,7,... apparently cannot; this difference can be explained by a relation between the K-groups of Q and the values of the Riemann zeta function. We discuss this, and a seemingly ad hoc generalization for every prime number, illustrating everything with examples.
  
  
• Wednesday 19 September, 16:00-17:00: TALK CANCELLED
  Hansjörg Geiges (University of Cologne)
  A contact geometric proof of the Whitney-Graustein theorem
  
  
• Wednesday 20 June, 16:00-17:00, room S2.01: Mathisca de Gunst (VU Amsterdam)
  Statistics for neuronal networks
  
  
• Wednesday 6 June, 16:00-17:00, room S2.01: Frits Beukers (Utrecht University)
  Algebraic hypergeometric functions
  In the first half of the lecture we give a few elementary examples of hypergeometric functions which are at the same time algebraic function of their argument(s). Then we introduce a general class of several variable hypergeometric functions, the so-called GKZ-functions, and describe a combinatorial criterion for their algebraicity.
  
  
• Wednesday 23 May, 16:00-17:00, room S2.03: Ronald Meester (VU Amsterdam)
  1/2=p_c
  
  
• Wednesday 9 May, 16:00-17:00, room S2.01: Bill Kalies (Florida Atlantic University)
  Building a Database for Global Dynamics of Multi-parameter Systems
  Nonlinear dynamical systems can exhibit complicated behavior occurring on a variety of spatial scales and changing subtly with respect to system parameters. In many applications there are models for dynamics but specific parameters are unknown or not directly measurable. This suggests the need to be able to search through parameter space for specific types of dynamical behavior. Ideally, this would be done computationally in some automated manner, and then later the researcher would be able to query the results. In this talk, we discuss computational topological methods which can extract coarse, but rigorous, global descriptions of dynamics and changes with respect to parameters. Moreover, we discuss ongoing efforts to develop a method for building databases that contain useful, rapidly identifiable information about the types of dynamics computed. We will emphasize the essential information that such a database must contain and the open problems that must be resolved before such a database can be efficiently constructed and queried.
  
  
• Wednesday 25 April, 16:00-17:00, room S2.01: Joost Hulshof (VU Amsterdam)
  Why are the Navier-Stokes equations difficult?
  The Navier-Stokes equations describe the flow of an incompressible fluid in a container which is completely filled. Assuming the fluid velocity at the boundary to be zero (no-slip), it would seem obvious that the initial velocity field uniquely determines the velocity field for all future times. I will explain why this problem is so hard that the Clay institute decided to put a price on it.
  The physically less relevant 2-dimensional version of this problem does come with the expected answer. This can be seen from integral estimates (such as the Sobolev estimates) which are dimension dependent. Scaling arguments lie at the heart of this dependence. As it turns out dimension 2 is critical. A version of Navier-Stokes with the dimension N as a parameter would be hard for N>2.
  Joint work by (not with) Leray et al.
  
  
• Wednesday 11 April, 16:00-17:00, room S2.01: Erik Broman (VU Amsterdam)
  Percolation in general and continuity of percolation functions in particular
  I intend to introduce a basic model in statistical mechanics called percolation, which is a parametrized model. I will motivate the usefulleness of the model and discuss some basic properties of it. I will introduce the so called percolation function which describes a very central macroscopic behaviour and talk about some of its properties. Some of the results presented dates back to the 50's while other results will be presented here for the first time.
  
  
• Farewell party Geurt Jongbloed
  Wednesday 4 April, 15:00-16:00, room S2.09: Piet Groeneboom (TU Delft and VU Amsterdam)
  Isotonic considerations
  When I started thinking about a topic for my dissertation (at a time when Ph. D. students were often still deciding on these matters themselves), I first thought of the area of isotonic regression. But then one of the Dutch professors of Statistics assured me that "the topic was dead". So, for this reason (and possibly other reasons as well), my dissertation was on probabilities of large deviations and not on isotonic regression, although I presently think that isotonic regression is a much more interesting topic. What makes isotonic regression problems so fascinating is that they arise quite naturally in lots of contexts and that, at the same time, there is usually no standard machinery available to tackle them. So, when I got my chance with my own Ph. D. students, such as Geurt Jongbloed, I encouraged them to work on topics related to isotonic regression. In my lecture I will try to explain what isotonic regression is all about and will also discuss some recent work in the area.
  The drinks following the colloquium will be in G0.76
  
  
• Wednesday 28 March, 16:00-17:00, room S2.03: Gunther Cornelissen (Utrecht University)
  Graphs: their zeta functions and their operator algebras
  On the space integer linear combinations of oriented edges of a finite graph, consider the linear operator T that assigns to an edge the sum of its outgoing edges. The operator was constructed by Bass and Hashimoto in connection with the zeta function of the graph. I will show an elementary way to calculate the kernel and cokernel of 1-T on these integral spaces, and then apply this to a classification problem in the theory of C*-algebras. Joint work with Oliver Lorscheid (Utrecht) and Matilde Marcolli (MPIM Bonn).
  
  
• Wednesday 14 March, 16:00-17:00, room S2.03: Guit-Jan Ridderbos (VU Amsterdam)
  Power homogeneity in Topology
  A topological space is called homogeneous if all of its points are topologically equivalent. An example of such a space is the real line. The unit interval is not homogeneous, but an infinite power of it is. Spaces with this property are called power homogeneous. In this talk we investigate the topological behaviour of power homogeneous spaces. It turns out that some of the homogeneity in a power space reflects down to the space itself. These observations can be used for showing that certain spaces are not power homogeneous.
  
  
• Wednesday 28 February, 16:00-17:00, room F2.53: Jussi Behrndt (TU Berlin)
  Sturm-Liouville operators with indefinite weights
  In this talk we first review the classical spectral theory of Sturm-Liouville differential operators of the form
          |r|^-1 [-d/dx (p d/dx) + q]
  and then we drop the assumption on the definiteness of the weight function, i.e., we replace |r| by r. We will discuss some of the spectral properties of such indefinite Sturm-Liouville operators, and it will turn out that they differ essentially from the spectral properties of usual definite Sturm-Liouville operators.
  
  
• Wednesday 14 February, 16:00-17:00, room S2.05: André Ran (VU Amsterdam)
  Stability of invariant subspaces of matrices
  In several instances problems that appear in applications of mathematics in science and engineering can be solved if one can find an invariant subspace (with certain properties) of a given matrix. From point of view of computation it is then interesting to study the behaviour of the invariant subspace under small perturbations of the given matrix. This will be discussed in the talk.
  
  
• No colloquium on Wednesday 31 January.
  
  
• Wednesday 17 January, 16:00-17:00, room S2.03: Aad van der Vaart (VU Amsterdam)
  Bayesian estimation with Gaussian process priors
  A Bayesian method to estimate a function (log probability density, regression function, logit classifier, etc.) is to model the function a-priori as the sample path of a Gaussian process, to assume that the data is generated according to the distribution specified by this sample path, and next to derive the distribution of the function given the data using Bayes' rule. We explain this principle on an example (perhaps Brownian motion in log density estimation), and present some results on the accuracy of the method in terms of properties of the Gaussian process.