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General Mathematics Colloquium

This colloquium takes place every other Wednesday afternoon, 16:00-17:00. For more information, please contact one of the organizers: Rob de Jeu and Bob Rink.

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

Upcoming talks in 2012:

Wed. 8 Feb: Bob Planque (VU), Room C-147, 16:00-17:00
Title: Building giant ant colonies from single queens
Abstract: Ant colonies spanning a million or more are among nature's greatest wonders. Some raid the tropical forest floor in huge armies, others rely on agriculture invented millions of years ago. Just how such insect city states work and indeed are initially founded is largely unknown. Especially for those species whose colonies start as single fertilized queens, we may still only marvel how a colony's organization changes as numbers change over six orders of magnitude. In this talk, I will focus on the role of diversity in recruitment mechanisms to harvest food, using differential equation models, The main question will be to understand how some of the most efficient such mechanisms, usually employed by large numbers of ants, may be employed in small colonies.
Wed. 22 Feb: Hansjoerg Geiges (Koeln), Room C-147, 16:00-17:00
Title: How to visualise manifolds up to dimension 5
Abstract: We usually think of 2-dimensional manifolds as surfaces embedded in Euclidean 3-space. Since most humans, including the speaker, cannot visualise Euclidean spaces of higher dimensions, it appears to be impossible to give pictorial representations of higher-dimensional manifolds. However, one can in fact draw 1-dimensional pictures truly representing the topology of surfaces. By analogy, one can draw 2-dimensional pictures of 3- manifolds (Heegaard diagrams), and 3-dimensional pictures of 4-manifolds (Kirby diagrams). With a little trick, one can even draw 2-dimensional (sic!) pictures of at least some 5-manifolds. In this talk I shall explain how to draw such pictures and how to use them for answering topological and geometric questions. The work on 5-manifolds is joint with Fan Ding and Otto van Koert.
Wed. 7 March: Speaker: Michael McAssey (VU), Room C-147, 16:00-17:00
Title: Spectral data clustering using a regulated random walk.
Abstract: Identifying clusters among data is a common goal of exploratory data analysis. Spectral clustering has become a popular technique that extracts cluster information from the spectrum of the graph Laplacian associated with a graph whose vertices are the data points. However, its effectiveness is limited when, for example, the clusters are non-convex, or their intra-cluster scales are heterogeneous. We present a regulated random walk on the graph by which we obtain a similarity measure based on an intuitive definition of a cluster. From this similarity measure we obtain a graph Laplacian that extends the effectiveness of spectral clustering to a much wider variety of data settings. We illustrate this method on both simulated and real data sets.
Wed. 21 March: Speaker TBA, Room C-147, 16:00-17:00
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Wed. 4 April: Speaker TBA, Room M-623, 16:00-17:00
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Wed. 18 April: Speaker TBA, Room M-623, 16:00-17:00
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Wed. 2 May: Speaker TBA, Room M-623, 16:00-17:00
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Wed. 16 May: Speaker TBA, Room M-623, 16:00-17:00
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Previous talks in 2011/2012:

Wed. 2 Feb: Stephan van Gils (Twente), Room M623, 16:00-17:00
Title: Detailed and population models for a microcolumn of the cortex
Abstract: We present two models developed to study neuronal activity during normal and pathological state. A detailed model describes a microcolumn of the neocortex. It contains many parameters, whose values are based on experimental data. Depending on global parameters (the total network excitation and inhibition), the model exhibits different types of behavior like saturated desynchronized activity, irregular bursts, fast oscillations and burst suppression. The second model is a lumped population model. It describes the activity of two interacting excitatory populations in terms of a system of delay differential equations with two point delays. In this model we analyze steady states and we perform bifurcation analysis in two parameters. Finally, the behavior of the two completely different models is compared. These different states are compared with the stable states in a delay differential population model for the activity of neuronal populations.
Wed. 16 Feb: Arjeh Cohen (Eindhoven), Room M623, 16:00-17:00
Title: Algebraic models for some Hurwitz surfaces
Abstract: Compact Riemann surfaces are equivalent mathematical objects to smooth complex projective algebraic curves. But finding the curve corresponding to a given Riemann surface is not easy. For five Hurwitz surfaces, instances of Riemann surfaces with relatively large automorphisms, Maxim Hendriks and I were able to compute the curve. Two of these are known; one of these is the classic Klein quartic. In my talk, I will provide an introduction to the basic theory, show nice pictures of the Riemann surfaces by Jack van Wijk, and describe the method of construction.
Wed. 2 March: Han Peters (UvA), Room M623, 16:00-17:00
Title: Fatou Theory in two complex dimensions
Abstract: In complex dynamical systems we study the orbits under the iteration of holomorphic maps. Roughly said, an initial value is said to lie in the Fatou set if the orbits of all nearby initial values are similarly. In other words, the dynamical system behaves orderly (not chaotically) near the initial value. Connected components of the Fatou set are called Fatou components, and these components play an important role in our understanding of complex dynamical systems. Since 1985 the Fatou components that can occur for rational functions in the Riemann sphere are completely described. I will review these classical one-dimensional results, and discuss what is known (and not known) in two complex dimensions.
Wed. 16 March: Tobias Mueller (CWI), Room M623, 16:00-17:00
Title: Random geometric graphs
Abstract: If we pick n points at random from d-dimensional space (i.i.d. according to some probability measure) and fix an r > 0, then we obtain a random geometric graph by joining two points by an edge whenever their distance is at most r. I will give a brief overview of some of the main results on random geometric graphs and then describe my own work on Hamilton cycles and the chromatic number of random geometric graphs.
Wed. 30 March: Rommert Dekker (Rotterdam), Room M623, 16:00-17:00
Title: In search of a reliable timetable for the Dutch Railways
Abstract: Real-time railway operations are subject to stochastic disturbances. Thus a timetable should be designed in such a way that it can cope with these disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. Traditionally the Dutch Railways uses a time supplement of 7% for all connections over the country, yet there is no clear explanation of the choice of that percentage. This presentation studies the aspects of timetable robustness. We first consider a single line and derive some results which resemble results from hospital appointment planning. Next we consider a deterministic model for cyclic railway timetables. We adapt it into a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called ‘‘Zaanlijn”. The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable. If time allows we will also consider the extension to liner shipping schedules.
Wed. 13 April: Roberto Fernandez (Utrecht), Room M623, 16:00-17:00
Title: Gibbsianness and the transformations that destroy it
Abstract: Gibbs measures are the main characters of equilibrium statistical mechanics. They enjoy a fully developed theory that has lead to their widespread application well beyond their original field. Nevertheless, examples show us that Gibbsianness can not be taken for granted, because it can be destroyed by simple transformations and even during spin-flip simulations. The talk will review the notion of Gibbsianness and will present examples of loss of Gibsianness illustrating the mechanisms behind the Gibbs-nonGibbs transitions.
Wed. 27 April: Steven Wepster (Utrecht), Room M623, 16:00-17:00
Title: Preparing a translation of Ludolph van Ceulen's "Vanden Circkel"
Abstract: Currently we are working on a translation into English, plus commentary, of Ludolph van Ceulen's book "Vanden Circkel" ("On the circle"), originally published in 1596. Through a number of examples I will show why such a translation is of interest to a modern mathematician and/or historian of mathematics: partly because the book falls in with the tradition of mathematical practice at the time, partly because it contributes to reshaping that tradition, and partly because it contains some very advanced results (to 16th century standards). There is even a kind of "open problem": in specific instances we still do not know the computational methods that Van Ceulen applied.
Wed. 11 May: Wieb Bosma (Nijmegen), Room M623, 16:00-17:00
Title: Some intriguing problems on continued fractions
Abstract: For ages, continued fractions have been known to provide alternative representations of real numbers (instead of decimal or binary expansions). They have advantages, particularly for the approximation by rational numbers, but also severe disadvantages, for real arithmetic, for example, because the digits can be arbitrarily large, for instance. In this talk some aspects of continued fractions with bounded partial quotients (digits) will be discussed. By elementary geometric and topological means some results on such representations can be found, and a surprising recent result for complex continued fraction will be derived: the existence of algebraic numbers of arbitrary degree with bounded complex partial quotients.
Wed. 25 May: Pierre Nolin (NYU), Room M143, 16:00-17:00
Title: Universality of some random interfaces: inhomogeneity and SLE(6)
Abstract: We present classical lattice models of statistical mechanics, particularly percolation and the Ising model. In two dimensions, these two models feature a sharp change of behavior - a phase transition - at a certain value of the macroscopic parameter (density, temperature), and for this specific critical value, they both possess a conformal invariance property, as proved by Smirnov (2001, 2007). This strong property has important consequences for the models considered, at and near their critical point. In particular, we discuss the formation of "universal" random shapes, observed in various concrete situations (chemical etching, erosion...): fractal interfaces with dimension 7/4, coming from density fluctuations, arise spontaneously.
Wed. 7 Sept: Bert Zwart (CWI/VU), Room M-639, 16:00-17:00
Title: Using probability to develop rules of thumb
Abstract: I will discuss several research problems I have been involved with which are mathematically challenging and at the same time have a story our grandmothers would be able to understand. These all relate to measuring the performance of and/or designing systems that operate in a random environment. Examples are call centers, computer systems, and communication networks. Although the focus will be on explaining the physical intuition behind the results, I will indicate the mathematical challenges as well.
Wed. 21 Sept: Michael Levin (Ben Gurion), Room M-639, 16:00-17:00
Title: Revisiting two classical results of Dimension Theory
Abstract: The talk is focused on the following classical results of Dimension Theory: the Menger-Urysohn formula and the Hurewicz theorem on dimension lowering maps. We will examine ways of strengthening these results by means of Cohomological Dimension and Extension Theory.
Wed. 5 Oct: Ale Jan Homburg (UvA/VU), Room M-639, 16:00-17:00
Title: From iterated function systems to partially hyperbolic dynamics
Abstract: I'll provide an overview of topics in chaotic dynamical systems I've been working on, and discuss their relations. I'll proceed from iterated function systems to forced circle diffeomorphisms to partially hyperbolic dynamics on the 3-torus. A common theme will be the search for dynamical properties that occur robustly (that persist when perturbing the system), such as the robust occurrence of dense orbits.
Wed. 19 Oct: Jan Hogendijk (Utrecht), Room M-639, 16:00-17:00
Title: Aspects of mathematics in medieval Islamic civilization
Abstract: I will discuss some characteristic aspects of mathematics in medieval Islamic civilization, on the basis of the works of the mathematician and astronomer Abu Rayhan Biruni (973-1046). My examples will include applications such as the astrolabe and an instrument for finding the direction of Mecca (the qibla).
Wed. 2 Nov: Anish Sarkar (Delhi), Room M-639, 16:00-17:00
Title: Some models of random oriented trees
Abstract: Random oriented trees originate in many physical models. In many river
network models such as Howards model, Scheidegger model etc.,
random oriented trees can be found. In this talk, I will describe some
of these above models and also describe models from other fields. I will state some
of the results and describe a few open problems.
Scaling limits of these models are also of interest, which brings out
the connection of Brownian web with these models. If time permits, I
will discuss this connection briefly.
Wed. 16 Nov: Speaker: Aner Shalev (Jerusalem), Room M-639, 16:00-17:00
Title: Words and Waring type problems
Abstract: Non-commutative analogues of Waring problem in number theory were studied extensively in recent years, where the goal is to express group elements as short products of special elements; these may be powers, commutators, values of a general word w, or elements of a given conjugacy class, or of certain subgroups or subsets. Such problems arise naturally in profinite groups, finite groups, and finite simple groups in particular. I will describe background, recent results (with various coauthors), and relations to representations, geometry, and growth. I will conclude with some applications and conjectures. The talk will be accessible for a wide audience.
Wed. 30 Nov: Speaker: Shota Gugushvili (VU), Room M-639, 16:00-17:00
Title: Parametric inference for stochastic differential equations: a smooth and match approach
Abstract: In this talk we will consider a parameter estimation problem for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. In the first, less technical part of the talk we will supply some remarks on the history of discovery and study of a physical phenomenon known under the name of Brownian motion and the impact it had on the development of probability theory. In particular, we will show how explanation of the Brownian motion phenomenon led to writing down the first ever stochastic differential equation by Langevin in 1908 (even prior to formulation of a rigorous mathematical theory of stochastic differential equations). Next, after some basic information on the modern theory of stochastic differential equations, in the second, more technical part of the talk we will turn to the parameter estimation problem itself. For construction of our estimator of the parameter of interest we will propose a specific two-step procedure with steps being referred to as a smoothing step and a matching step. We will highlight computational advantages furnished by our procedure and will discuss the asymptotic behaviour of the estimator. Our main result is that under suitable assumptions our procedure leads to an estimator with an optimal, square root of n convergence rate. Finally, we will also discuss a further improvement of our estimator through a one-step Newton-Raphson type procedure. The talk is based on a joint work with Peter Spreij.

Wed. 14 Dec: Speaker Gunther Cornelissen (Utrecht), Room M-639, 16:00-17:00
Title: Number theory and physics, an eternal rusty braid
Abstract: I will describe joint work with Matilde Marcolli in which we apply ideas from quantum statistical mechanics and dynamical systems to solve the number theoretical analogue of the problem "how to hear the shape of a drum".