Wed May 8, 2013,
16:00-17:00
Snellius 174
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Xing Chaoping (Nanyang Technological University):
Algebraic curves over finite fields and applications
Kloosterman lecture.
Abstract.
For a long time, the study of algebraic geometry belonged to the realm of pure mathematicians.
After a series of three papers in the period 1977 - 1982, Goppa found fascinating applications of
algebraic curves over finite fields, and especially of those with many rational points, to coding
theory. This created much stronger interest in the area and attracted new groups of researchers
such as coding theorists, cryptographers, theoretical computer scientists and algorithmically
inclined mathematicians.
In this talk, we first give a brief survey on algebraic curves over finite fields with many rational
points and then present three applications.
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April 18, 2013
Snellius 412
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Jan Bouwe van den Berg (VU Amsterdam):
Braids in dynamics
Abstract.
Pieces of string or curves in three dimensional space may be knotted or
braided. This physical idea can be used as a topological tool 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.
We discuss applications to ordinary and partial differential equations.
Finally, we illustrate how the topological arguments can be combined
with a computer-assisted approach to obtain insight
in an evolution equation from the field of pattern formation.
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April 11, 2013
Snellius 312
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Eric Cator (Nijmegen):
A randomly forced Burgers equation on the real line
Abstract.
In this talk I will consider the Burgers equation with a homogeneous Possion process as a forcing potential. In recent years, the randomly forced Burgers equation, with forcing that is ergodic in time, received a lot of attention, especially the almost sure existence of unique global solutions with given average velocity, that at each time only depend on the history up to that time. However, in all these results compactness in the space dimension of the forcing was essential. It was even conjectured that in the non-compact setting such unique global solutions would not exist. However, we have managed to use techniques developed for first and last passage percolation models to prove that in the case of Poisson forcing, these global solutions do exist almost surely, due to the existence of semi-infinite minimizers of the Lagrangian action. In this talk I will discuss this result and explain some of the techniques we have used.
This is joined work Yuri Bakhtin and Konstantin Khanin.
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March 28, 2013
Snellius 312.
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Vitaly Bergelson (Ohio State University):
Ergodic Theorems Along Polynomials and Combinatorics
Abstract.
We will start with discussing various recurrence and convergence results which demonstrate that dynamical systems exhibit surprisingly regular behavior along polynomials times. Besides being of interest in their own right, these polynomial results have strong applications in combinatorics and number theory. We will discuss some of these applications including various polynomial generalizations of Szemeredi's theorem on arithmetic progressions. We will conclude by formulating and discussing some open problems and conjectures. The talk is intended for a general audience.
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December 6, 2012
Snellius 174.
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Frank Vallentin (Delft/CWI):
Upper bounds for geometric packing problems
Abstract.
How densely can one pack given objects into a given container? Problems of this sort, generally called packing problems, are fundamental problems in geometric optimization. In this talk I present a method based on semidefinite optimization and harmonic analysis which can be used to compute upper bounds for the optimal density. I will show how to apply it to a variety of situations: packing spherical caps on the unit sphere, packing spheres (of potentially different radii) into Euclidean space, packing translates of regular tetrahedra into Euclidean space.
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November 22, 2012
Snellius 174.
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Aad van der Vaart (Leiden):
On Bayesian curve fitting
Abstract.
We illustrate the "nonparametric Bayesian paradigm" by
some practice and some theory for the problem of finding a curve
y=f(x) that "best" fits a given set of (noisy) points (x_i,y_i). After
starting from just curve fitting by smoothing splines we
add probability to the description of the problem in two
steps, and show the mathematical theory that this enables,
with reference to Bayes, Laplace, Gauss and Fisher.
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November 8, 2012
Snellius 312.
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Hermen Jan Hupkes (Leiden):
Differential equations with delayed and advanced terms: where, why & how
Abstract.
We discuss the modelling motivation for using MFDEs (functional
differential equations of mixed type, also known as
delay-advanced differential equations) and
illustrate their distinguishing mathematical
features.
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May 24
Snellius B1.
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Filmvertoning:
Late style - Yuri I. Manin Looking Back on a Life in Mathematics
Studievereniging De Leidsche Flesch zal de onlangs verschenen biografische documentaire "Late Style - Yuri I. Manin Looking Back on a Life in Mathematics" vertonen gemaakt door Agnes Handwerk en Harrie Willems. Late Style vertelt het verhaal over Yuri Manin tijdens de gouden jaren van de wiskunde in Moskou tijdens de jaren zestig en zeventig - een periode die niet alleen in het teken van de wiskunde stond, maar zeker ook beïnvloed werd door de plitieke situatie in Rusland. Voorafgaand aan de filmvertoning zal Frans Oort een introductie geven.
Programma: 15:45 koffie en thee, 16:00 inleiding Frans Oort, 16:30 vertoning "Late Style"
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May 10, 2012
Snellius 174.
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Sander Dahmen (Utrecht):
Solving Diophantine equations: the modular method
Abstract.
Since the proof of FLT, many Diophantine problems have been solved
using deep results about elliptic curves, modular forms, and
associated Galois representations. The purpose of this talk is to
discuss some of these results and explain how they can be applied to
explicitly solve certain Diophantine equations. We shall focus in
particular on so-called generalized superelliptic equations, i.e.
exponential Diophantine equations of the form F(x,y)=z^n where F is a
binary form over the integers (to be solved in integers x,y,z,n with
n>1 and x and y coprime).
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April 26, 2012
Snellius 174.
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Roeland Merks (CWI & Leiden):
Modeling stochastic self-organization of multicellular tissues: on the growth of blood vessels and glands
Abstract.
Morphogenesis, the formation of biological shape and pattern during embryonic development, is a topic of intensive experimental investigation, so the participating cell types and molecular signals continue to be characterized in great detail. Yet this only partly tells biologists how molecules and cells interact dynamically to construct a biological tissue. Mathematical and computational modeling are a great help in answering such questions on biological morphogenesis. Cell-based simulation models of blood vessel growth describe the behavior of cells and the signals they produce. They then simulate the collective behavior emerging from these cell-cell interactions. In this way cell-based models help analyze how cells assemble into biological structures, and reveal the microenvironment the cells produce collectively feeds back on individual cell behavior. In this way, our simulation models, based on a Cellular Potts model combined with partial-differential equations, have shown that the elongated shape of cells is key to correct spatiotemporal in silico replication of vascular network growth. The models have also helped identify a new stochastic mechanism for the formation of branched structures in epithelial gland tissues. I will discuss some recent insights into these mechanisms. Then I will discuss our more recent cell-based modeling studies of cell-extracellular matrix interactions during angiogenesis. I will conclude by suggesting some interesting continuum and stochastic mathematical problems that our cell-based simulations suggest.
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April 19, 2012
Snellius 174.
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Anthony Wickstead (Queen's University Belfast):
The Riesz Decomposition Property for some spaces of real-valued functions
Abstract.
An ordered space V has the Riesz Separation Property (RSP) if
f_1, f_2, h_1, h_2 \in V and f_1, f_2 \leq h_1, h_2 implies there is a g in V with f_1, f_2 \leq g \leq h_1, h_2.
Many, but not all, interesting vector spaces of functions have the RSP
even though they do not possess the stronger property of being a
vector lattice. The talk will survey results on this topic due to H.H.
Schaefer, L. Fuchs and A. Nagel & W. Rudin.
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March 22, 2012
Snellius 174.
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André Henriques (Utrecht):
What is an elliptic object?
Abstract.
Elliptic cohomology (also called "topological modular forms" of "TMF")
is a cohomology theory that was constructed in the 90ties by homotopy
theoretical means.
Several strong indicators make people believe that there exist
geometric objects that represent elliptic cohomology classes. However,
despite multiple attempts by many people, nobody has managed to
define those elusive "elliptic objects".
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February 23, 2012
Snellius 174
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John F. Bukowski (Juniata College & Leiden):
The Diverse Interests of Christiaan Huygens: Mechanics and Music
Abstract.
Christiaan Huygens contributed to the early history of the problem of the hanging chain when he proved at age 17 that the chain did not take the shape of a parabola. We will examine his proof in detail. Huygens was also one of many seventeenth-century mathematicians interested in the tuning of the musical scale. We will see how he used logarithms to divide the octave into a 31-tone scale, and we will compare his tuning to other tunings of the scale.
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