Autumn 2004 schedule

# MathematicsDepartmentColloquium : Spring 2005 schedule

 Monday, January 10, 1600-1700

Speaker : Boris Shapiro, Stockholms Universität.

Title : James Maxwell on critical points of a system of point charges

 Monday, January 24, 1600-1700

Speaker : Volodymyr Mazorchuk, Uppsala.

Title : Categorification - a new idea in algebra and topology.

Abstract :In this talk I would like to describe the relatively new idea of categorification, which was formulated for the first time by M. Khovanov a couple of years ago. This idea is now rather popular, intensively studied and widely used, in particular, in algebra and topology. In contrast to the usual mathematical practice of "making things easier", categorification is actually an idea to "make things more complicated", for example to upgrade a positive integer to a vector space, or a vector space to a category. The point is that sometimes this allows one to get more information, wich was not visible on the original level. .

 Monday, February 7, 1600-1700

Speaker : Giuseppe Toscani, Pavia.

Title : Overpopulated tails in nonconservative kinetic systems.

Abstract :To be announced. .

 Monday, February 28, 1600-1700

Speaker : Christian Krattenthaler, Universität Wien.

Title : Exact and asymptotic enumeration of watermelons with a wall interaction.

Abstract :I consider an instance of the vicious walker model of Michael Fisher, proposed by Owczarek, Essam and Brak, in which their is an interaction of the walkers with a fixed wall. I show how to completely solve the problem of determining the asymptotic behaviour of the corresponding partition function (and of another interesting parameter). In the course of doing that, we shall meet some of my deer friends: determinants, a tableau bijection, and hypergeometric series.. .

 Monday, March 21, 1600-1700.

Speaker : Gerhard Rein, University of Bayreuth (Germany).

Title : Nonlinear stability of Newtonian galaxies and stars.

Abstract : In astrophysics, the dynamics of a galaxy is often modelled by the Vlasov or collisionless Boltzmann equation coupled to the Poisson equation. We will show that certain steady states of this system are minimizers of so-called energy-Casimir functionals. From this fact the nonlinear stability of these steady states can be derived. The approach is such that it yields as a bonus also the nonlinear stability of barotropic stars described as steady states of the Euler-Poisson system.

 Monday, May 16, 1600-1700 (OBS! NEW DATE FOR THE SECOND TIME)

Speaker : Viktor Berbyuk, Mechanical Engineering, Chalmers.

Title : Control and optimization of semi-passively actuated mechatronic systems.

Abstract : here. .

 Monday, May 23, 1600-1700

Speaker : Sergey Kislyakov, PDMI, St. Petersburg

Title : Stability of approximation under singular integral operators and Calderon-Zygmund type decompositions.

Abstract : In their classical paper "On existence of certain singular integrals" (Acta Math., 88 (1952), 85-139), Calderon and Zygmund used quite efficiently a simple procedure of splitting a function in a "good" and "bad" part. Since then, this procedure has been reproduced in many textbooks; moreover, many related constructions suitable for other purposes have been invented. For example, it is fairly well known by now that for many spaces of $X$ "smooth" functions (like $Lip_\alpha$, or Sobolev classes, or BMO), a specific Calderon-Zygmund type algorithm can be used to exhibit an element $u$ of almost optimal $L^1$-approximation of a given function $f\in L^1$ by a ball of a fixed radius in $X$. The main new result of the talk sais that for most of the singular integral operators $T$ the function $Tu$ also approximates $Tf$ in the same $L^1$-optimal sense provided $Tf$ is integrable. This is a part of a joint work with N. Kruglyak .

 Monday, May 30, 1600-1700.

Speaker : Andrei Toom, Universidade Federal de Pernambuco (Brazil).

Title : Geometrical methods in cellular automata.

Abstract : To be announced.

 Tuesday, June 7, 1600-1700 (OBS! TUESDAY)

Speaker : Mihai Ciuci, Georgia Tech.

Title : A random tiling model for two-dimensional electrostatics.

Abstract : We consider random lozenge tilings with a finite number of triangular holes. We define the correlation of such holes by including them in large lattice regions and considering an appropriate normalization of the number of tilings of the complement of the holes. We show that in the scaling limit the correlation is obtained from a multiplicative superposition principle that parallels two dimensional electrostatics. Our results apply or any finite collection of lattice triangular holes of even side. We also indicate how a lattice refinement parameter accounts for physical temperature.