UIUC Mathematics Weekly Calendar

Weekly Calendar

January 22 - 26, 2001

Monday Tuesday Wednesday Thursday Friday

Seminars

Announcements

Conferences

Calendar Archive

Items for inclusion in the Weekly Calendar can now be submitted using the new submission form. Other questions or comments related to the Weekly Calendar should be sent to Hilda Britt. Deadline for inclusion in the Weekly Calendar is noon every Wednesday. Speakers are encouraged to provide abstracts.

$Orange & Blue Bar$

MONDAY, JANUARY 22

441 Altgeld Hall, 2:00 p.m.: SPECIAL SEMINAR; Scott Ahlgren, Colgate University; Congruence Properties for the Partition Function; Abstract:Eighty years ago, Ramanujan discovered some beautiful congruences for the ordinary partition function. From Ramanujan's time until very recently, only a few further such congruences had been found. In recent joint work with Ken Ono, we show that such congruences are much more common than was previously known. Our results, which rely on the theory of modular forms, provide a theoretical framework which explains every known partition function congruence.

143 Altgeld Hall, 4:00 p.m.: PROBABILITY AND STATISTICS SEMINAR; Jenny Bryan, Departments of Biostatistics, University of California, Berkeley; Gene Expression Analysis from DNA Microarrays; Abstract: Microarrays allow researchers to capture the intensity of expression for thousands of genes at once. Often we compare expression in two tissues (for example, healthy versus cancerous or pre-treatment versus post-treatment) and attempt to identify genes that exhibit biologically meaningful expression profiles. For example, we might be interested in genes that are differentially expressed or that exhibit strong coexpression with other genes. In this talk, I describe the use of a deterministic rule, applied to the parameters of the gene expression distribution, to select a target subset of genes. The target subset is the parameter of interest, which can be estimated by applying the subset rule to observed sample statistics. I will discuss the conditions necessary for consistency of the subset estimator and will provide a sample size formula. Important features of the sampling distribution are estimated with the parametric bootstrap. The practical performance of the method is illustrated with a data analysis in breast cancer.
P.S.: If you are interested in meeting Jenny Bryan on Monday, January 22, please contact Usha Dhar at u-dhar.edu or call 244-7192 to set up a time.

314 Altgeld Hall, 4:00 p.m.: SPECIAL SEMINAR; Maria Gordina, University of California at San Diego; Diffusions and heat kernel analysis in infinite dimensions; Abstract: The motivation for my work comes from a well known identity used in the quantum field theory (due to Bargmann, Segal et al.). This identity relates Taylor coefficients of a holomorphic function with the L²-norm of this function with respect to the heat kernel measure. Similar results for finite dimensional Lie groups were obtained by Driver and Gross. I'll begin from a construction of the heat kernel measure determined by an infinite dimensional Lie algebra. The main tool in the construction is stochastic differential equation in an infinite dimensional space. Then I'll describe holomorphic functions and their properties. One of interesting new features in infinite dimensions is the existence of a Cameron-Martin subgroup. This subgroup has zero measure, but this is where functions are holomorphic. In addition, I'll talk about an isometry which is an infinite dimensional analog of the Taylor expansion. I'll describe the setting for orthogonal and symplectic (infinite dimensional) groups as well as for a hyperfinite II₁-factor.
Refreshments at 3:15 pm in Room 321 Altgeld Hall

245 Altgeld Hall, 8:00 p.m.: MONDAY NIGHT MATH CLUB; Videomath Reel: Berlin98 will be shown

TUESDAY, JANUARY 23

243 Altgeld Hall, 12:00 p.m.: SEVERAL COMPLEX VARIABLES SEMINAR; Professor John P. D'Angelo, Department of Mathematics, UIUC; Some facts about plurisubharmonic functions

241 Altgeld Hall, 1:00 p.m.
ANALYTIC NUMBER THEORY
Speaker and title to be announced

243 Altgeld Hall, 1:00 p.m.
LOGIC SEMINAR
Professor Anand Pillay, Department of Mathematics, UIUC
A compact complex manifold with the DOP
Abstract: I point out that a certain (three-dimensional) compact complex manifold X, produced some years ago by Lieberman and studied further by Campana, has certain ``bad'' model-theoretic properties when viewed naturally as a first order structure. Specifically the theory of X has Morley rank 3 but U-rank 2, and also has the DOP (Shelah's dimensional order property). X is a certain family of abelian varieties and I also point out that the ``generic fibre" is not Kahler (in a sense that can me made precise).

159 Altgeld Hall, 3:00 p.m.
COMMUTATIVE RING THEORY RAP
Marco Schlichting, Doob Assistant Professor, Department of Mathematics, UIUC
Intersection Multiplicities, continued

241 Altgeld Hall, 3:00 p.m.
GEOMETRIC POTPOURRI SEMINAR
Professor John Wetzel, Department of Mathematics, UIUC
Rectangles in triangles
Abstract: We determine the dimensions of the largest rectangle of given aspect ratio that fits in a given triangle, thereby giving a necessary and sufficient condition on the sides u, v, a, b, c for a n×v rectangle to fit into a triangle with sides a, b, c.

345 Altgeld Hall, 3:00 p.m.
COMBINATORICS AND GRAPH THEORY
Professor Alexandr Kostochka, Department of Mathematics, UIUC
On the chromatic number of simple hypergraphs
Abstract: A typical extremal problem in hypergraph coloring is to determine the minimum number of edges in a hypergraph of a given kind that is not k-colorable. Let m_k(r) denote the minimum number of edges in a simple r-uniform hypergraph that is not k-colorable, where a hypergraph is simple if no distinct edges share more than one vertex. Erdos and Lovász proved that m_k(r) is at least k^2r-4/[16r(r-1)²] and at most 1600r⁴k^2r+2. Grable, Phelps, and Rödl improved the upper bounds for every r and infinitely many k using Steiner systems.
Our results improve this upper bound, and we also improve the bounds of Erdos and Lovász for sufficiently large k in terms of r. Asymptotically, we match the order of magnitude in the Grable-Phelps-Rödl upper bound by proving for each fixed r and sufficiently large k that m_k(r) ł c k^2r-2ln² k, where c depends only on r. This is joint work with Dhruv Mubayi, Vojtech Rödl, and Prasad Tetali.

245 Altgeld Hall, 4:00 p.m.
SPECIAL SEMINAR
Jim Bryan, Tulane University, New Orleans
Counting curves on K3 surfaces and modular forms
Abstract: In the last fifteen years, mathematicians and physicists have discovered suprising connections between the topology of symplectic manifolds and the enumerative algebraic geometry of projective manifolds. In this talk we will explain the sorts of questions that enumerative algebraic geometry asks through many elementary examples. We will explain what K3 surfaces are and formulate the enumerative geometry problems for them. We will sketch how topological ideas and a version Gromov-Witten invariants lead to the complete solution of these questions. The answer turns out to be suprising and quite beautiful: the numbers are given as the coefficients in the fourier expansions of well known modular forms.
Refreshments at 3:15 pm in Room 321 Altgeld Hall

WEDNESDAY, JANUARY 24

114 CSRL, 4:30 p.m.
INFORMATION PROTECTION SEMINAR
Organizational meeting

THURSDAY, JANUARY 25

241 Altgeld Hall, 1:00 p.m.
ANALYTIC NUMBER THEORY
Professor Florin Boca, Cardiff University, Wales
On the spacing statistics of certain sequences
Abstract: I will first discuss some recent results on the h-spacing distributions of Farey fractions and related topics, including the proof of a conjecture of Hall ([MR95f:11074]) and estimates for the average length of the trajectory on a billiard table with pockets in the unit square. The second theme of the talk will be related with the pair correlation of fractional parts of polynomials.

347 Altgeld Hall, 1:00 p.m.
GROUP THEORY SEMINAR
Professor Ilya Kapovitch, Department of Mathematics, UIUC
Boundaries of Hyperbolic Groups, continued

243 Altgeld Hall, 2:00 p.m.
ALGEBRAIC NUMBER THEORY
Organizational meeting

347 Altgeld Hall, 2:00 p.m.
ANALYSIS SEMINAR
Professor Alexander Tumanov, Department of Mathematics, UIUC
Exceptional Analytic Disks, continued

145 Altgeld Hall, 3-5 p.m.
COLORING THEORY RESEARCH GROUP
Discussion of open problems

243 Altgeld Hall, 3:00 p.m.: COMMUTATIVE RING THEORY; Professor Marco Schlichting, Doob Assistant Professor, Department of Mathematics, UIUC

347 Altgeld Hall, 3:00 p.m.: GALOIS MODULES; Professor Marcin Mazur, Department of Mathematics, UIUC; Application of trees and Euler systems to the lifted root number conjecture, I.; Abstract: This is the first of a sequence of lectures devoted to a recent proof by C. Greither and R. Kucera of the Lifted Root Number Conjecture for abelian extensions of prime degree over the rationals.

245 Altgeld Hall, 4:00 p.m.: SPECIAL SEMINAR; Professor Alexander Teplyaev, University of California at Riverside); Analysis on fractals; Abstract: Fractals arise in many areas of science as they can be used to represent percolation clusters, quasicrystals, fractal electrical networks and porous materials. The study of the Laplacian on fractals started only a few years ago. First the Laplacian was considered from a probabilistic point of view, and then an analytic approach was also developed. In this talk I'll describe the properties of the Laplacian, and its spectrum in terms of the Julia set of a rational function. I will also discuss the relation between symmetries of a fractal, and existence and completeness of localized eigenfunctions of the Laplacian. Although the Laplacian on fractals is now relatively well understood, the first order derivatives are less studied. At the end of my talk I will present an approach to defining a gradient on fractals.
Refreshments at 3:15 pm in Room 321 Altgeld Hall

FRIDAY, JANUARY 26

314 Altgeld Hall, 2:00 p.m.: SPECIAL SEMINAR; Florin Boca, Cardiff University; Non-commutative tori - a scenery for non-commutative Fourier analysis

243 Altgeld Hall, 4:00 p.m.: MODEL THEORY SEMINAR; Speaker and title to be announced

245 Altgeld Hall, 4:00 p.m.: SPECIAL SEMINAR; Rinat Kedem, University of California at Berkeley; Algebraic Structures in Integrable Field Theories and Statistical Mechanics; Abstract; Refreshments at 3:15 pm in Room 321 Altgeld Hall