HOLIDAY - LABOR DAY. Campus wide.

  

Symplectic and Contact Geometry RAP,  143 Henry,  10:00 a.m.

  

Organizational meeting

  

Abstract: The RAP will concentrate on group actions on contact and symplectic manifolds with emphasis on classification problems and applications to completely integrable systems. We will begin with known results; progress to recent, unpublished work; and then begin discussing open problems.

  

Max Newman Topology,  345 Altgeld,  11:00 a.m.

  

Professor Charles Rezk (UIUC)

The Logarithm for K-theory

  

RAP ``Spaces of non-positive curvature'',  243 Altgeld Hall,  11:00 a.m.

  

Professor Ilya Kapovich

M_k-complexes

  

Abstract: We will describe so called M_k-complexes, which are metric spaces obtained by gluing polyhedral pieces of the model space M_k. We shall also explore when an M_k-complex has curvature bounded above by k.

  

Several Complex Variables Seminar,  243 Altgeld Hall,  12:00 p.m.

  

Professor Robert Kaufman

Function Algebras and Several Complex Variables

  

Probability and Statistics Seminar,  2 Illini Hall,  11:00 p.m.

  

Professor Barbara Bailey (Department of Statistics, UIUC)

Quantifying the Predictability of Noisy Nonlinear Biogeochemical Systems

  

Abstract: Statistical modeling of dynamical systems makes the estimation and construction of confidence intervals for interesting quantities from data possible. When noise is an integral part of the system's dynamics, a nonlinear time series approach can be used to quantify the dynamics and predictability of the system. This involves fitting nonlinear models and estimating dynamical systems quantities of interest such as global and local Lyapunov exponents, along with measures of uncertainty for these estimates. This approach will be used quantify the predictability of the effects of different types of noise on a simple biogeochemical model of plankton dynamics. The models consist of nonlinear systems of first-order differential equations for the flows or intercompartmental exchanges among nutrients, phytoplankton, zooplankton and detritus.

  

Analytic and Elementary Number Theory,  243 Altgeld Hall,  1:00 p.m.

  

Professor Scott Ahlgren (UIUC)

The zeta functions of a family of K3 surfaces

  

Abstract: The zeta function of a surface is a function which contains information about the number of points on the surface over finite fields. The explicit determination of these functions is a well-known problem in number theory. In this talk I will show how one can compute the zeta functions of an infinite family of so-called ``K3 surfaces."

  

Logic Seminar,  345 Altgeld Hall,  1:00 p.m.

  

Yevgeniy Vasilyev (UIUC)

Generic Pairs of SU-Rank 1 Structures

  

Abstract: For a supersimple SU-rank 1 theory $T$, we introduce the notion of a ``generic" elementary pair of models of $T$. The theory $T^*$ of all such pairs is complete and supersimple, of SU-rank 1, 2 or $\omega$. We use generic pairs to study the geometric properties of supersimple SU-rank 1 structures, in particular the properties of linearity and pseudolinearity.

  

Differential Geometry Seminar,  347 Altgeld Hall,  1:00 p.m.

  

Professor Eugene Lerman (UIUC)

Integrable geodesic flows, toric varieties and contact manifolds

  

Abstract: Motivated by the work of Toth and Zelditch (Riemannian Manifolds With Uniformly Bounded Eigenfunctions, math-ph/0002038) we study geodesic flows with global homogeneous action-angle variables, the so called toric integrable flows. This leads to an investigation of torus actions on contact manifolds and a related study of non-compact toric varieties. As an application we prove three conjectures of Toth and Zelditch on toric integrable geodesic flows.

  

Geometric Potpourri Seminar,  243 Altgeld Hall,  2:00 p.m.

  

Lawrence Evans

A unified construction of basic triangle centers and a polyhedral scheme summarizing collinearities of centers

  

Abstract: First we present a unified construction of 15 triangle centers which consists of drawing 6 circles, then a series of lines. This yields the centroid, orthocenter, circumcenter, nine-point center, Fermat points, Napoleon points, isodynamic points and several other fundamental centers in one simple construction. It is well-known that there are many constancies among the positions of triangle centers, such as collinearities, trapezoids, concyclycities, etc. Clark Kimberling has likened such arrangements of centers to constellations in the night sky. In the spirit of this beautiful metaphor, we illustrate how by labeling the vertices and sides of regular polyhedra with centers we can symmetrically summarize 25 collinearities among 17 triangle centers as a point in the middle of an icosahedron inscribed in an octahedron inscribed in a tetrahedron. This condenses lots of information in a single figure. The talk will be elementary, and unfamiliar triangle centers will be illustrated by how they were originally defined.

  

Stochastic and Nonlinear Analysis,  347 Altgeld Hall,  2:00 p.m.

  

Professor Benny Sudakov (Princeton University and IAS)

A sharp threshold for network reliability

  

Abstract: One of the most interesting phenomena in the theory of random structures is the ßharp threshold behavior" of random graph properties. In this talk we will illustrate the well-known method for proving sharp thresholds on one particualr example: network reliability.

  

Graph Theory and Combinatorics,  241 Altgeld Hall,  3:00 p.m.

  

Benny Sudakov (Princeton University and IAS)

Vertex list coloring by the semirandom method

  

Abstract: The semirandom method (Rödl Nibble) is the general approach to proving the existence of something by generating it through many iterations, applying probabilistic reasoning at each step. One area of Combinatorics where the semirandom method has had the greatest impact is graph coloring. In fact, many of the strongest result in graph coloring over the past decade are examples of this method. In this talk we will illustrate how the semirandom method works by proving the following result:

Let G = (V,E) be a graph with the sets of lists S(v), one for each vertex v of G, and let d be an integer such that 1. for every vertex |S(v)| = (1+o(1))d, and 2. for each c Î S(v), at most d neighbors of v have c in their lists.

Then there exist a proper coloring of G from these lists.

This result, which is asymptotically tight, is joint work with Bruce Reed.

  

Math New Faculty Reception,  321 Altgeld Hall Common Room,  3:00 p.m.

You are most cordially invited a reception to meet new Mathematics Department faculty, visitors and postdocs.

  

Refreshments will be served.

  

RAP - Conformal invariance, intersection exponents and critical percolation,  145 Altgeld Hall,  4:00 p.m.

Speaker and topic TBA

  

Information Protection Seminar,  114 CSRL,  4:30 p.m.

  

Mr. Kevin O'Bryant

Lock Picking

  

Abstract: Most people have 5 keys with them at all times, and it isn't uncommon to see a key ring with more than 20 keys. A key for your front door, your office, your desk, your car, your mailbox, Altgeld Hall, etc. We consent to this nuisance because the locks provide us with a (false) sense of security. I will describe the most common sorts of locks, and how they can be picked, tricked or bypassed.

  

Math - Physics (BCDE) Lunch Seminar,  6-110 Engineering Science Bldg,  12:00 p.m.

  

Professor Sheldon Katz (UIUC)

Geometry of Large N Dualities, I

  

Abstract: The large N limit of certain SU(N) Chern-Simons gauge theories is believed to be dual to a string theory. This series of lectures includes an overview together with connections between these physical theories and a range of areas of mathematics including knot theory, deformation theory of curves on Calabi-Yau threefolds, and the enumerative geometry of holomorphic maps of bordered Riemann surfaces with Lagrangian boundary conditions.

  

Several Complex Variables Seminar,  243 Altgeld Hall,  12:00 p.m.

  

Bernhard Lamel (Doob Research Asst. Prof)

Mapping Problems in Several Complex Variables, I

  

Analytic and Elementary Number Theory,  243 Altgeld Hall,  1:00 p.m.

  

Professor Kevin Ford (UIUC)

The trouble with totients

  

Abstract: One of the most important functions in number theory is Euler's totient function f(n). This talk will be a survey of various known properties of f(n), conjectures and open questions.

  

Group Theory,  347 Altgeld Hall,  1:00 p.m.

  

Professor Derek Robinson (UIUC)

Algorithms for Polycyclic-by-Finite Groups, I

  

Abstract: In this series of talks a survey of known algorithms for PF-groups will be given. Then new algorithms to test surjectivity of derivations will be presented, with application to the problem of deciding of two given subgroups of a PF-group permute.

  

RAP Seminar on noncommutative L_p spaces,  345 Altgeld Hall,  1:00 p.m. (cont. at 3:00 p.m.)

  

Professor Anthony Kye Yew

Introduction to noncommutative L_p spaces with trace, II

  

Abstract: Definition of L_p spaces

  

Algebraic Number Theory,  241 Altgeld Hall,  2:00 p.m.

  

Mr. Bogdan Petrenko

K(a,b) need not equal K(a + b), II

  

Abstract: We investigate this question when K is a finite field and K(a,b) is a finite extension of K. We use Galois theory and group theory.

  

Analysis Seminar,  243 Altgeld Hall,  2:00 p.m.

  

Professor Manfred Denker (IUIC and Göttingen)

Sierpi\`nski gasket as a Martin boundary

  

Abstract: It will be shown that the Sierpi\`nski gasket in any dimension is homeomorphic to the Martin boundary of some canonical Markov chain. If time permits a Laplace operator is introduced on the Sierpi\`nski gasket.

  

Knot Theory RAP,  345 Altgeld Hall,  2:00 p.m.

  

Professor Brinkmann (J. L. Doob Research Assistant Professor)

Introduction to knot theory

  

Commutative Ring Theory Seminar,  243 Altgeld Hall,  3:00 p.m.

  

Sheldon Katz

Moduli of curves and sheaves on Calabi-Yau threefolds, and an application of string theory, http://www.math.uiuc.edu/ ssather/MATH/crt_fa01.html

  

Abstract: The deformation theory of algebraic curves on threefolds has been profitably investigated over the last 20 years. New insight has been obtained recently from string theory. This leads to conjectures about moduli spaces of coherent sheaves on Calabi-Yau threefolds which appear to be amenable to proof.

  

Mathematics Colloquium,  245 Altgeld,  4:00 p.m.

  

Edward G. Effros (Mathematics Department, UCLA)

Some geometrical notions in Banach space theory and their quantum analogues

  

Abstract: A Banach space can always be realized as a linear space of bounded functions. The prototype for a ``quantized Banach space'' is a linear space of bounded operators on a Hilbert space. One of the main objectives of operator space theory is find analogs of Banach space notions. Some of the key invariants are purely geometrical properties of the unit balls, and it has required some ingenuity to find the corresponding ``quantum analogues''. We will illustrate this with a discussion of smoothness and rotundity.

Refreshments at 3:15 pm in Room 321 Altgeld Hall

  

RAP - Conformal invariance, intersection exponents and critical percolation,  145 Altgeld Hall,  4:00 p.m.

Speaker and topic TBA

  

Model Theory Seminar,  141 Altgeld Hall,  4:00 p.m.

  

Professor Lou van den Dries

Problems about addition and divisibility of integers (part II)

Last modified September 4, 2001