Max Newman Topology

  

345 Altgeld, 11:00 a.m.

Organizational meeting

RAP ``Spaces of non-positive curvature''

  

243 Altgeld Hall, 11:00 a.m.

Ilya Kapovich

Review of the material from the last semester

Abstract: We will review the material covered during the last semester and discuss future topics. New participants are welcome!

  

Analytic and Elementary Number Theory

  

243 Altgeld Hall, 1:00 p.m.

Professor Bruce Berndt

A broad survey of the work of Srinivasa Ramanujan

  

  

Logic Seminar

  

345 Altgeld Hall, 1:00 p.m.

Professor Yevgeniy Vasilyev

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 w. We use generic pairs to study the geometric properties of supersimple SU-rank 1 structures, in particular the properties of linearity and pseudolinearity.

  

Stochastic and Nonlinear Analysis

  

347 Altgeld Hall, 2:00 p.m.

Professor Bob Jerrard

Conservative vortex filament dynamics

  

  

Geometric Potpourri Seminar

  

243 Altgeld Hall, 2:00 p.m.

John E. Wetzel (UIUC)

Triangles and Squares

  

  

Commutative Ring Theory RAP

  

243 Altgeld Hall, 3:00 p.m.

Per Jensen

Local Computations on the Grassmannian

  

  

Graph Theory and Combinatorics

  

241 Altgeld Hall, 3:00 p.m.

Zoltan Furedi

Triangle-free triple systems

  

  

The classical extremal function \roman ex(n,H) is the maximum number of edges in a k-uniform hypergraph with n vertices that does not contain a configuration isomorphic to H. In 1974, Bollobás proved that \roman ex(n,BC) = n₀n₁n₂, where n_i = ë(n+i)/3 û. This means that every triple system with more than n³/27 edges contains a copy of B or C.

Here we review all 16 possibilities for avoiding triangles. For example, we show that for a completely triangle-free system \roman ex(n,ABCD) = ën²/8û and that \roman ex(n,CD) = ë(n-1)²/4û (for sufficiently large n). (This is joint work with G. Simonyi.)

Information Protection Seminar

  

114 CSRL, 4:30 p.m.

Organizational meeting

Analytic and Elementary Number Theory

  

243 Altgeld Hall, 1:00 p.m.

Professor Alex Zaharescu

The distribution of Farey fractions (survey talk)

  

  

Group Theory/Knot Theory RAP

  

347 Altgeld Hall, 1:00 p.m.

Organizational meeting

K Diagram groups

  

  

Several Complex Variables Seminar

  

241 Altgeld Hall, 1:00 p.m.

Professor John P. D'Angelo

Remarks on the seminar, and some accessible open problems in several complex variables

  

  

RAP Seminar on noncommutative L_p spaces

  

345 Altgeld Hall, 1:00 p.m. (cont. 3:00 p.m.)

Anthony Kye YewIntroduction to noncommutative L_p spaces with trace, I

Abstract: We introduce the space of measurable operators affiliated with a von Neumann trace.

  

Algebraic Number Theory

  

241 Altgeld Hall, 2:00 p.m.

Bogdan Petrenko

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

  

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.

Karen Shuman

Cyclic functions in L^p(R), 1 £ p < ¥

Abstract: We examine conditions under which translates of a Schwartz-class function span L^p(R) for certain values of p and not for others. Joint work with Prof. Rosenblatt.

  

Commutative Ring Theory RAP

  

243 Altgeld Hall, 3:00 p.m.

Per Jensen

Local Computations on the Grassmannian

  

  

Mathematics Colloquium

  

245 Altgeld, 4:00 p.m.

Igor Mineyev (University of South Alabama, Mobile)

Amenable groups, hyperbolic groups, and Baum-Connes conjecture

Abstract: B.E.Johnson introduced the bounded cohomology of groups (though the term "bounded cohomology" came later) and characterized the amenable groups by vanishing of bounded cohomology. We present the following characterization of Gromov hyperbolic groups by bounded cohomology: a finitely presented group G is hyperbolic if and only if all 2-dimensional cohomology classes of G are bounded for all coefficients. This boundedness of cocycles for hyperbolic groups (for real coefficients) was claimed by Gromov and was used by Connes and Moscovici to prove the Novikov conjecture for hyperbolic groups.

Our characterization of hyperbolic groups resembles Johnson's characterization of amenable groups, though the proof is of course completely different. The main step in the proof is a combinatorial version of straightening that works for any hyperbolic group. Another application of similar combinatorial techniques is constructing a nice metric on any hyperbolic group that allows us to prove the Baum-Connes conjecture for hyperbolic groups (this result is a joint work with Guoliang Yu). In particular, this implies the Kadison-Kaplansky conjecture for torsion-free hyperbolic groups.

  

Refreshments at 3:15 pm in Room 321 Altgeld Hall