UIUC Dept. of Mathematics Seminar Calendar

Monday, November 30, 2009

Math 499: Introduction to Graduate Mathematics: A random walk in probability
4:00 pm Monday, November 30, 2009 in 245 Altgeld Hall

Renming Song (Department of Mathematics, University of Illinois)
Abstract: In this talk, I will start with the simple symmetric random walk, go into some important concepts and results in stochastic analysis, like martingales, Brownian motion, stochastic integrals and stochastic differential equations.

Tuesday, December 1, 2009

Analysis Seminar: The best bound of the area-length ratio in Ahlfors' covering surface theory
2:00 pm Tuesday, December 1, 2009 in 241 Altgeld Hall

Guan Yuan Zhang (Tsing Hua University, China)
Abstract: Let $D$ be a closed disk in the complex plane and let $S$ be the unit Riemann sphere. A basic consequence of Ahlfors' theory of covering surfaces is that there exists an absolute constant $h$ such that for any nonconstant holomorphic mapping $f$ from $D$ into $S$, if $f$ does not take the three values $0$, $1$ and infinity, then $A/L < h$, where $A$ is the area of the image of $D$ and $L$ is the length of the image of the boundary of $D$, both counting multiplicities. We will introduce our recent work that give the precise bound of the ratio $A/L$. We indeed develop a new method whose starting points are a classical isoperimetric inequality of unit sphere due to F. Bernstein, a few simple observations, and some new results, such as the Triangle Lifting Lemma, the $4\pi$-Reducing Lemma, and a Theorem for treating non-convex vertices of polygonal boundary value curves of normal mappings defined in our paper.

Wednesday, December 2, 2009

Thursday, December 3, 2009

Analysis Seminar: Linear orthogonality preservers of Hilbert C∗-modules
2:00 pm Thursday, December 3, 2009 in 243 Altgeld Hall

Prof. ChiKeung Ng (Chern Institute of Mathematics, Nankai University, Tianjin, China)
Abstract: Let A be a C*-algebra, and let E and F be Hilbert A-modules with E being full. A linear map T: E -> F is said to be local if T(x)a = 0 whenever xa=0 for x in E and a in A, and T is said to be orthogonality preserving if = 0 whenever = 0 (x,y in E). In this talk, we consider the following question: If T is an orthogonality preserving local linear map, does there exist a central positive multiplier u in M(A) such that < T(x), T(y) > = u < x, y > (x,y in E) ? We show that this question has a positive answer in the following 5 situations: 1. A is a commutative C*-algebra; 2. A is a W*-algebra; 3. A is a standard C*-algebras; 4. A is a unital properly infinite C*-algebra; 5. T is an A-module map (with no assumption on A).

Friday, December 4, 2009

Tuesday, December 8, 2009

Thursday, December 10, 2009