UIUC Dept. of Mathematics Seminar Calendar

    September 2010          October 2010          November 2010    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
           1  2  3  4                   1  2       1  2  3  4  5  6
  5  6  7  8  9 10 11    3  4  5  6  7  8  9    7  8  9 10 11 12 13
 12 13 14 15 16 17 18   10 11 12 13 14 15 16   14 15 16 17 18 19 20
 19 20 21 22 23 24 25   17 18 19 20 21 22 23   21 22 23 24 25 26 27
 26 27 28 29 30         24 25 26 27 28 29 30   28 29 30            
                        31

Thursday, October 14, 2010

Number Theory
1:00 pm in 241 Altgeld Hall, Thursday, October 14, 2010

Del

Edit

Copy

Submitted by berndt.

Kagan Kursungoz (Pennsylvania State University)
A Generalization of Algorithm-Z with an Application
Abstract: We will review algorithm-Z, and show how it is used in proving the q-binomial theorem bijectively. Then we will describe a generalization with one additional parameter, and show how this is used in proving the q-Gauss summation formula bijectively. If time allows, we will give a small open problem, and discuss possibilities for future research. This is joint work with Ae Ja Yee.

Special Algebraic Geometry Seminar
2:00 pm in 447 Altgeld, Thursday, October 14, 2010

Del

Edit

Copy

Submitted by nevins.

Ian Shipman (University of Chicago)
A Geometric Implementation of Orlov's Theorem
Abstract: Consider a smooth Calabi-Yau hypersurface X in P^{N-1} defined by homogeneous equation W. A celebrated result of D. Orlov states that the derived bounded category of coherent sheaves on X is triangulated-equivalent to the homotopy category of graded matrix factorizations of W over C[x_1 , . . . , x_N ]. In this talk I will define the category of matrix factorizations and explain how to realize this equivalence using functors and categories that are sheaf-theoretical and avoids direct mention of the category of singularities. To accomplish this, we work with matrix factorizations over non-affine schemes in the framework of E. Segal. We confirm Knorrer periodicity and localization on the critical set of the potential and use these to get links in a chain of equivalences. Then we use Segal’s result relating matrix factorizations over inverse GIT quotients of an affine space to complete the chain of equivalences.

Differential Geometry Seminar
3:00 pm in 347 Altgeld Hall, Thursday, October 14, 2010

Del

Edit

Copy

Submitted by clein.

Gabriele La Nave (UIUC Math)
Finite time singularities of the Kahler-Ricci flow and symplectic reductions.
Abstract: In the last few years, the Ricci flow has been used extensively (by Hamilton, Perelman et al.) as a powerful tool in the Geometric and Topological study of compact three-manifolds. The Ricci flow has been recently applied to study the geometry of compact Kaehler manifolds of arbitrary dimension in a manner that encompasses and geometrizes the Minimal Model Program of Birational Geometry. The major stumbling block for such a program is the formation of finite time singularities. In recent work with G. Tian, we propose a link between the Kaehler-Ricci flow and a new static equation of (degenerate) elliptic type on a manifold endowed with a holomorphically hamiltonian S^1-action. We then describe the singularity formation and the surgery necessary to bypass such singularities in one stroke as a variation of symplectic quotients. I will discuss the construction and some of the analysis that is behind solving the relevant equations.