Rice University Math Department Calendar

      March 2013             April 2013              May 2013      
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 31

4:00 pm Tuesday, April 2, 2013
Algebraic Geometry Seminar: The McKay correspondence via tilting
by Morgan Brown (University of Michigan) in HB 227

Let $G$ be a subgroup of $SL_n(\mathbb{C})$. When $n=2$, $\mathbb{C}^n/G$ has a unique minimal resolution, and the classical McKay correspondence relates the representation theory of $G$ with the structure of this resolution. For $n=3$, Bridgeland, King, and Reid used categorical techniques to show that $\mathbb{C}^n/G$ has a distinguished crepant resolution Y=$G$-Hilb. Specifically, they showed that there is an equivalence between the derived categories $D^G(\mathbb{C}^n) and $D(Y)$. I will show how one can use this equivalence to describe the coherent sheaves on $Y$ in terms of $G$-equivariant objects on $X$ by a process called tilting. This is joint work with Ian Shipman. Host Department: Rice University-Mathematics
Submitted by btl1@rice.edu

4:00 pm Thursday, April 4, 2013
Colloquium: Symmetries of the Field of Algebraic Numbers
by Avner Ash (Boston College) in HB 227

One of the central concerns of Algebraic Number Theory is understanding the solution sets to systems of polynomial equations with integer coefficients (Diophantine equations). For example, the equation x^n+y^n=z^n has no solutions in positive integers if n > 2 (Fermat's Last Theorem, or FLT). We gain a lot by first studying single polynomials in one variable, and we do it by looking at the symmetries satisfied by their roots. We then combine this with a study of how polynomials interact with the prime numbers, and we make comparisons wtih data (lists of Hecke operator eigenvalues, one for each prime) coming from various geometric objects. This leads to Reciprocity Laws, of which the first was Quadratic Reciprocity. I will give an introduction to these subjects, explaining how Reciprocity Laws are brought to bear on the study of Diophantine equations. There has been a lot of progress in this area in the last few years, but the best example is still Wiles' proof of FLT.Host Department: Rice University-Mathematics
Submitted by jtanis@rice.edu

4:00 pm Friday, April 5, 2013
Special Lecture : Infinite Determinantal Measures
by Alexander Bufetov (Rice-CNRS-Steklov-IITP-HSE) in HB227

Abstract: Infinite determinantal measures introduced in the talk are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of a determinantal process and a convergent, but not integrable, multiplicative functional. The main result of the talk gives an explicit description for the ergodic decomposition of infinite Pickrell measures on the spaces of infinite complex matrices in terms of infinite determinantal measures obtained by finite-rank perturbations of Bessel point processes. The talk is based on the preprint arXiv:1207.6793.Host Department: Rice University-Mathematics
Submitted by hardt@rice.edu