Difference between revisions of "NTS/Abstracts/Fall2010"

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(Jared Weinstein, IAS)
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The family of modular curves X(p^n) provides the geometric link between two types of objects:  On the one hand, 2-dimensional representations of the absolute Galois group of Q_p, and on the other, admissible representations of the group GL_2(Q_p).    This relationship, known as the local Langlands correspondence, is realized in the cohomology of the modular curves.  Unfortunately, the Galois-module structure of the cohomology of X(p^n) is obscured by the fact that integral models have very bad reduction.  In this talk we present a new combinatorial picture of the resolution of
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singularities of the tower of modular curves, and demonstrate how this
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picture encodes some features of the local Langlands correspondence.
 
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== David Zywna, U Penn  ==
 
== David Zywna, U Penn  ==

Revision as of 17:05, 16 September 2010

Jordan Ellenberg, UW Madison

Title: Expander graphs, gonality, and Galois representations

Abstract: TBA



Shuichiro Takeda, Purdue

Title: On the regularized Siegel-Weil formula for the second terms and

non-vanishing of theta lifts from orthogonal groups

Abstract: In this talk, we will discuss (a certain form of) the Siegel-Weil formula for the second terms (the weak second term identity). If time permits, we will give an application of the Siegel-Weil formula to non-vanishing problems of theta lifts. (This is a joint with W. Gan.)


Xinyi Yuan

Volumes of arithmetic line bundles and equidistribution

In this talk, I will introduce equidistribution of small points in algebraic dynamical systems. The result is a corollary of the differentiability of volumes of arithmetic line bundles in Arakelov geometry. For example, the equidistribution theorem on abelian varieties by Szpiro-Ullmo-Zhang is a consequence of the arithmetic Hilbert-Samuel formula by Gillet-Soule.



Jared Weinstein, IAS

Title: Semistable reduction of modular curves

Abstract: The family of modular curves X(p^n) provides the geometric link between two types of objects: On the one hand, 2-dimensional representations of the absolute Galois group of Q_p, and on the other, admissible representations of the group GL_2(Q_p). This relationship, known as the local Langlands correspondence, is realized in the cohomology of the modular curves. Unfortunately, the Galois-module structure of the cohomology of X(p^n) is obscured by the fact that integral models have very bad reduction. In this talk we present a new combinatorial picture of the resolution of singularities of the tower of modular curves, and demonstrate how this picture encodes some features of the local Langlands correspondence.


David Zywna, U Penn

Title

Abstract.


Soroosh Yazdani, UBC and SFU

Title: Local Szpiro Conjecture

Abstract.


Zhiwei Yun, MIT

Title: From automorphic forms to Kloosterman sheaves (joint work with J.Heinloth and B-C.Ngo)

Abstract: Classical Kloosterman sheaves are rank n local systems on the punctured line (over a finite field) which incarnate Kloosterman sums in a geometric way. The arithmetic properties of the Kloosterman sums (such as estimate of absolute values and distribution of angles) can be deduced from geometric properties of these sheaves. In this talk, we will construct generalized Kloosterman local systems with an arbitrary reductive structure group using the geometric Langlands correspondence. They provide new examples of exponential sums with nice arithmetic properties. In particular, we will see exponential sums whose equidistribution laws are controlled by exceptional groups E_7,E_8,F_4 and G_2.



Bryden Cais, UW Madison

Title

Abstract.


David Brown, UW Madison

Title

Abstract.



Jay Pottharst, Boston University

Title: Iwasawa theory at nonordinary primes

Abstract.


Alex Paulin, Berkeley

Title

Abstract.



Samit Dasgupta, UC Santa Cruz

Title

Abstract.



David Geraghty, Princeton and IAS

Title

Abstract.


Toby Gee, Northwestern

Title

Abstract.




Organizer contact information

David Brown:

Bryden Cais:



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