Difference between revisions of "NTS/Abstracts/Fall2010"

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| bgcolor="#DDDDDD" align="center"| Title
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| bgcolor="#DDDDDD" align="center"| Volumes of arithmetic line bundles and equidistribution
 
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Abstract.
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In this talk, I will introduce equidistribution of small points in
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algebraic dynamical systems. The result is a corollary of the
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differentiability of volumes of arithmetic line bundles in Arakelov
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geometry. For example, the equidistribution theorem on abelian varieties
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by Szpiro-Ullmo-Zhang is a consequence of the arithmetic Hilbert-Samuel
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formula by Gillet-Soule.
 
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Revision as of 23:25, 9 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.



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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