Seminar on Geometry and Arithmetic, Fall 2007

Friday afternoons in South Hall, Room 6635 (usually!)

Organisers: A. Agboola, P. Cascini, D. Morrison

 
October 5, 2007, 1:30pm--3:30pm 
Organisational meeting


Abstract: None

October 12, 2007, 1:30pm-3:30pm 
Bisi Agboola, UCSB

$p$-adic L-functions of CM elliptic curves

Abstract: I shall discuss special values of the Katz two-variable p-adic L-function. This will be a warmup for the next speaker.

MONDAY, October 15, 2007, 1:30pm-3:30pm 
NOTE UNUSUAL DAY!!!!
Henri Darmon, McGill

Rational points on CM elliptic curves and the Katz p-adic L-function: a geometric approach to a formula of Rubin.

Abstract:This is a report on an ongoing joint project with Massimo Bertolini and Kartik Prasanna.

October 19, 2007, 1:30pm--3:30pm 
No Meeting


Abstract:

October 26, 2007, 1:30--3:30pm 
Paolo Cascini, UCSB

Rational Points on Algebraic Varieties: Campana's Program I

Abstract: A classical problem in mathematics is the study of the rational solutions of a Diophantine problem, i.e. a finite system of polynomial equations with integral coefficients. In particular, one might ask when the number of these solutions is infinite. At least conjecturally, the answer to these questions is closely related to the geometry of the varieties defined by such polynomials. Campana's program is a new method to approach these problems. This talk will be accessible to a general audience and no prior knowledge of the subjects involved is required.

November 2, 2007, 1:30pm--3:30pm 
No meeting


Abstract:

November 9, 2007 
Paolo Cascini, UCSB

Rational Points on Algebraic Varieties: Campana's Program II

Abstract: A classical problem in mathematics is the study of the rational solutions of a Diophantine problem, i.e. a finite system of polynomial equations with integral coefficients. In particular, one might ask when the number of these solutions is infinite. At least conjecturally, the answer to these questions is closely related to the geometry of the varieties defined by such polynomials. Campana's program is a new method to approach these problems. This talk will be accessible to a general audience and no prior knowledge of the subjects involved is required.

TUESDAY, November 13, 2007, 11am-1pm 
Michael McQuillan, University of Glasgow

Old and New Methods in Function Field Arithmetic

Abstract: None

November 23, 2007 
Thanksgiving Holiday
November 30, 2007, 1:30pm-3;30pm 
Bisi Agboola, UCSB

Rational Points on Algebraic Varieties: Vojta's Conjectures

Abstract: I shall discuss certain conjectures of Paul Vojta concerning rational points on algebraic varieties.

December 7, 2007 
TBA

TBA

Abstract:


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