Graduate Colloquium Fall 2013

Thursday - 4:00 p.m.
McHenry Building - Room 4130
Refreshments served at 3:30 in room 4161
For further information, please contact Wei Yuan

Thursday October 3, 2013

Conformal Geometry of Submanifold

Jingyang Zhong, Department of Mathematics, UC Santa Cruz

In this talk we are interested in establishing a fundamental theorem for surfaces in conformal 3-sphere and conformal 3-manifolds in general. To do so we regard 3-sphere is the projectivized positive light cone in Minkowski space-time of 5 dimension and, in the same spirit, as the conformal infinity of hyperbolic 4-space. We construct corresponding surfaces in Minkowski space-time as well as in hyperbolic 4-space and apply fundamental theorem for surfaces in (pseudo)-Riemannian geometry.

Thursday October 10, 2013

Shintani’s Theorem and its Applications

Alex Beloi, Department of Mathematics, UC Santa Cruz

We'll discuss some of the work of Takuro Shintani as a generalization of Dirichlet's unit theorem and Shintani's 'geometry of numbers' style approach to computing the value of partial zeta functions at s=1.

Thursday October 24, 2013

Blow-up Theory for Some Yamabe Type Equations on Riemannian Manifolds

Fang Yi, University of Science and Technology of China

In this talk, we will mainly introduce the blow-up analysis technique for the Yamabe type equations on compact Riemannian manifolds without boundary. Furthermore, we will apply this technique to some Yamabe type equations with certain boundary conditions and the fractional Yamabe type equations.

Thursday October 31, 2013

Introduction to the Sato-Tate Conjecture

Mitchell Owen [UCSC]

I will begin by introducing the Sato-Tate conjecture as a numerical coincidence using only polynomials and modular arithmetic, then demonstrate how the structure of elliptic curves gives these coincidences significance, building up to the connections to modular Galois Representations.