# Graduate Colloquium Fall 2013

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**

**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.

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