# Graduate Colloquium Fall 2014

McHenry Building - Room 4130

Refreshments served at 3:30 in room 4161

For further information, please contact Wei Yuan or call 831-459-2969

**Thursday October 2, 2014 TBA**

**Thursday October 2, 2014 TBA**

**Thursday October 9, 2014**

**"Deformations of Q-Curvature."**

**Wei Yuan, University of California, Santa Cruz**

Q-curvature, first was introduced as an analogue of Gaussian curvature for 4-dimensional Riemannian manifolds, is one of the most fundamental quantity in the study of conformal geometry. In this talk, I will introduce a different approach, a more Riemannian approach, to study the Q-curvature, which was inspired by some of my recently joint research work with Professor Jie Qing on scalar curvature. With this approach, I will define a new category of Riemannian manifolds and use it to study Q-curvature systematically. This is a joint work with Dr. Yi Fang from University of Science and Technology of China and Dr. Yueh-Ju Lin from University of Michigan, Ann Arbor.

**Thursday October 16, 2014** **TBA**

**Thursday October 23, 2014**In this talk I want to explain some of the main ideas in the proof of FLT by Wiles. This will be a talk for a general math audience and I'll try to assume very little, giving intuitive descriptions of all objects and techniques involved. Some of the main goals will be to explain using very basic ideas what are elliptic curves and their moduli spaces, the so-called modular curves, and describe the concept of modularity.

*"Fermat's Last Theorem"*Gabriel Martins,

**University of California, Santa Cruz**

**Thursday October 30, 2014 TBA**

**Thursday November 6, 2014 **Many people believe that a degree in mathematics can lead only to a career as a teacher or as an academic researcher. That is not the case, especially as computer technology gets increasingly sophisticated -- having a career as a mathematician in a computer industry is becoming more common as more jobs are created which demand minds geared toward technical mathematical analysis of problems.

*"Mathematizing in Industry"*Victor Dods, Mathematician at Leap Motion

The crucial bridge between worlds of abstract mathematics and industry/application is communicating with computers via programming languages. In this talk, I will discuss the details of this bridge and motivate crossing it for all mathematicians -- those in industry, in academia, as well as amateurs. I will discuss some of my work at my current job at Leap Motion, as well as other experiences in industry.

**Thursday November 13, 2014 TBA**

**Thursday November 20, 2014 No Colloquium**

**Thursday November 27, 2014** *No Colloquium* - THANKSGIVING HOLIDAY

**Thursday December 4, 2014** **TBA**

**Thursday December 11, 2014** In this talk, I will define and discuss several rings that are used for studying the representations of a fixed finite group. In each of these representation rings, there is a sense of duality, and so we can consider the situation in which the inverse of a unit is the unit's dual element. These so-called orthogonal units form a subgroup of the full unit group. I will discuss some properties of these orthogonal unit groups and ways we can go about studying them.

*"Representation Rings and Orthogonal Units"*Rob Carman, University of California, Santa Cruz