We are proud to report that Jiahua Liu has been selected to receive the International Studies Office Award for international undergraduate student academic excellence. He will be honored at the awards ceremony for graduating international students and their families this May. Congratulations, Jiahua Liu!

The 2016 Putnam Award Winners include Sifan Ye, Juan Velasco, and Arun Kannan. Congratulations to all three on this impressive accomplishment!

The award announcements at the Gordon E. Keller Mathematics Majors Dinner revealed this year's recipient of the E.J. McShane Prize in Mathematics to be Alexander Grieser. Congratualtions to Alexander on this accomplishment!

Congratulations to Ben Webster! He is one of two 2016 recipients of the prestigious Cory Family Teaching Awards, and joins David Sherman (2013) among the award recipients from the Mathematics department. The Cory Family Teaching Awards are "designed to reward and incentivize excellence in teaching among junior faculty." Since 2013 and continuing through 2017, two junior faculty members are chosen as recipients and honored at Fall Convocation. Each recipient is awarded $25,000 thanks to the generosity of Mr. and Mrs. Charles R. Cory. Well done, Ben!

One of the central problems in solid state physics consists of finding

effective models which describe the dynamics of electrons in periodic

potentials. Exponentially localized Wannier functions, if they exist,

enable us to replace the periodic and unbounded Schroedinger operator

with a discrete Jacobi-type infinite matrix.

We shall consider a real analytic and time reversal symmetric family of

Bloch projections of rank N and construct an orthonormal basis for its

range, which is both real analytic and periodic with respect to its

d-dimensional quasi-momenta when $1\leq d\leq 3$ and $N\geq 1$. We will

also show what can go wrong in dimensions higher than three, and make

the connection with topological degree theory.

This lecture is intended to anyone who has a basic knowledge of

functional analysis and a minimal interest in the rigorous mathematical

description of solid state physics. Following the first lecture would

help a lot.

We shall review the Bloch-Floquet-Gelfand-Zak transform for discrete

periodic Schroedinger operators and show how their spectral projections

generate Bloch bundles. Knowledge of the Fourier inversion theorem is

the only needed background.

We continue with reviewing the 'adiabatic' parallel transport and use it

to construct locally smooth orthonormal bases of the tangent bundle of a

smooth manifold. This will lead to an elementary proof of the Hairy Ball

Theorem for the two-sphere. The methods used here are quite simple but

very useful for understanding the nature of various topological

obstructions in other more complicated situations.

At the Gordon E. Keller mathematics majors dinner, it was announced that Peter Dillery was the 2016 recipient of the Edwin E. Floyd Prize in Mathematics. Congratualtions to Peter on his accomplishment!

**Tuesday, April 12, 2015**

The Gordon E. Keller Mathematics Majors Dinner will be held on Tuesday, April 12th, 2016 at the Courtyard- Marriott located on Main Street.

This Dinner was conceived and organized by a former major advisor, Professor Gordon Keller, as a way of expressing the department’s appreciation for you. It is a great opportunity for all of you to connect with the faculty and other math majors in a relaxed and lighthearted environment.

In addition to a delicious dinner, there will be an awards presentation and a talk by Dr. Berrien Moore III, who holds a PhD in Mathematics from our own department. He is currently the Dean of the College of Atmospheric and Geographical Sciences at the University of Oklahoma, as well as the Vice President of Weather and Climate Programs and the Director of the National Weather Center. Additionally, he holds the position of Chesapeake Energy Corporation Chair in Climate Studies. His talk is entitled *From S*TS=T to CO2 and Climate; An Improbable Journey.*

Congratulations to the following mathematics majors who were elected to the Beta Chapter of Virginia of Phi Beta Kappa this week:

Peter Dillery

Ji Won Kim

Honglei Li

Hexuan Liu

Megan Marcellin

Qi Tang

Yingze Song

Boya Yang

Stephanie Gulley

Carrie Douglass, President of the Beta Chapter of Virginia of Phi Beta Kappa, explains the significance of this accomplishment:

"As the oldest and most distinguished honor society in the country, Phi Beta Kappa offers membership to less than one percent of all undergraduates. Many of the leading figures in American history and culture have begun their careers with election to the society, including seventeen presidents of the United States. As a result, membership is a remarkable accomplishment, both for the student who achieves it and the faculty and staff whose support and guidance has led to this milestone."

**Karen Smith (University of Michigan) **

*Algebra, Geometry and Analysis over Finite Fields*

**Lecture 1:** Monday, February 29th, 2016

Time: 5:00PM-6:00PM

Location: Clark 108

Abstract: In this lecture, we review how Noether's introduction of the concept of an abstract ring changed the course of mathematics in the twentieth century by enabling us to apply the methods of "reduction modulo p" to solve problems in algebraic geometry. Specifically, I'll discuss how understanding solutions to polynomials over finite fields can help understand the geometry of geometric objects (called varieties) defined by real or complex polynomials. Miraculously, rings of characteristic p have some very special properties that can be powerful tools in analyzing them, often replacing tools like integration for real manifolds.

**Lecture 2: **Tuesday, March 1st, 2016

Time: 5:00PM-6:00PM

Location: Clark 108

Abstract: In the second lecture, we review Hironaka's famous theorem on the resolution of singularities of a complex algebraic variety. We show this theorem can help us understand and measure the singularities of complex varieties. Amazingly, it turns out that the only algebraic characterization of a geometric condition called "rational singularities" involves reduction to characteristic p. Specifically, we will see how algebraic tools such as Frobenius splitting impact different areas of math, including the minimal model program for complex algebraic varieties and cluster algebras in combinatorics/representation theory.

**Lecture 3**: Wednesday, March 2nd, 2016

Time: 3:30-4:30

Location: Physics 203

Abstract: In the final lecture, we discuss a numerical invariant of singularities called the analytic index of singularities, which is defined by the convergence of a certain integral. Amazingly, this invariant turns out to have a prime characteristic description as well, as the limit, over all primes p, of another invariant called the F-pure threshold. The study of these F-pure thresholds leads to some very interesting and mysterious fractal like behavior.