# News

### James Arthur (University of Toronto): November 14th-16th, 2016

Monday, November 14, 2016

Lecture 1:  L-functions and Number Theory, November 14, 2016, room and time: TBA

Lecture 2:  The Trace Formula and Automorphic Forms, November 15, 2016, room and time: TBA

Lecture 3:  Beyond Endoscopy and Functoriality, November 16, 2016, room and time: TBA

Abstract:  Number theory is founded on the basic properties of integers and prime numbers. But its study these days is increasingly leading us to the far reaches of some of the most diverse and powerful areas of mathematics. Nowhere is this more apparent than in the Langlands program, which represents a profound unifying force for mathematics.

We shall try to introduce the Langlands program through the theory of L-functions. These are infinite series that look like the famous Riemann zeta function, except that they have nontrivial coefficients. The information that goes into the coefficients is in fact very interesting, and gives an elegant way of organizing fundamental data from number theory, representation theory and algebraic geometry. The Langlands program postulates deep relationships among different L-functions, and hence also the data in their coefficients.

We shall discuss these matters, and explain how they are part of the theory of automorphic forms. We shall then describe the trace formula, which has led to important results in the classification of automorphic representations. If time permits, we shall also say something about Beyond Endoscopy, a proposal by Langlands for attacking the central conjecture of the subject known as the Principle of Functoriality.

### Eugene C. Paige, Jr. 1929-2016

Thursday, June 30, 2016

Tuesday, May 31, 2016

We are happy to announce that the department of mathematics' Outstanding Graduate Teaching Assistant award for 2015-16 has been awarded to Xiang Wan. As winner of the departmental award, Xiang was nominated to compete for a University-wide award, and was selected as one of the top 15 of a very accomplished group of teachers. He was presented with a Jefferson Cup in honor of his achievement.

The department also recognizes two graduate teaching assistants with Honorable Mentions for our teaching award: they are Peter Bonventre and Jonathan Simone. All three of these outstanding GTAs will receive recognition and a cash prize at this year’s graduation ceremony.

Congratulations to Xiang, Peter, and Jon!

### Final Exercises Ceremony for the College and Graduate School of Arts and Sciences

Saturday, May 21, 2016

In 2016, the Final Exercises ceremony for the College and Graduate School of Arts & Sciences will be on Saturday, May 21 with the department graduation ceremonies following that afternoon.  The fair-, inclement-, and severe-weather ceremony sites for Mathematics will be:

Fair Weather:  Finals on the Lawn, fair-weather sites for department graduation ceremonies
Pavilion I Lower Garden
Ceremony Start Time: 12:15 p.m.

Inclement Weather:  Finals on the Lawn, all department ceremonies inside
Gilmer Hall Room 130
Ceremony Start Time: 12:45 p.m.

Severe Weather:   Finals in John Paul Jones Arena, all department ceremonies inside
Gilmer Hall Room 130
Ceremony Start Time: 12:45 p.m.

*Please note that Gilmer Hall Room 130 is a Remote Viewing Location for Finals on the Lawn.  We anticipate that the remote viewing will conclude prior to 12 p.m.

Under the severe-weather plan, ALL degree candidates (undergraduate and graduate) will participate in the ceremony at John Paul Jones Arena.  Each graduating student will receive six guest seating tickets for the Lawn.  Since we cannot accommodate as many people in the arena compared to the Lawn, graduates will be restricted to three guests if the ceremony is moved inside.  Tickets are required for all guests either on the Lawn or at the arena.  Guests without tickets can watch a live broadcast of the ceremony at one of the remote viewing locations across Grounds.

### Horia Cornean: Wannier functions, Bloch bundles and topological degree theory, part II

Friday, April 15, 2016

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.