## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

**University COVID-19 update:** visit our Coronavirus Information website for more information.

Please note: The University of Waterloo is closed for all events until further notice.

Thursday, May 30, 2013 — 2:30 PM EDT

I am going to establish some results concerning rational maps into abelian varieties. In no particular order, these are the following results:

1) Any rational map from a smooth variety to an abelian variety is in fact a morphism 2) Any rational map from An or Pn to an abelian variety is constant 3) Birationally equivalent abelian varieties are isomorphic (as abelian varieties).

Wednesday, May 29, 2013 — 2:30 PM EDT

Joint with Mikhail Gavrilovich, Sergei Nikolenko and Alexander Luzgarev. New generation proofs of normal subgroup structure, commutator formulae, and the like, over an ARBITRARY commutative ring are given, based on the study of minimal modules of exceptional groups.

Tuesday, May 28, 2013 — 10:30 PM EDT

Tuesday, May 28, 2013 — 1:00 PM EDT

Pure Mathematics Department, University of Waterloo

Throughout the spring 2013 term, we will (as a group) be reading through and lecturing on ”The Geometry of Yang-Mills Fields” by Sir Michael Atiyah. All are welcome to attend.

Friday, May 24, 2013 — 3:30 PM EDT

In January, 1967, the oversized Department of Mathematics in

the Faculty of Arts started a new life, as the Faculty of Mathematics,

complete with its now famous five departments of mathematics. The

1960s was an exceptionally glorious time for academic

institutions---there was nothing like it before, and nothing like it

Thursday, May 23, 2013 — 2:30 PM EDT

Last time we discussed our algebraic analogue of compactness. More precisely, a variety V over a field k is said to be complete (over k) if for all varieties W over k, the map V ×W → W is closed.

Thursday, May 23, 2013 — 1:30 PM EDT

Many objects in number theory and related areas are associated to L-functions. Examples include algebraic varieties, automorphic representations, Galois representations, and modular forms. I will discuss what L-functions can tell us about other objects, and what those objects can tell us about L-functions.

Wednesday, May 22, 2013 — 2:30 PM EDT

In an abstract group, an element of the commutator subgroup is not necessarily a commutator. However, the famous Ore conjecture, recently completely settled by Ellers—Gordeev and by Liebeck—O’Brien—Shalev—Tiep, asserts that any element of a finite simple group is a single commutator.

Tuesday, May 21, 2013 — 1:00 PM to 4:00 PM EDT

Throughout the spring 2013 term, we will (as a group) be reading through and lecturing on ”The Geometry of Yang-Mills Fields” by Sir Michael Atiyah. All are welcome to attend.

Thursday, May 16, 2013 — 3:30 PM EDT

Abstract: TBA

Thursday, May 16, 2013 — 3:30 PM EDT

Thursday, May 16, 2013 — 2:00 PM EDT

Abelian varieties are the algebraic equivalent of compact lie groups - they are complete (=compact) varieties with morphisms turning them into groups. Besides being interesting in their own right, they have played a major role in number theory and the theory of curves in the last 75 years.

Wednesday, May 15, 2013 — 2:30 PM EDT

We finish the proof that groups of invertible matrices with the property that all of the eigenvalues of each element are roots of unity.

Tuesday, May 14, 2013 — 1:00 PM to 4:00 PM EDT

Pure Mathematics Department, University of Waterloo

Throughout the spring 2013 term, we will (as a group) be reading through and lecturing on ”The Geometry of Yang-Mills Fields” by Sir Michael Atiyah. All are welcome to attend.

Monday, May 13, 2013 — 11:30 AM EDT

A great deal is known about the Pisot-Vijayaraghavan (P.V.) numbers. However, less is known about the set of Salem numbers. The main

result in this area, due to Salem, is that each P.V. number is a limit

point of the set of Salem numbers. The smallest known P.V. number is

approximately $\theta_0=1.3247$. Any interval $(0,a)$, $a\geq\theta_0,$ contains infinitely many Salem numbers. Therefore it is reasonable to be interested in small Salem numbers.

Wednesday, May 8, 2013 — 2:30 PM EDT

This week we look at groups of matrices with the property that all of the eigenvalues of each element are roots of unity. Modifying an argument due to Burnside and Schur, we show that all such groups have the property that they have a normal solvable subgroup of finite index.

Tuesday, May 7, 2013 — 3:00 PM EDT

I will continue my aside on full versus emptyset-induced structure and the connection with stable embedability and weak stable embedability. I will then continue with section 3.2 of Simon’s notes.

Monday, May 6, 2013 — 11:30 AM EDT

Given a sequence of natural numbers ω, we define rn(ω) = |{(a, b) : a+b = n, a < b, and a, b ∈ ω}|. In this talk, we present the proof that there exists a sequence ω such that log n ≪ rn(ω) ≪ log n.

Wednesday, May 1, 2013 — 2:30 PM EDT

Yangians were originally introduced by Drinfeld in the 1980's to

quantize current Lie algebras. In geometric representation theory

subquotients of Yangians arise as quantizations of symplectic leaves of

the affine grassmannian. We will discuss ongoing work with Kamnitzer,

Webster, and Weekes to study categories of representations of these

subquotients. We will begin by explaining the construction of these

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1