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Events - May 2013

Thursday, May 30, 2013 — 2:30 PM EDT

Robert Garbary, Pure Mathematics University of Waterloo

“Rational Maps”

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

Nikolai Vavilov, St. Petersburg

“Structure of Chevalley groups: the proof from the book”

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

Thai Hoang Le, University of Texas at Austin

“Intersective polynomials and Diophantine approximation”

Tuesday, May 28, 2013 — 1:00 PM EDT

Pure Mathematics Department, University of Waterloo

Tyrone Ghaswala

“The geometry of Yang-Mills fields, Part 03”

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

Stanley Burris, Pure Math Department, University of Waterloo

"Early Days in the Faculty of Mathematics"

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

Richard Garbary, Pure Mathematics, University of Waterloo

“More about completeness”

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

David Farmer, American Institute of Mathematics

“L-functions: finding, calculating, and using them”

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

Nikolai Vavilov, St. Petersburg

“The Yoga of Commutators (joint work with Roozbeh Hazrat, Alexei Stepanov and Zuhong Zhang)”

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

Artane Siad

“The geometry of Yang-Mills fields, Part 02”

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

Richard Wentworth, University of Maryland

"The Yang-Mills flow on Kaehler manifolds"

Abstract: TBA

Thursday, May 16, 2013 — 3:30 PM EDT

Daniel Pareja, Pure Mathematics, University of Waterloo

"Friable Numbers"

Thursday, May 16, 2013 — 2:00 PM EDT

Robert Garbary, Pure Mathematics University of Waterloo

“Roadmap and the basics”

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

Jason Bell, Pure Mathematics, University of Waterloo

"Gromov's theorem IX: solvable linear groups, continued"

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

Matthew Beckett

“The geometry of Yang-Mills fields, Part 01”

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

Blake Madill, Pure Mathematics, University of Waterloo

"Small Salem Numbers"

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

Jason Bell, Department of Pure Mathematics, University of Waterloo

“Gromov’s Theorem VIII: solvable linear groups”

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

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

“NIP Theories XI”

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

Shuntario Yamagishi, Pure Mathematics Department, University of Waterloo

“Sidon Problem”

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

Oded Yacobi, University of Toronto

Subquotients of Yangians and categorical representation theory

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

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