Events

Eeshan Wagh and Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo

“NIP Theories XV”

We will continue to go through section 2.2 of Pierre Simon’s notes. In particular, we plan on discussing invariant types, definability of types and Morley Sequences, and looking at examples in the O-minimal case.
 

Jason Bell, Department of Pure Mathematics University of Waterloo

“Gromov’s theorem XII: Kleiner’s theorem, continued”

We continue with Kleiner’s proof of Gromov’s thorem.

Vijay Patankar, ISI Chennai

“Intersective polynomials and Diophantine approximation”

We consider Tate cycles on an Abelian variety A defined over a sufficiently large number field K and having complex multiplication. We show that there is an effective bound C = C(A,K) so that to check whether a given cohomology class is a Tate class on A, it suffices to check the action of the Frobenius automorphisms at primes v of K of norm less than C.

Robert Garbary, Pure Mathematics, University of Waterloo

“More on Jac(C)”

I’m going to keep going where David left off, talking about Jac(C) in terms of symmetric powers of C. More precisely, for some large n (large meaning big enough to make the Riemann-Roch theorem have a nice form), we define J to be the set of linear systems of degree n on C. There is a natural fibration from Symn(C) → J, whose fibres are projective spaces.

Robert Garbary, Pure Mathematics, University of Waterloo

“Jac(C) over any (perfect) field”

Let C be a smooth projective curve of genus g ≥ 1. Then the Riemann-Roch theorem says that for any C-divisor D satisfying deg(D) ≥ 2g − 1, we have l(D) = deg(D) + 1 − g. Let N = 2g−1 - we define Jac(C) to be the set of all degree N linear systems on C, which is the same as SynN(C) modulo the relation of linear equivalence.

Saifuddin Syed & Artane Siad, Pure Mathematics Department, University of Waterloo

"The geometry of Yang-Mills fields, Part 06"

"The geometry of Yang-Mills fields, Part 07"

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.
 

Eeshan Wagh and Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo

“NIP Theories XVI”

We will continue to go through section 2.2 of Pierre Simon’s notes. We will finish discussing our characterization of invariant 1-types in O-minimal theories and then discuss products and Morley sequences in O-minimal theories.

Jason Bell, Department of Pure Mathematics, University of Waterloo

“Gromov’s theorem XII: This week it ends!”

We finally finish the proof of Gromov’s theorem.

David Belanger, Cornell University

“Disjunctions in reverse mathematics”

The main question of reverse mathematics is: ”What axioms are needed are needed to prove a given theorem of ordinary math?” Implicit is the assumption that if there is more than one proof, there is a best proof among them using axioms weaker than all the rest.

Blake Madill, Department of Pure Math, University of Waterloo

“The Chebotarev Density Theorem”

In this talk we present a 1922 theorem of Chebotarev in the number field setting. This theorem is a generalization of Dirichlet’s theorem on primes in arithmetic progression and a theorem of Frobenius involving factorization patterns of polynomials with integral coefficients.