Events

Peter Sinclair, University of Waterloo

"Pre-Smoothness - Part II"

In this talk, we will introduce a broader definition of
pre-smoothness for general constructible sets, and discuss some
properties of pre-smooth sets. Time permitting, we will also look at
the specific case when the pre-smooth set is an algebraic curve.

Benoit Charbonneau & Ren Zhu, Pure Mathematics, University of Waterloo

Omar Leon Sanchez, Department of Pure Mathematics, University of Waterloo

“Morphisms between spectrums.”

We will see why a ring homomorphism A → B naturally induces a morphism (SpecB,OB) → (Spec A, OA) and why the converse is also true.

Shanta Laishram Indian Statistical Institute (ISI)

“Baker’s Explicit ABC-Conjecture and Applications”

The conjecture of Masser-Oesterl ́e, popularly known as abc-conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures. This is a joint work with T. N. Shorey.

Xiaomei Zhao, Pure Mathematics Department, University of Waterloo

"New strategies for minor arc estimates: Part I"

We have seen the outline of the circle method in Waring's
problem from Shuntaro's talks, where the minor arc contribution was
established by combining Weyl's inequality with Hua's lemma. In my two
talks, we will continue to see some improvements on minor arc estimates.

Peter Sinclair, Pure Mathematics Department, University of Waterloo

"Universal Specializations and Elementary Extensions"

Abstract: We will begin this talk by introducing universal
specializations (section 2.2.1 in Zilber), which are specializations
that behave very nicely when extended further. We will then discuss
irreducible coverings (section 3.5.2), and begin to show that an

Spiro Karigiannis, Pure Mathematics Department, University of Waterloo will speak on:

Talk #1: Special types of Hermitian connections, Part I."

Abstract: I will discuss natural classes of connections on almost Hermitian manifolds, including the Bismut connection. I will be following closely the hard-to-find paper by Paul Gauduchon entitled "Hermitian Connections and Dirac Operators".

Carrie Knolls, Pure Mathematics Department, University of Waterloo

"Back and forth relations - Part II"

We will prove that, for all countable ordinals β, there is a natural connection between the back-and-forth relation ≤β and the Πβ and Σβ formulas. This result suggests that, in general, it is difficult to “compute” the relations ≤β. For practical purposes, we would like to consider structures where the back-and-forth relations are c.e.

David McKinnon, Pure Mathematics Department, University of Waterloo

"Proj, coherent sheaves, and O(1)"

Abstract: Proj, coherence, and O(1) are all scary things in Hartshorne section II.5.  I’ll do my best to explain them, and make them seem less scary.