Events - February 2018

Matt Satriano, Department of Pure Mathematics, University of Waterloo

"Short Ride in a Height Machine"

This talk is meant to be a quick introduction to the theory of height functions on projective varieties defined over number fields.  After describing the fundamental case of heights on projective space, we go into the basics of Weil's height machine.  For any projective variety, this gives a height function attached to each linear equivalence class of Cartier divisors (or each line bundle), satisfying a variety of pleasant functorial properties.

Boyu Li, Department of Pure Mathematics, University of Waterloo

"Examples of Free Semigroupoid Algebras"

Justin Laverdure, Department of Pure Mathematics, University of Waterloo

"Facts about finite algebras"

If an algebra A is finite, what can we say about the variety HSP(A)? We'll show that such varieties are locally finite, i.e. its members which are finitely generated are in fact finite. Further, if such a variety has any infinite subdirectly irreducible algebras, then in fact it has arbitrarily large finite ones as well.

MC 5479

David Urbanik, Department of Pure Mathematics, University of Waterloo

"Chevalley's Theorem on Constructible Sets in the Language of Schemes"

Matt Satriano, Department of Pure Mathematics, University of Waterloo

"Introduction to the work of Baker and DeMarco"

We give an overview of the following result of Baker--DeMarco: if $\varphi,  \psi \in\mathbb{C}(z)$ have infinitely many preperiodic points in common, then all of their preperiodic points are the same. We discuss the connection between this complex analytic statement and non-archimedean Berkovich spaces.

MC 5403

Sam Kim, Department of Pure Mathematics, University of Waterloo

"On Synchronous Quantum Games"

Christopher Schafhauser, Department of Pure Mathematics, University of Waterloo

"An Embedding Theorem for C*-algebras"

Diana Castaneda Santos, Department of Pure Mathematics, University of Waterloo

"Finite and integral morphisms"

We will continue studying properties of finite and integral morphisms. We will use properties of algebra homomorphisms to prove that finite morphisms have finite fibers and that they are affine local on the target. We will also prove that integral morphisms are closed and we will study some examples. Time permitting we will introduce morphisms (locally) of finite type.

MC 5417

Chris Schafhauser, Department of Pure Mathematics, University of Waterloo

"More on GL_q(2) and SL_q(2)"

Last week Hongdi constructed the Hopf algebra structure on GL_q(2) and SL_q(2).  I will discuss the natural coaction of these objects on the quantum plane k_q(2).

MC 5403

John Sawatzky, Department of Pure Mathematics, University of Waterloo

"Ultraproducts and some loose ends"

We'll complete the metric ultraproduct construction, and show that a sofic group embeds in an ultraproduct of symmetric groups equipped with the Hamming distance. If possible we'll tie up some of the loose ends from last time, e.g. the dependence on that constant r, and residually finite groups.

MC 5403
 

Eli Shamovich, Department of Pure Mathematics, University of Waterloo

"Real Fibered Morphism and Definite Determinantal Representations"