Events

Matt Satriano (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501

Fateme Peimany, University of Waterloo

DCCM: the differential expansion of CCM

We introduce the theory of compact complex spaces called CCM and expand it to DCCM, the theory of differentially closed CCM-structures. Finally, we will explain the good model-theoretic properties of DCCM and open problems in this theory.

MC 5403

Boris Li, University of Waterloo

Filtered Deformations of Trivariate Polynomial Rings

Among non-commutative rings, those satisfying a polynomial identity (PI) are especially well-behaved. They share many properties with commutative rings, which we understand well. Etingof asked whether every filtered deformation of a finitely generated commutative domain, over an algebraically closed field of positive characteristic, is PI. In this talk, we will answer this question of Etingof affirmatively for deformations of polynomial rings in three variables. In the pre-seminar, I will define and discuss the properties of filtered deformations

MC 5403

Jerry Wang (University of Waterloo)

Julius Frizzell (University of Waterloo)

Lehmer's Conjecture and Related Problems

The Mahler measure of a polynomial is the product of the moduli of it's roots lying outside the unit disk. Lehmer's conjecture says that, among polynomials with integer coefficients that are not cyclotomic, there exists a polynomial with minimal Mahler measure. We will discuss the history and original motivation behind Lehmer's problem and the known partial results. We will also look at other problems related to Mahler measure, such as questions arising from looking at the divisors of Newman polynomials.

MC 5479

Wentang Kuo (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501

Rahim Moosa (University of Waterloo)

Around the wild automorphism conjecture

The wild automorphism conjecture, of Reichstein, Rogalski, and Zhang from 2006, proposes that if a projective algebraic variety X (in characteristic zero) admits an automorphism that leaves no proper subvariety invariant then X is an abelian variety. I will discuss recent work with Jason Bell where we use tools from the model theory of difference fields (developed last year by Moshe Kamensky and I) to resolve the “compound fundamental isotrivial” case. I will also give a counterexample to the naive nonautonomous generalisation of the conjecture, exhibiting some of the difficulties in applying a model-theoretic analysis.

MC 5403