Events

Owen Sharpe, University of Waterloo

The Selberg-Delange Method

For complex w and z, the expression w^z is ambiguous, requiring a choice of branch of log(w). In particular, there is no way to make w^z an entire function of w; a branch cut will always be present. In turn, this makes it difficult to perform contour integration and calculate residues with functions of the form f(w)^z, which are fundamental operations in number theory. We describe Selberg's method for performing such computations and some of its applications, such as those by Selberg and Delange. Incidentally, we will also discuss Hankel's formula for the Gamma function and Perron's formula for partial sums of Dirichlet series.

MC 5403

Amanda Maria Petcu, University of Waterloo

Cohomogeneity one solitons of the hypersymplectic flow

Given a manifold X^4 x T^3 where X^4 is hypersymplectic, one can give a flow of hypersymplectic structures that evolve according to the equation dt(w) = d(Q d^*(Q^{-1} w)), where w is the triple that gives the hypersymplectic structure and Q is a 3x3 symmetric matrix that relates the symplectic forms w_i to one another. We will let X^4 be R^4 with a cohomogeneity one action and explain what it means to be a soliton for the hypersymplectic flow and examine a (potentially hyperkahler) metric that comes from this set-up.

MC 5479

Rahim Moosa, University of Waterloo

Curve excluding fields III

We continue to read the paper by Johnson and Ye.

MC 5403

Kaleb Ruscitti, University of WaterlooA category theory joke

A category theory joke

In this talk I will tell one joke. To ensure that all participants find the joke funny, I will spend the first 50 minutes explaining the background material (applied category theory) required for the joke.

MC 5501

Joey Lakerdas-Gayle, University of Waterloo

Compactness and connectives in continuous logic

We will look at the compactness theorem and systems of connectives following "Model Theory for Metric Structures" by Ben Yaacov, Berenstein, Henson, and Usvyatsov.

MC 5403

Ben Webster, University of Waterloo

Intro to 3-d mirror symmetry

This will be an overview talk, aiming to get people hyped up for the 3-d mirror symmetry seminar.

MC 2017

Kevin Hare, University of Waterloo

Computational progress on the unfair 0-1 polynomial Conjecture

Let c(x) be a monic integer polynomial with coefficients 0 or 1. Write c(x)=a(x)b(x) where a(x) and b(x) are monic polynomials with non-negative real (not necessarily integer) coefficients. The unfair 0-1 polynomial conjecture states that a(x) and b(x) are necessarily integer polynomials with coefficients 0 or 1. We will discuss recent computationally progress towards this conjecture.

MC 5479

Kaleb D Ruscitti, University of Waterloo

Moduli of Line Bundles

As an example of a moduli problem that does not admit a fine moduli space, I have been studying the moduli space of line bundles. This admits a coarse moduli space: the quotient stack [pt/T], where T is a (algebraic) torus.

At first glance, [pt/T] seems very arcane, so I have been learning how one should understand this object. However it is an instructive simple case for motivating and working with moduli stacks. In this talk, I hope to present some different interpretations of [pt/T], so we can all be more comfortable with stacks.

MC 5479

Christine Eagles, University of Waterloo

Quantifier free internality and binding groups in ACFA

In ACFA, the definable closure of a set is not well understood. This presents an obstacle to understanding internality to the fixed field. Instead, we look at quantifier-free internality. In this talk we will follow Kamensky and Moosa (2024) by presenting quantifier-free internality and then stating a binding group theorem for rational types which are quantifier-free internal to the fixed field.

MC 5479

Gian Cordana Sanjaya, University of Waterloo

Squarefree discriminant of polynomials with prime coefficients

In 1991, Yamamura computed the density of monic polynomials of degree n which has discriminant not divisible by p^2 for any prime number p and positive integer n > 1. It is natural to conjecture that the density of monic polynomials of degree n with squarefree discriminant is the product of these local densities. This conjecture has been proved in 2022 by Bhargava, Shankar, and Wang in their paper, "Squarefree values of polynomial discriminants I".

In this talk, we consider a variant where the monic polynomials have prime coefficients. We compute the density of polynomials of degree n > 1 in this class which has squarefree discriminant, as an asymptotic density plus an explicit big-O error term. This is a joint work with Valentio Iverson and Xiaoheng Wang.

MC 5403