# Events - October 2022

Monday, October 31, 2022 — 2:30 PM EDT

## Colloquium

Joseph H. Silverman, Brown University

"Finite Orbits of Points on Surfaces that Admit Three Non-commuting Involutions"

Friday, October 28, 2022 — 10:30 AM EDT

## Logic Seminar

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Relations enumerable from positive information"

Thursday, October 27, 2022 — 2:30 PM EDT

## Geometry & Topology Seminar

Ethan Cotterill, University of Campinas

"Cuspidal curves in P^n, and partition arithmetic"

Thursday, October 27, 2022 — 1:00 PM EDT

## Horospherical MMP Seminar

Yash Singh, Department of Pure Mathematics, University of Waterloo

"Properties of horospherical varieties"

We study when a given horospherical variety is affine. Additionally, we study G-orbits of horospherical varieties and their correspondence with colored cones.

This seminar will be held jointly online and in person:

Thursday, October 27, 2022 — 10:30 AM EDT

## Computability Learning Seminar

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"A proof sketch of Hilbert's tenth problem"

Tuesday, October 25, 2022 — 2:30 PM EDT

## Number Theory Seminar

Gian Cordana Sanjaya, Department of Pure Mathematics, University of Waterloo

"On the squarefree values of $a^4 + b^3$"

Tuesday, October 25, 2022 — 2:00 PM EDT

## Differential Geometry Working Seminar

Lucia Martin Merchan, Department of Pure Mathematics, University of Waterloo

"A compact non-formal closed G2 manifold with b1=1"

Tuesday, October 25, 2022 — 12:30 PM EDT

## Algebraic Geometry Working Seminar

Robert Harris, Department of Pure Mathematics, University of Waterloo

"Abelian Covers and Line Arrangements in CP^2"

Friday, October 21, 2022 — 4:30 PM EDT

Xingchi Ruan, Department of Pure Mathematics, University of Waterloo

"Lower bounds on solubility of Diophantine systems"

Given a system of r homogeneous polynomial equations with degree d with rational coefficients, we study the number of variables it needs to possess a non-trivial p-adic solution. We focus on the lower bound of this number. We learn the history and prototype of the problem, as well as the most precise estimation of the lower bound so far.

MC 5479

Friday, October 21, 2022 — 10:30 AM EDT

## Logic Seminar

Ross Willard, Department of Pure Mathematics, University of Waterloo

"Finite axiomatizability problems for finite algebras"

Thursday, October 20, 2022 — 2:30 PM EDT

## Geometry & Topology Seminar

Duncan McCoy, Université du Québec à Montréal

"The quest for alternating surgeries"

Thursday, October 20, 2022 — 1:00 PM EDT

## Horospherical MMP Seminar

Nicole Kitt, Department of Pure Mathematics, University of Waterloo

"Morphisms of horospherical varieties"

In this talk, we define and look at examples of morphisms of horospherical varieties. Additionally, we will see how morphisms of horospherical varieties are related to maps of the coloured fans.

This seminar will be held jointly online and in person:

Thursday, October 20, 2022 — 10:30 AM EDT

## Computability Theory Learning Seminar

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Scott Complexity Part 3"

Tuesday, October 18, 2022 — 2:00 PM EDT

## Differential Geometry Working Seminar

Amanda Petcu, Department of Pure Mathematics, University of Waterloo

"An Introduction to Calibrated Geometry"

Tuesday, October 18, 2022 — 12:30 PM EDT

## Algebraic Geometry Working Seminar

Changho Han, Department of Pure Mathematics, University of Waterloo

"Periods II: Hodge Theory and K3 Surfaces"

Tuesday, October 18, 2022 — 10:00 AM EDT

## Student Number Theory Seminar

Owen Sharpe, Department of Pure Mathematics, University of Waterloo

"Primality Testing and Integer Factorization"

Primality testing and integer factorization are mathematical problems which have occupied number theorists throughout the centuries. They have become very important in the field of cryptography over the last fifty years. We give a brief history of primality testing and integer factorization algorithms, from the sieve of Eratosthenes to the AKS test, and from trial division to Shor's algorithm.

Monday, October 17, 2022 — 2:30 PM EDT

## Colloquium

**This talk is rescheduled for November 28, 2022**

Catherine Pfaff, Queen's University

"Deformation Spaces, R-Trees, & What Happens When You Iterate a Free Group Automorphism"

Friday, October 7, 2022 — 10:30 AM EDT

## Logic Seminar

Leo Jimenez, Department of Pure Math, University of Waterloo

"Expansions of the group of integers"

Thursday, October 6, 2022 — 2:30 PM EDT

## Geometry & Topology Seminar

Daniel Platt, King's College London

"A construction of associative submanifolds near the singular limit"

Thursday, October 6, 2022 — 1:00 PM EDT

## Horospherical MMP Seminar

Sean Monahan, Department of Pure Mathematics, University of Waterloo

“Combinatorics of horospherical varieties”

In this talk we finish our brief introduction of horospherical varieties by examining their
combinatorial interpretation. In the case of toric varieties, we have a combinatorial interpretation
using fans; in the case of horospherical varieties, we use so-called “coloured fans” which
account for the colours that we discussed in the last talk.
This seminar will be held jointly online and in person:

Tuesday, October 4, 2022 — 2:30 PM EDT

## Number Theory Seminar

Anton Mosunov, Department of Pure Mathematics, University of Waterloo

“On the Representation of Integers by Binary Forms Defined
by Means of the Relation (x + yi)n = Rn(x, y) + Jn(x, y)i”

Let F be a binary form with integer coefficients, degree d ≥ 3 and non-zero discriminant. Let
RF (Z) denote the number of integers of absolute value at most Z which are represented by F. In
2019 Stewart and Xiao proved that RF (Z) ∼ CFZ2/d for some positive number CF . We compute CRn

Tuesday, October 4, 2022 — 2:00 PM EDT

## Differential Geometry Working Seminar

Xuemiao Chen, Department of Pure Mathematics, University of Waterloo

“Restriction of slope semi-stable bundles”

Given a slope semi-stable bundle over a projective manifold, a classical theorem by Mehta
and Ramanathan states that its restriction to a generic high degree hyper-surface is still slope
semi-stable. This plays a key role in Donaldson’s proof for the existence of Hermitian-Einstein
metrics for stable vector bundles over projective manifolds. We will discuss Flenner’s proof of

Tuesday, October 4, 2022 — 12:30 PM EDT

## Algebraic Geometry Working Seminar

Changho Han, Department of Pure Mathematics, University of Waterloo

“Periods I: Elliptic Curves and Hodge Theory”

This is the first talk in the series of two talks with the goal of introducing a method of
parametrizing isomorphism classes of certain varieties using analytic techniques; even if it’s
analytic, this particular construction (of using ”periods”) plays key roles in algebraic side of
algebraic geometry and number theory as well. In this first talk, I will showcase the standard

Tuesday, October 4, 2022 — 9:30 AM EDT

## Student Number Theory Seminar

Sourabh Das, Department of Pure Math, University of Waterloo

"On the Omega function"

### December 2022

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