# Events by month

## October 2022

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### Student Number Theory Seminar

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

Sourabh Das, Department of Pure Math, University of Waterloo

"On the Omega function"

### Algebraic Geometry Working Seminar

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

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

### Differential Geometry Working Seminar

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

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

### Number Theory Seminar

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

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

### Horospherical MMP Seminar

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

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:

### Geometry & Topology Seminar

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

Daniel Platt, King's College London

"A construction of associative submanifolds near the singular limit"

### Logic Seminar

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

Leo Jimenez, Department of Pure Math, University of Waterloo

"Expansions of the group of integers"

### Colloquium

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

**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"

### Student Number Theory Seminar

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

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.

### Algebraic Geometry Working Seminar

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

Changho Han, Department of Pure Mathematics, University of Waterloo

"Periods II: Hodge Theory and K3 Surfaces"

### Differential Geometry Working Seminar

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

Amanda Petcu, Department of Pure Mathematics, University of Waterloo

"An Introduction to Calibrated Geometry"

### Computability Theory Learning Seminar

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

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Scott Complexity Part 3"

### Horospherical MMP Seminar

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

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:

### Geometry & Topology Seminar

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

Duncan McCoy, Université du Québec à Montréal

"The quest for alternating surgeries"

### Logic Seminar

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

Ross Willard, Department of Pure Mathematics, University of Waterloo

"Finite axiomatizability problems for finite algebras"

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

### Algebraic Geometry Working Seminar

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

Robert Harris, Department of Pure Mathematics, University of Waterloo

"Abelian Covers and Line Arrangements in CP^2"

### Differential Geometry Working Seminar

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

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

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

### Number Theory Seminar

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

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

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

### Computability Learning Seminar

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

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"A proof sketch of Hilbert's tenth problem"

### Horospherical MMP Seminar

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

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:

### Geometry & Topology Seminar

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

Ethan Cotterill, University of Campinas

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

### Logic Seminar

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

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Relations enumerable from positive information"

### Colloquium

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

Joseph H. Silverman, Brown University

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

### November 2022

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