## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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"**

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

**Luke MacLean, Department of Pure Mathematics, University of Waterloo**

**"Relations enumerable from positive information"**

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

**Ethan Cotterill, University of Campinas**

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

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:

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

**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

**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

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

**"A compact non-formal closed G _{2} manifold with b_{1}=1"**

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

**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

**Ross Willard, Department of Pure Mathematics, University of Waterloo**

**"Finite axiomatizability problems for finite algebras"**

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

**Duncan McCoy, Université du Québec à Montréal**

**"The quest for alternating surgeries"**

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:

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

**Rachael Alvir, Department of Pure Mathematics, University of Waterloo**

**"Scott Complexity Part 3"**

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

**Amanda Petcu, Department of Pure Mathematics, University of Waterloo**

**"An Introduction to Calibrated Geometry"**

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

**Changho Han, Department of Pure Mathematics, University of Waterloo**

**"Periods II: Hodge Theory and K3 Surfaces"**

Tuesday, October 18, 2022 — 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.

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"**

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

**Leo Jimenez, Department of Pure Math, University of Waterloo**

**"Expansions of the group of integers"**

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

**Daniel Platt, King's College London**

**"A construction of associative submanifolds near the singular limit"**

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:

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

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

Tuesday, October 4, 2022 — 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

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

**Sourabh Das, Department of Pure Math, University of Waterloo**

**"On the Omega function"**

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.