## 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

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

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

**"On the Omega function"**

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

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 — 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

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.