Events by date

Tuesday, October 4, 2022

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

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