Events by date

Sourabh Das, Department of Pure Math, University of Waterloo

"On the Omega function"

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

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

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