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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

Benoit Charbonneau, Department of Pure Mathematics, University of Waterloo

"Hyperkähler structure of bow varieties"

My aim is to discuss some of the background material necessary to understand the recent paper of Roger Bielawski, Yannic Borchard, and Sergey Cherkis titled “Deformations of instanton metrics” (https://arxiv.org/abs/2208.14936).

MC 5403

Xiao Zhong, Department of Pure Mathematics, University of Waterloo

"$p$-Adic interpolation of orbits under rational maps"

Rivera-Letelier’s characterization of possible analytic uniformizations of $p$-adic analytic maps has played an important role within arithmetic dynamics over the past fifteen years. The characterization is given by a trichotomy of indifferent, attracting and superattracting cases near a fixed point of a map.

Yuming Zhao, Department of Pure Mathematics, University of Waterloo

"Positivity and sum-of-squares"

Daniel Platt, King's College London

"A construction of associative submanifolds near the singular limit"

Izar Alonso Lorenzo, Oxford University

"Balanced SU(3)-structures and coclosed $G_2$-structures in cohomogeneity one manifolds"

Jerry Wang, Department of Pure Mathematics, University of Waterloo

"An improvement to the Schmidt bound"

Counting number fields of fixed degree and bounded discriminant is a classical question in arithmetic statistics. The problem is known in degrees at most 5. In this talk, we will talk about an improvement to Schmidt's upper bound for general degree n, which beats existing improvements for n up to 94. This is joint work with Manjul Bhargava and Arul Shankar.

This seminar will be held jointly online and in person:

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Scott Complexity"

**Note: change of meeting time - this seminar will be held from 12:30-1:30 pm.**

Michael Albanese, Department of Pure Mathematics, University of Waterloo

"The Kodaira-Enriques Classification of Surfaces"

I will give a brief overview of the classification of compact complex surfaces and mention some related results. 

This seminar will be held jointly online and in person:

• Room: MC 5403
• Zoom information: Meeting ID: 817 1030 9714; Passcode: 063438

Paul Cusson, Department of Pure Mathematics, University of Waterloo

"Infinite Flag Manifolds and Vector Bundle Filtrations"