Duncan McCoy, Université du Québec à Montréal
"The quest for alternating surgeries"
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
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.
**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"
Changho Han, Department of Pure Mathematics, University of Waterloo
"Periods II: Hodge Theory and K3 Surfaces"
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
Sourabh Das, Department of Pure Math, University of Waterloo
"On the Omega function"
Leo Jimenez, Department of Pure Math, University of Waterloo
"Expansions of the group of integers"
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:
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