Events

Li Chen, Pure Mathematics, University of Waterloo

Talk #2: "Symmetry groups of differential Equations Part II - Symmetry of algebraic equations"

This will be the second part of a three part series on applications of Lie groups to differential equations. This time, we will focus on determining necessary and sufficient conditions for a system of algebraic equations and their level sets to be invariant under a group action.

Matthew Harrison-Trainor, Pure Mathematics, University of Waterloo

"$n$-systems - Part II"

We will continue our discussion of $n$-systems, and prove a  
general "metatheorem'' with a list of conditions that guarantee the  
success of a priority construction.

Xiaomei Zhao, Pure Mathematics, University of Waterloo

"New strategies for minor arc estimates: Part II"

Abstract: We have seen the outline of the circle method in Waring's problem from Shuntaro's talks, where the minor arc contribution was established by combining Weyl's inequality with Hua's lemma. In my two talks, we will continue to see some improvements on minor arc estimates. The first method is to replace Hua's lemma by Vinogradov's mean value theorem (VMVT).

Pure Mathematics Department, University of Waterloo

Matthew Beckett “Non-minimal Yang-Mills solutions”

Abstract:

Matthew Harrison-Trainor, Pure Mathematics, University Of Waterloo

"Pairs of computable structures"

We will begin by finishing the proof of the meta-theorem on n-systems, and then we will look at an application of back-and-forth relations and n-systems.

Adam Gutter, University of Waterloo

"Zariski Structures: Non-Standard Analysis"

In this seminar, our focus is on introducing several new geometrically
motivated concepts, namely coverings, multiplicity, and local
functions. Time permitting, we may also discuss topological sorts, a
tool that allows us to generate new Zariski structures from a given
Zariski structure.

Stanley Xiao, Pure Mathematics Department, University of Waterloo

"SOME RESULTS ON POWERFREE VALUES OF POLYNOMIALS IN ONE OR TWO VARIABLES"

In this talk I will discuss the problem of finding powerfree values of polynomials in one or two variables, with an emphasis on the determinant method of D.R. Heath-Brown.

Li Chen & Jordan Rose, Pure Mathematics Department, University of Waterloo

Li Chen

"Symmetry groups of differential Equations Part III - Symmetry of differential equations with examples"

This will be the last of a series of three talks on symmetry groups of DE. In this talk, I will use the tools developed in the second talk, namely, symmetry of algebraic equations, to study differential equations when we view them as algebraic equations in higher jet spaces.

Ian Payne, Pure Mathematics Department, University of Waterloo

“Determining CSP complexity using universal algebra”

Given a finite relational structure, A, the complexity of the constraint satisfaction problem for A can sometimes be determined using universal algebra. There are several known algebraic conditions on the polymorphism algebra of a structure that imply the NP-completeness of its CSP.

Matthew Harrison-Trainor, Pure Mathematics University of Waterloo

“Pairs of computable structures”

Let A and B be two structures over the same language. We consider the question of which sets S can be coded by those structures as follows: there is a uniformly computable sequence of structures (Cn)n ∈ ω such that Cn is isomorphic to A if n ∈ S and to B otherwise.