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Tuesday, October 20, 2026 10:00 am - 11:00 am EDT (GMT -04:00)

Number Theory Seminar | Xingchi Ruan | The Hilbert-Kamke Problem in Number Fields

Xingchi Ruan (University of Waterloo)
The Hilbert-Kamke Problem in Number Fields
The Hilbert-Kamke problem is a generalization of Waring’s problem to a system of equations, in which the sums of the first n powers of the same variables are given. By the circle method, the existence of solutions depends on a positive lower bound for the singular series. In this talk, we study this problem over a number field. We set up the circle method, following Siegel and Wang, and write the singular series as a product of local densities. Under a necessary arithmetic condition, and with enough variables, we prove that the singular series is bounded below by a positive constant depending only on the number of equations and the degree of the field. The proof is given first for quadratic fields and then for every number field.
MC 5501
Thursday, October 22, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Pure Math Colloquium | Nigel Hitchin | Geometry and Physics in two dimensions

Nigel Hitchin (University of Oxford)
Geometry and Physics in two dimensions
Fifty years ago, gauge theory in four dimensions brought new techniques into play in geometry and established a dialogue between physicists and mathematicians which has persisted. The talk will discuss ways in which these aspects have been adopted in studying quite concrete problems in two dimensions of interest to both communities. They reveal both the benefits and limitations of having alternative viewpoints.
DC 1302
Thursday, October 29, 2026 2:30 pm - 3:30 pm EDT (GMT -04:00)

Intro to My Research | Matt Satriano

Matt Satriano (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501

Thursday, November 5, 2026 2:30 pm - 3:30 pm EST (GMT -05:00)

Intro to My Research | Wentang Kuo

Wentang Kuo (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501

Thursday, November 12, 2026 2:30 pm - 3:30 pm EST (GMT -05:00)

Intro to My Research | Ty Ghaswala

Ty Ghaswala (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501

Ergun Yalcin (Bilkent University and University of Waterloo)
Free Actions on Products of Real Projective Spaces
There are many conjectures on restrictions on finite groups that can act freely on a topological space with prescribed homotopy type. The most famous of these conjectures is the rank conjecture, which claims that if an elementary abelian p-group of rank r acts freely on a product of k spheres, then r is less than or equal to k. In 1983, Cusick made a similar conjecture for free actions on products of real projective spaces. We recently solved the homotopy-theoretic version of Cusick’s conjecture. I will explain some of the main ideas used in the proof of this conjecture, after introducing the necessary background.
MC 5417
Thursday, November 19, 2026 2:30 pm - 3:30 pm EST (GMT -05:00)

Intro to My Research | Ruxandra Moraru

Ruxandra Moraru (University of Waterloo)

Intro to My Research

This is a series of talks by faculty members explaining their research at a level aimed at master's students. All other department members are welcome as well.

MC 5501