Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Pseudo-finite dimensions IX"
I will discuss the description of approximate subgroups of simple algebraic groups in Udi's "Stable groups and approximate subgroups".
MC 5403
Patrick Naylor, Department of Pure Mathematics, University of Waterloo
"Trisections of 4-manifolds"
Trisections were introduced by Gay and Kirby in 2013 as a way to study 4-manifolds. They are similar in spirit to a common tool in a lower dimension: Heegaard splittings of 3-manifolds. These both have the advantage of changing problems about manifolds into problems about combinatorics of curves on surfaces. This talk will be a relaxed introduction to these decompositions. Time permitting, we will talk about some recent applications.
MC 5413
Remi Jaoui, Department of Pure Mathematics, University of Waterloo
"Failure of essential surjectivity"
We consider Example 3.2 of the Bakker-Brunebarbe-Tsimerman paper, of an analytic line bundle on Gm that does not definably trivialise.
MC 5479
Vandita Patel, University of Toronto
"A Galois property of even degree Bernoulli polynomials"
Let $k$ be an even integer such that $k$ is at least $2$. We give a (natural) density result to show that for almost all $d$ at least $2$, the equation $(x+1)^k + (x+2)^k + ... + (x+d)^k = y^n$ with $n$ at least $2$, has no integer solutions $(x,y,n)$. The proof relies upon some Galois theory and group theory, whereby we deduce some interesting properties of the Bernoulli polynomials. This is joint work with Samir Siksek (University of Warwick).
MC 5417
Ben Webster, Department of Pure Mathematics, University of Waterloo
"Coulomb, Galois, Gelfand-Tsetlin"
In the grand tradition of naming objects after mathematicians who knew nothing about them, I'll talk a bit about Galois orders, their Gelfand-Tsetlin modules, and how most important examples are Coulomb branches.
Ragini Singhal, Department of Pure Mathematics, University of Waterloo
"Surfaces, Minimal surfaces, Willmore surfaces and much more"
Andre Kornell, UC Davis
"Quantum Extensions of Ordinary Maps"
Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Generalizing $\omega^k$-c.e. for Relativization - Part 2"
We finish the proof of a characterization of $A \leq_{bT} B^b$ that we started last time. We then use this to motivate a more general characterization, namely when $A \leq{bT} B^{nb}$. Finally, we begin the proof of a weak non-collapse theorem which uses this expanded characterization.
MC 5413
Tobias Fritz, Perimeter Institute for Theoretical Physics
"Real algebra, random walks, and information theory"
Martin Pinsonnault, Western University
"Stability of Symplectomorphism Groups of Small Rational Surfaces"