Events

Alexei Oblomkov, University of Massachusetts

"Planar curve singularities, knot invariants and representation theory"

Parham Hamidi, Department of Pure Mathematics, University of Waterloo

"Integral advice on going up in the world¹!"

Now that we are done with definitions and a few boring results about integral homomorphisms, we can prove the Lying over and Going up Theorems. I will prove Nakayama’s Lemma using a simple trick and talk about some of its applications. Finally we would see how the Lying over and Going up Theorems can be interpreted geometrically in number theory in the theory of ramifications.

Michael Deveau, Department of Pure Mathematics, University of Waterloo

"Isomorphisms that cannot be coded by computable relations -- Part 2"

Last time, we saw why it is so useful to code an isomorphism by the image of a computable relation and also explored some cases where this is always possible. We now turn to constructing a pair of structures where this is not possible. That is, we construct two structures -- isomorphic to $(\omega, <)$ -- where this method of establishing the degree of the isomorphism between them will not work.

MC 5413

Deirdre Haskell, McMaster University

"Residue field domination in theories of valued fields"

Mehdi Karimi, Department of Combinatorics & Optimization, University of Waterloo

"Sum-of-Squares Proofs in Optimization"

The old concept of sum-of-squares found its way into optimization and even machine learning. I will talk about this quickly evolving research area known as convex algebraic geometry.

MC 5501

Divyum Sharma, Department of Pure Mathematics, University of Waterloo

"Joint distribution of the base-q and Ostrowski digital sums"

Xinliang An, University of Toronto

"On Singularity Formation in General Relativity"

Arthur Mehta, Department of Pure Mathematics, University of Waterloo

"Chromatic numbers and a Lovász type inequality for non-commutative graphs"

Nickolas Rollick, Department of Pure Mathematics, University of Waterloo

"Definitions are relative"

Having spent the last two weeks on algebraic preliminaries, we now take a sharp right turn to explore the scenic route to our destination.  Specifically, we will see how to "relativize" the notions of quasicompactness and quasiseparatedness, to make them properties of morphisms rather than properties of schemes.  Along the way, we verify as much as possible that these classes of morphisms are good ones in the sense of Vakil.

MC 5413