Events

Anthony McCormick, Department of Pure Mathematics, University of Waterloo

"Cotangent Complexes of $C^{\infty}$-Rings"

A $C^{\infty}$-ring is essentially an $\mathbb{R}$-algebra equipped with a smooth multivariate functional calculus. We'll study notions of smoothness and transversality for useful generalizations of manifolds in differential geometry; making use of this formalism.

MC 5479

Ty Ghaswala, Department of Pure Mathematics, University of Waterloo

"Morphisms of schemes"

We will define morphisms of schemes and prove some basic facts about said morphisms.  If anyone has a clever pun for the title of this talk, please let me know. I couldn't think of one.

MC 5403

Shouzhen Gu, Department of Pure Mathematics, University of Waterloo

"Roth's Theorem"

Roth's Theorem states that any subset of the integers with positive density will contain three numbers in an arithmetic progression. We will give a proof of Roth's Theorem using Fourier analysis. Then, we will discuss an analogous result in the context of polynomial rings over finite fields that can be proved using the same technique.

MC 5403

Adam Morgan, Department of Applied Mathematics, University of Waterloo

"Finite Element Exterior Calculus, Part 2"

We will continue the theoretical developments from part 1, defining precisely how we intend to "discretely replicate" de Rham complexes. Following this, we will set up our notation for triangulations and define Lagrange elements.

MC 5479

Ian Payne, Department of Pure Mathematics, University of Waterloo

"2-Semilattices: Residual Properties and Applications to Constraint Satisfaction Problems"

Stephen Wen, University of Waterloo

An analog of Sarközy's theorem on squares in difference sets

Adam Dor On, Department of Pure Mathematics, University of Waterloo

"Techniques in operator algebras: Classification, dilations and 
non-commutative boundaries"

Matthew Harrison-Trainor, Department of Pure Mathematics, University of Waterloo

"Computable Categoricity"

We will continue our discussion of computable categoricity by characterizing it for structures with some amount of decidability, and then separating it from relative computable categoricity.

MC 5403

Jaspar Wiart, Department of Pure Mathematics, University of Waterloo

"Four Years in Thirty Minutes"

In my four years at UW I completed two research projects. For the first project I computed the C*-envelopes of a family of isometric semicrossed products arising from number theory. In the second I characterized the Jacobson radical of certain semicrossed products of simple unital C*-algebras with sufficiently nice semigroups. In this talk I will briefly summarize what I did in reverse chronological order.

MC 2009

Nickolas Rollick, Department of Pure Mathematics, University of Waterloo

"Categorizing schemes in the wild"

Last time, we laid the groundwork necessary to make sense of the category of schemes.  This week, we get a feel for this category via some examples and structural facts.  In particular, we will learn what the final object is, construct non-trivial morphisms from a one-point scheme to itself, and look at the seemingly odd notion of scheme-valued points of a scheme.  It's truly a wild world these schemes live in...

MC 5403