## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, July 27, 2017 — 2:30 PM EDT

**Diana Castaneda Santos, Department of Pure Mathematics, University of Waterloo**

"More about morphisms of schemes"

We will continue with the discussion about morphisms of schemes. We

will see an explicit example of constructing morphisms of schemes by

cutting up into affine open sets and then gluing them together. Then, we

will define $Z$-valued points, where $Z$ is a given scheme. This

notion will lead us to determine a morphism not by its values at points

but rather by its induced map of $Z$-valued points.

Thursday, July 27, 2017 — 1:00 PM EDT

**Anthony McCormick, Department of Pure Mathematics, University of Waterloo**

"The Homological Algebra of PDEs"

Wednesday, July 26, 2017 — 4:00 PM EDT

**Leanne Stuive, Department of Combinatorics & Optimization, University of Waterloo**

"Approximating Convex Bodies by Polytopes"

Monday, July 24, 2017 — 10:00 AM EDT

**David Urbanik, University of Waterloo**

"What is a reciprocity law?"

There are numerous theorems in algebraic number theory which are "reciprocity laws". The simplest of these is quadratic reciprocity, for which there are many elementary proofs. For higher powers, there are many similar-looking statements, but whose proofs become progressively harder. We survey a number of reciprocity laws, give proofs of some simple ones, and try to show that they are all related.

MC 5403

Friday, July 21, 2017 — 2:00 PM EDT

**Adam Morgan, Department of Applied Mathematics, University of Waterloo**

"Finite Element Exterior Calculus, Part 3"

We will finish covering the concepts intended for the previous week's lecture, introducing discretizations of de Rham complexes and some rudimentary definitions in finite element analysis.

MC 5417

Thursday, July 20, 2017 — 4:00 PM EDT

**Brandon Doherty, Department of Pure Mathematics, University of Waterloo**

"Goodstein sequences and the Hydra game"

Gödel's incompleteness theorem proves the existence of certain statements about the natural numbers that can be neither proven nor disproven using basic first-order arithmetic. The kinds of statements constructed in the standard proof of the incompleteness theorem, however, are extremely technical, and not very interesting in and of themselves.

Thursday, July 20, 2017 — 2:30 PM EDT

**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

Thursday, July 20, 2017 — 9:30 AM EDT

**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

Tuesday, July 18, 2017 — 3:30 PM EDT

**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

Monday, July 17, 2017 — 1:30 PM EDT

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

"Techniques in operator algebras: Classification, dilations and

non-commutative boundaries"

Monday, July 17, 2017 — 10:00 AM EDT

**Stephen Wen, University of Waterloo**

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

Thursday, July 13, 2017 — 1:30 PM EDT

**Ian Payne, Department of Pure Mathematics, University of Waterloo**

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

Tuesday, July 11, 2017 — 12:00 PM EDT

**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

Monday, July 10, 2017 — 10:00 AM EDT

**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

Thursday, July 6, 2017 — 2:30 PM EDT

**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

Tuesday, July 4, 2017 — 2:30 PM EDT

**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

Tuesday, July 4, 2017 — 12:00 PM EDT

**Adam Morgan, Department of Applied Mathematics, University of Waterloo**

"Geometric Aspects of Finite Element Analysis, Part 1: Lagrange Elements"

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1