## 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

Tuesday, January 31, 2017 — 3:00 PM EST

**Jonny Stephenson, Department of Pure Mathematics, University of Waterloo**

"Existential atomicity and universal types"

We will continue our study of existentially atomic models. We will introduce and prove a characterization of existential atomicity in terms of the universal types realized in the structure - this characterization is analogous to the standard model-theoretic definition of atomicity.

MC 5403

Tuesday, January 31, 2017 — 11:00 AM EST

**Levon Haykazyan, Department of Pure Mathematics, University of Waterloo**

"Groups with Pregeometries"

We will prove that groups that carry locally modular homogeneous pregeometries are commutative.

MC 5403

Monday, January 30, 2017 — 2:30 PM EST

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

"Nonlinear Spaces of Smooth Maps"

We will discuss the infinite dimensional smooth manifold structure on the space of smooth maps M\to N where M, N are finite dimensional smooth manifolds with M compact.

M3 3103

Friday, January 27, 2017 — 3:30 PM EST

**Sam Harris, Pure Mathematics, University of Waterloo**

"Unitary Correlation Sets"

Friday, January 27, 2017 — 2:30 PM EST

**Chris Kottke, New College of Florida**

"Compactification of monopole moduli spaces and Sen's conjecture"

Thursday, January 26, 2017 — 4:00 PM EST

**Ertan Elma, Pure Mathematics, University of Waterloo**

We will start reading the book 'An Introduction to Sieve Methods and their Applications' by A.C. Cojocaru and M.R. Murty. In this first talk, we will cover some basic results from the first chapter and if time permits we will start Gallagher's 'larger' sieve.

If you are interested in these talks, please send an e-mail to eelma@uwaterloo.ca for some possible time/room changes and for some documents that we may share.

MC 5403

Thursday, January 26, 2017 — 1:30 PM EST

**Sacha Mangerel, University of Toronto**

"Some Applications of Pretentiousness in the Theory of Dirichlet Characters"

Thursday, January 26, 2017 — 1:30 PM EST

**Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo**

"Solvable algebraic groups"

A linear algebraic group is a Zariski-closed group of matrices. We'll study the Lie-Kolchin Theorem that every connected, solvable linear algebraic group G is conjugate to a group of upper-triangular matrices, and see how it is applied to show that $G=N\rtimes T$ where N is a nilpotent group and T is a "maximal torus" in G.

MC 5413

Wednesday, January 25, 2017 — 2:30 PM EST

**Shubham Dwivedi, Pure Mathematics, University of Waterloo**

"The Monotonicity formula"

We will continue our discussion of minimal submanifolds. After discussing some consequences of the First Variation formula, we will state and prove the Monotonicity formula of volume for minimal submanifolds. We will also state (and might prove) the coarea formula.

M3 3103

Tuesday, January 24, 2017 — 3:00 PM EST

**Jonny Stephenson, Pure Mathematics, University of Waterloo**

"The back-and-forth property and uniform computable categoricity"

Cantor's back-and-forth argument gives a condition allowing one to construct isomorphisms between different copies of mathematical structures by a process of finite extension. We will give a condition which shows when such a procedure can be carried out, as well as demonstrating a link between back-and-forth procedures, effective atomicity, and uniform computable categoricity of structures.

MC 5403

Monday, January 23, 2017 — 2:30 PM EST

**Akos Nagy, Department of Pure Mathematics, University of Waterloo**

"Seiberg--Witten equation with multiple spinors in dimension 3 --- Part I"

Following Haydys and Walpuski, I will introduce a generalization of the SW equations on 3-manifolds, and prove a compactness theorem for the moduli space of solutions.

In the first talk, I will define the problem (the SW equations with multiple spinors), state the main theorem of the paper, and prove a couple a priori estimates.

M3 3103

Monday, January 23, 2017 — 11:30 AM EST

**Matthew Satriano, Pure Mathematics, University of Waterloo**

"Hodge theory for combinatorial geometries"

Now that we have an overview of the main results of Adiprasito–Huh–Katz, we start going into the details.

MC 5403

Friday, January 20, 2017 — 3:30 PM EST

**Boyu Li, Department of Pure Mathematics, University of Waterloo**

"Regular Dilation on Graph Products of $\mathbb{N}$"

Friday, January 20, 2017 — 2:30 PM EST

**Ali Aleyasin, Université du Québec à Montréal**

"The Calabi problem on edge-cone manifolds"

Thursday, January 19, 2017 — 1:30 PM EST

**Asif Zaman, University of Toronto**

"A variant of Brun-Titchmarsh for the Chebotarev density theorem"

Thursday, January 19, 2017 — 1:30 PM EST

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

"Solvable Algebraic Groups"

After finishing our examples from last time, we will discuss some of the structure theory of solvable algebraic groups. This will be a useful stepping-stone towards the theory of reductive and semisimple algebraic groups, which we will study next.

MC 5413

Thursday, January 19, 2017 — 12:30 PM EST

**Nickolas Rollick, Department of Pure Mathematics, University of Waterloo**

"Staying connected"

Wednesday, January 18, 2017 — 2:30 PM EST

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

"Nuclearity of Spaces of Distributions"

We will discuss the nuclearity of various useful locally convex spaces such as the spaces of smooth functions, compactly supported smooth functions, distributions, polynomials and formal power series. The notion of a parametrix, interpreted using the formalism we develop here, will provide valuable intuition when we discuss operator product expansions and vertex algebras in later talks.

MC 5417

Tuesday, January 17, 2017 — 3:00 PM EST

**Mohammad Mahmoud, Pure Mathematics, University of Waterloo**

"Existentially Algebraic Structures"

This week we talk about existentially algebraic structures. We will prove that every existentially algebraic structure is in fact existentially atomic. We will also try to establish a necessary and sufficient condition for a structure \mathcal{A}=(A,<, Adj) (linear order with the adjacency relation) to be existentially atomic.

MC 5403

Tuesday, January 17, 2017 — 11:00 AM EST

**Ilya Shapirovsky**

"Locally tabular modal logics"

Monday, January 16, 2017 — 11:30 AM EST

**Yoav Len, Department of Combinatorics & Optimization, University of Waterloo**

"Combinatorial Hodge Theory"

Friday, January 13, 2017 — 3:30 PM EST

**Ken Dykema, Texas A & M University**

"Commuting operators in finite von Neumann algebras"

We find a joint spectral distribution measure for families

of commuting elements of a finite von Neumann algebra. This

generalizes the Brown measure for single operators. Furthermore, we

find a lattice (based on Borel sets) consisting of hyperinvariant

projections that decompose the spectral distribution measure. This

leads to simultaneous upper triangularization results for commuting

operators.

Friday, January 13, 2017 — 2:30 PM EST

**Tyrone Ghaswala, Department of Pure Mathematics, University of Waterloo**

"Mapping class groups, coverings, braids and groupoids"

Suppose you are handed a finite sheeted (possibly branched) covering space between closed 2-manifolds by an eccentric mathematician. A natural question to ask is what is the relationship between the mapping class group of the covering surface and the mapping class group of the base surface?

Thursday, January 12, 2017 — 4:00 PM EST

**Hongdi Huang, Pure Mathematics, University of Waterloo**

"On *-clean group algebras"

A ring $R$ is called a $*$-ring (or a ring with involution $*$) if there exists an operation $*$: $R \rightarrow R$ such that $(x+y)^*=x^*+y^*, \,\ (xy)^*=y^*x^* \,\ $ and $(x^*)^*=x$,

for all $x, y\in R$. An element in a ring $R$ is called $*$-clean if it is the sum of a unit and a projection ($*$-invariant idempotent). A $*$-ring is called $*$-clean if each of its elements is the sum of a unit and a projection.

Thursday, January 12, 2017 — 1:30 PM EST

**Ghaith Hiary, Ohio State University **

“Computing quadratic Dirichlet L-functions”

An algorithm to compute Dirichlet L-functions for many quadratic characters is derived. The algorithm is optimal (up to logarithmic factors) provided that the conductors of the characters under consideration span a dyadic window.

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