## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, December 5, 2017 — 2:30 PM EST

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

"Borel Reducibility and Linear Orderings"

We define Borel reducibility introduced by Friedman and Stanley between classes of countable structures. We will define what it means for a class of structures to be complete with respect to Borel reducibility and then we will go through their proof of the fact that the class of countable linear orderings is complete with respect to Borel reducibility.

MC 5413

Friday, December 1, 2017 — 2:30 PM EST

**Ákos Nagy, University of Waterloo and The Fields Institute**

"Vortex-like instantons on the Euclidean Schwarzschild manifold"

Thursday, November 30, 2017 — 1:30 PM EST

**Simon Myerson, University College London**

"Forms in many variables: an iterative approach"

Wednesday, November 29, 2017 — 4:45 PM EST

**Jitendra Prakash, Department of Pure Mathematics, University of Waterloo**

"Bell's Theorem"

Bell's theorem is one of the celebrated cornerstones in physics, being described as "the most profound discovery of science". In this talk we shall discuss this theorem from a mathematical perspective, and as an example we shall derive the CHSH inequality. We shall also see what more general questions this theorem raises. Knowledge of physics is not required, however some basic linear algebra will be used.

MC 5501

Tuesday, November 28, 2017 — 1:30 PM EST

**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

Friday, November 24, 2017 — 3:30 PM EST

**Arthur Mehta, Department of Pure Mathematics, University of Waterloo**

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

Friday, November 24, 2017 — 2:30 PM EST

**Xinliang An, University of Toronto**

"On Singularity Formation in General Relativity"

Thursday, November 23, 2017 — 1:30 PM EST

**Divyum Sharma, Department of Pure Mathematics, University of Waterloo**

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

Wednesday, November 22, 2017 — 4:30 PM EST

**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

Tuesday, November 21, 2017 — 4:00 PM EST

**Deirdre Haskell, McMaster University**

"Residue field domination in theories of valued fields"

Tuesday, November 21, 2017 — 2:30 PM EST

**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

Tuesday, November 21, 2017 — 1:30 PM EST

**Parham Hamidi, Department of Pure Mathematics, University of Waterloo**

"Integral advice on going up in the world^{1}!"

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.

Monday, November 20, 2017 — 4:00 PM EST

**Alexei Oblomkov, University of Massachusetts**

"Planar curve singularities, knot invariants and representation theory"

Friday, November 17, 2017 — 3:30 PM EST

**Paul Skoufranis, York University**

"Bi-Free Versions of Entropy"

Friday, November 17, 2017 — 2:30 PM EST

**Eric Woolgar, University of Alberta**

"Curvature-dimension conditions in relativity and Lorentzian geometry"

Thursday, November 16, 2017 — 3:30 PM EST

**Renzhi Song, Department of Pure Mathematics, University of Waterloo**

"Series parallel posets and polymorphisms, part 2"

In this two part series I will talk about the poset retraction problem on the class of series parallel posets. Having classified those series-parallel posets whose retraction problem can be solved in polynomial time, I will now show that these same posets admit what is known as SD-join polymorphisms. Equivalently, their retraction problems are in nondeterministic log space.

MC 5413

Thursday, November 16, 2017 — 1:30 PM EST

**Farzad Aryan, McGill University**

"On an extension of the Landau-Gonek formula"

Wednesday, November 15, 2017 — 3:30 PM EST

**Rita Gitik, University of Michigan**

"A New Algorithm in Group Theory"

We describe a new algorithm which determines if the intersection of a quasiconvex subgroup of a negatively curved group with any of its conjugates is infinite. The algorithm is based on the concepts of a coset graph and a geodesic core of a subgroup. This algorithm is utilized in several other new algorithms computing breadth, height, and width of a quasiconvex subgroup of a negatively curved group.

MC 5403

Tuesday, November 14, 2017 — 4:00 PM EST

**Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo**

"Qualitative probability theory and types, part 2"

We continue Tao's blog post; we define random variables, and we examine qualitative probability measures on definable sets. Time permitting, we study random variables on groups and the group chunk theorem.

MC 5403

Tuesday, November 14, 2017 — 1:30 PM EST

**Parham Hamidi, Department of Pure Mathematics, University of Waterloo**

"Bermuda, Bahama, come on Nakayama^{1}!"

Monday, November 13, 2017 — 4:00 PM EST

**Kevin Costello, Perimeter Institute**

"An introduction to the AdS/CFT correspondence for mathematicians"

The AdS/CFT correspondence has been of central importance in theoretical physics for the past 10 years. It is a correspondence between conformal field theories in d dimensions and gravity in d + 1 dimensions.

This talk will be an attempt to introduce this topic to a mathematical audience. No previous knowledge of conformal field theory will be assumed.

MC 5501

Friday, November 10, 2017 — 3:30 PM EST

**Jitendra Prakash, Department of Pure Mathematics, University of Waterloo**

"Non-closure of the set of quantum correlations"

Friday, November 10, 2017 — 2:30 PM EST

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

"Tangent lines and the equation 28=7 x 4"

Thursday, November 9, 2017 — 3:30 PM EST

**Renzhi Song, Department of Pure Mathematics, University of Waterloo**

"Series parallel posets and polymorphisms"

In this two part series I will talk about the poset retraction problem on the class of series parallel posets. In this talk I will make introductions on series parallel posets and define what a polymorphism is and how their existence affects the complexity of the poset retraction problem.

MC 5413

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

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

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.