## 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

Friday, October 30, 2015 — 4:00 PM EDT

**Henry Liu, Department of Pure Mathematics, University of Waterloo **

“Path Integrals”

Friday, October 30, 2015 — 3:30 PM EDT

**Matthew Kennedy, Department of Pure Math, University of Waterloo **

“An intrinsic algebraic characterization of C*-simplicity for discrete groups”

Friday, October 30, 2015 — 2:30 PM EDT

**Yi Zhu, Pure Mathematics Department, University of Waterloo **

“Rational curves on open manifolds”

Thursday, October 29, 2015 — 4:00 PM EDT

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

“Hilbert’s 10th Problem”

In 1900, the German mathematician David Hilbert outlined 23 major mathematical problems to be studied in the coming century. His ”questions” ranged greatly in topic and precision. They were designed to serve as examples for the kinds of problems whose solutions would lead to the furthering of disciplines in mathematics.

Thursday, October 29, 2015 — 1:30 PM EDT

**Stanley Xiao, Department of Pure Mathematics, University of Waterloo**

“k-free values of binary forms”

Wednesday, October 28, 2015 — 3:00 PM EDT

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

“Martin-Lof Randomness and Solovay Tests”

We have seen that the Martin-Lof random real numbers are a reasonably natural notion: they are definable both in terms of Martin-Lof tests and in terms of complexity.

Tuesday, October 27, 2015 — 2:30 PM EDT

**Stanley Xiao, Department of Pure Mathematics, University of Waterloo**

“Basic definitions and examples”

Tuesday, October 27, 2015 — 11:30 AM EDT

**Chris Schafhauser, Department of Pure Mathematics, University of Waterloo **

“Noncommutative localisation”

Tuesday, October 27, 2015 — 10:30 AM EDT

**Ehsaan Hossain, University of Waterloo **

“Invariant basis number and finiteness”

Tuesday, October 27, 2015 — 9:00 AM EDT

**Sam Kim, Carleton University **

“Ultraproduct techniques for tracial von Neumann algebras”

Monday, October 26, 2015 — 4:00 PM EDT

**Florent Benaych-Georges, University Paris 5 **

“The Single Ring Theorem”

Monday, October 26, 2015 — 10:30 AM EDT

**Ross Willard, Department of Pure Mathematics, University of Waterloo **

“Fundamentals of finite modular lattices, I.”

Monday, October 26, 2015 — 9:00 AM EDT

**Andrej Vukovic, Carleton University **

“Enumerative Combinatorics and the Geometry of Number”

Friday, October 23, 2015 — 4:00 PM EDT

**Anton Borissov, Department of Pure Mathematics, University of Waterloo **

“Dirac Field”

This week we will discuss fermions. Starting from representations of the Lorentz group and traversing carefully through Clifford algebras and spinors, we will finally arrive at the quantization of the Dirac field.

MC 5403

Friday, October 23, 2015 — 3:30 PM EDT

**Ignacio Garcia, Department of Pure Math, University of Waterloo**

“Packing measure and a theorem of Besicovitch”

Packing measures, as well as Hausdorff measures, are used to provide fine information on the size of fractal sets. For many random sets, especially related to Brownian motion, packing measures (rather than Hausdorff measures) provide the right concept to measure the size of the set.

Thursday, October 22, 2015 — 1:30 PM EDT

**Tristan Freiberg, Department of Pure Mathematics, University of Waterloo**

“The distribution of primes in short intervals.”

Wednesday, October 21, 2015 — 3:30 PM EDT

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

“Randomness Continued”

Last time we introduced Martin-Lof randomness, and saw that most reals have this prop- erty.

This week, we will give an example of one specific Martin-Lof random real, discuss some of the properties which such reals satisfy, and give another characterization of them.

Wednesday, October 21, 2015 — 2:30 PM EDT

**Matt Kennedy, Department of Pure Mathematics, University of Waterloo **

“Invariant random subgroups and uniformly recurrent subgroups”

Wednesday, October 21, 2015 — 2:30 PM EDT

**Ignacio Garcia, Pure Math Department, University of Waterloo **

“On generalized dimension of self similar sets with overlaps.”

Tuesday, October 20, 2015 — 2:30 PM EDT

**Anton Mosunov, Department of Pure Mathematics, University of Waterloo**

“Modular Curves and Moduli Spaces”

Tuesday, October 20, 2015 — 11:30 AM EDT

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

“Semiprime rings, cont’d”

Continuing our discussion of prime and semiprimeness: a ring R is semiprime if it has no nilpotent ideals. We’ll relate this to prime rings, and show that if R is semiprime artinian then it satisfies the Artin–Wedderburn theorem.

MC 5403

Monday, October 19, 2015 — 4:00 PM EDT

**David Marker, University of Illinois at Chicago **

“Model Theory and Exponentiation”

Friday, October 16, 2015 — 4:30 PM EDT

**Anton Borissov, Department of Pure Mathematics, University of Waterloo **

“The Klein-Gordon Field”

Friday, October 16, 2015 — 3:30 PM EDT

**Jason Crann, Department of Pure Math, University of Waterloo**

“Homological manifestations of quantum group amenability”

Wednesday, October 14, 2015 — 3:30 PM EDT

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

“Martin-Lf Randomness”

We will continue last week’s discussion of prefix-free Kolmogorov complexity, but will begin to focus more on infinite sequences. We will discuss what we might mean when we say that an infinite sequence looks random from an algorithmic perspective.

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.