## 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 9, 2015 — 3:30 PM EDT

**Javad Mashreghi, Laval University**

"The Halmos Conjecture on the Numerical Range"

Wednesday, October 7, 2015 — 3:30 PM EDT

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

"Algorithmic Randomness: Introduction to Kolmogorov Complexity"

After we have established the machine existence (Kraft-Chaitin Theorem), this time we are going to give the proofs for the following "desirable" facts about $K$ which we stated before: (a) Incompressible (in the sense of $K$) strings have only short runs of zeros (i.e. blocks only consisting of zeros), and (b) Zeros and ones occur balancedly.

MC 5403

Wednesday, October 7, 2015 — 3:30 PM EDT

**Raymond Cheng, Department of Pure Mathematics, University of Waterloo**

"Hodge Decomposition and Kahler Manifolds"

Wednesday, October 7, 2015 — 2:30 PM EDT

**Kevin Matthews, Department of Pure Mathematics, University of Waterloo**

"Local Dimensions of Measures of Finite Type"

This talk will examine the multifractal analysis of a particular class of

equicontractive self-similar measures. We will begin by reviewing known

results in the area. Our focus will be on the set of attainable local

dimensions of these measures and a systematic way of computing them.

Several examples will be discussed.

MC 5403

Tuesday, October 6, 2015 — 2:30 PM EDT

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

**"**Complex tori and elliptic curves"

In this seminar, we will look at the connection that exists between elliptic curves defined over the field of complex numbers **C** and complex tori. A complex torus is merely a quotient of **C **by some two-dimensional lattice on the complex plane. This connection is fundamental for the understanding of the Modularity Theorem.

Tuesday, October 6, 2015 — 11:30 AM EDT

**Samuel Kim, Pure Mathematics, University of Waterloo**

"Proving the Hopkins-Levitzki Theorem"

Monday, October 5, 2015 — 4:00 PM EDT

**Gregory Smith, Queen's University**

"Non-negativity certificates on real projective curves**"**

How can one use sums of squares to characterize nonnegative polynomials? In this talk, we will review some general methods for certifying that a polynomial is nonnegative on a real projective subvariety. We will then present new optimal degree bounds for certificates on real projective curves. This talk is based on joint work with Grigoriy Belkherman and Mauricio Velasco.

Refreshments will be served in MC 5403 at 3:30pm. All are welcome!

Friday, October 2, 2015 — 3:30 PM EDT

**Nico Spronk, Pure Mathematics, University of Waterloo**

"On similarity for completely bounded representations of Fourier algebras"

Thursday, October 1, 2015 — 4:30 PM EDT

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

"The Zero Divisor Conjecture"

Groups, rings, and everything nice ... These were the ingredients chosen to create the perfect little rings. But Professor Algebronium accidentally added an extra ingredient to the concoction --- *Chemical $X^n*! Thus, the Zero Divisors were born. However, the converse remains open: can the Professor still create the Zero Divisors without the addition of Chemical $X^n$? Find out in the next episode of Powerpu--- I mean, the grad colloquium ...

M3 2134

Wednesday, September 30, 2015 — 3:30 PM EDT

Mohammad Mahmoud, Pure Mathematics, University of Waterloo

"Algorithmic Randomness: Introduction to Kolmogorov Complexity"

Last time we saw why the Kolmogorov complexity $K$ can be better than the plain complexity $C$ as it is subadditive and complexity doesn't dip. This time we are going to see more properties showing that $K$ matches our intuition. More precisely, (a) Incompressible (in the sense of $K$) strings have only short runs of zeros (i.e. blocks only consisting of zeros), and (b) Zeros and ones occur balancedly.

MC 5403

Wednesday, September 30, 2015 — 2:30 PM EDT

Jason Bell, Pure Mathematics, University of Waterloo

"The noncommutative Zariski Cancellation Problem"

Tuesday, September 29, 2015 — 2:30 PM EDT

Anton Mosunov, Pure Mathematics, University of Waterloo

"Congruence subgroups and examples of forms that are modular with respect to these subgroups"

This week, we will look at the definition of cusp forms, and consider the most famous example of the cusp form of weight 12, which is the discriminant function. Afterwords, we shall move to the discussion of congruence subgroups, and will look at forms that are modular with respect to particular congruence subgroups.

MC 5479

Tuesday, September 29, 2015 — 11:30 AM EDT

**Patrick Naylor, Pure Mathematics, University of Waterloo**

"Semisimplicity and the Hopkins--Levitski Theorem"

This semester we'll be meeting weekly to learn more about ring theory, mostly going through Lam's two books --- there are many interesting results in those books which will be "good to know". Starting off, we'll aim to learn the Hopkins--Levitski Theorem, one of whose (many) consequences is that the descending chain condition *implies* the ascending chain condition. Everyone is welcome. See you there!

MC 5403

Monday, September 28, 2015 — 9:30 PM EDT

**Ram Murty, Queen’s University **

“The theory of Ramanujan expansions”

Monday, September 28, 2015 — 4:00 PM EDT

**M. Ram Murty, Queen’s University **

“NEW DIRECTIONS IN SIEVE THEORY”

Friday, September 25, 2015 — 3:30 PM EDT

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

“Quasidiagonal Traces and Crossed Products”

Thursday, September 24, 2015 — 2:30 PM EDT

**Blake Madill, Department of Pure Mathematics, University of Waterloo **

“On rings graded by semigroups with a unique product property”

Wednesday, September 23, 2015 — 2:30 PM EDT

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

“Recent Methods for Computing the Hausdorff Dimension of a Self-Similar Set”

Tuesday, September 22, 2015 — 2:30 PM EDT

Juan Felipe Carmona, Universidad Antonio Nariño

"Flatness and CM-triviality in strongly minimal theories with a predicate"

Tuesday, September 22, 2015 — 2:30 PM EDT

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

“Basic definitions and examples in the theory of modular forms”

Monday, September 21, 2015 — 4:00 PM EDT

**Michael F. Singer North Carolina State University **

“Differential Groups and the Gamma Function”

Wednesday, September 16, 2015 — 3:30 PM EDT

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

“Algorithmic Randomness: Introduction to Kolmogorov Complexity”

The topic for the Computability Learning Seminar this term will be Algorithmic Random- ness. We will be following Nies’s book, Computability and Randomness.

Wednesday, September 16, 2015 — 10:30 AM EDT

**Jaspar Wiart, Department of Pure Math, University of Waterloo **

“Nuclear and exact C*-algebras”

This will be an overview of the two definitions of nuclear and exact C*-algberas via com- pletely positive maps and exact sequences, and an outline of how the equivalence is established.

MC 5403

Monday, September 14, 2015 — 4:00 PM EDT

**Dinesh Thakur, University of Rochester **

“What should be pi, e, zeta(3), Gamma(1/7), if integers are replaced by polynomials?”

We will explain the title and talk about relations between these quantities.

MC 5501

*Refreshments will be served in MC 5403 at 3:30 p.m. Everyone is welcome to attend. *

Thursday, August 27, 2015 — 2:00 PM EDT

**Michael Deveau, Department of Pure Mathematics, University of Waterloo **

“Embedding Lattices in the Computably Enumerable Degrees (Part 4)”

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.