Events

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

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

Jason Bell, Pure Mathematics, University of Waterloo

"The noncommutative Zariski Cancellation Problem"

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

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

Nico Spronk, Pure Mathematics, University of Waterloo

"On similarity for completely bounded representations of Fourier algebras"

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!

Samuel Kim, Pure Mathematics, University of Waterloo

"Proving the Hopkins-Levitzki Theorem"

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.

Kevin Matthews, Department of Pure Mathematics, University of Waterloo

"Local Dimensions of Measures of Finite Type"