## 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

The Pure Math colloquium is held roughly every other week during the fall and winter terms. The talks are at 4:00 pm on Mondays in the Math and Computer Building (MC) 5501, and are preceded by refreshments with the speaker at 3:30 pm in MC 5403.

Title: Diophantine curiosities

Abstract: A basic problem in Diophantine approximation is to determine how well n-tuples of real numbers can be approximated by n-tuples of rational numbers, the quality of an approximation being compared to the common denominator of its n rational components. Another problem deals with approximation to real numbers by algebraic numbers of degree at most n for some fixed integer n. In this talk, we present some old and some recent results related to these questions, together with conjectures and open problems. In particular, we stress the existence of family of real numbers with unexpected properties.

Room: MC 5501

Title: TBA

Abstract: TBA

Room: MC 5501

Title: An introduction to the AdS/CFT correspondence for mathematicians

Abstract: The AdS/CFT correspondence has been of central importace in theoretical physics for the past 10 years. It is a correspondence between conformal field theones in d dimensions and gravity in d+ 1 dimensions.
**Monday, January 15, 2018, 4:00 pm**
**Ragnar-Olaf Buchweitz, University of Toronto**

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

Room: MC 5501

**Monday, November 20, 2017, 4:00 pm
Alexei Oblomkov, University of Massachusetts**

Title: TBA

Abstract: TBA

Room: MC 5501

Title: The McKay Correspondence Then and Now

Abstract:

In his treatise on "Symmetry", Hermann Weyl credits Leonardo Da Vinci with the insight that the only finite symmetry groups in the plane are cyclic or dihedral.

Reaching back even farther, had the abstract notion been around, Euclid's Elements may well have ended with the theorem that only three further groups can occur as finite groups of rotational symmetries in 3-space, namely those of the Platonic solids. Of course, it took another 22 centuries for such a formulation to be possible, put forward by C. Jordan (1877) and F. Klein (1884).

Especially Klein's investigation of the orbit spaces of those groups and their double covers, the binary polyhedral groups, is at the origin of singularity theory and in the century afterwards many surprising connections with other areas of mathematics such as the theory of simple Lie groups were revealed in work by Grothendieck, Brieskorn, and Slodowy in the 1960's and 70's. A beautiful and comprehensive survey of that side of the story was given by G.-M. Greuel in the extended published version of his talk at the Centennial Meeting of the DMV in 1990 in Bremen.

It came then as a complete surprise when J. McKay pointed out in 1979 a very direct, though then mysterious relationship between the geometry of the resolution of singularities of these orbit spaces and the representation theory of the finite groups one starts from. In particular, he found a remarkably simple explanation for the occurrence of the Coxeter-Dynkin diagrams in the theory.

This marks essentially the beginning of "Noncommutative Singularity Theory", the use of representation theory of not necessarily commutative algebras to understand the geometry of singularities, a subject area that has exploded during the last decade in particular because of its role in the mathematical formulation of String Theory in Physics.

In this talk I will survey the beautiful classical mathematics at the origin of this story and then give a sampling of recent results and of work still to be done.

Room: MC 5501

**Monday, February 5, 2018, 4:00 pm
Boris Khesin, University of Toronto**

Title: TBA

Abstract: TBA

Room: MC 5501

Here is an archive of past colloquia.

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