Events

Spencer Whitehead, Department of Pure Mathematics, University of Waterloo

"Introduction to principal bundles"

In this talk we will cover the basic theory of principal bundles and their relation to vector bundles via the frame and associated bundle constructions. We will define connections on principal bundles and structure group reductions, and then if time permits introduce the groups Spin(n) and spin structures on manifolds.

MC 5403

Talk #1 (9:30am - 10:45am): Amanda Petcu, Department of Pure Mathematics, University of Waterloo

"Isometric Immersions, part 1"

This series of talks will cover Chapter 6 of Manfredo Do Carmo's book 'Riemannian Geometry'. In this specific talk we will introduce the notion of an isometric immersion and the second fundamental form. We will see some examples as well as some properties of isometric immersions and the creation of the second fundamental form for a Riemannian manifold. 

Benjamin Anderson-Sackaney, Department of Pure Mathematics, University of Waterloo

"Multipliers on Fourier Algebras"

We will give a brief introduction to multipliers on the Fourier algebra of a locally compact group. Then we will discuss weak amenability, which is a weakening of amenability from the perspective of Leptin's theorem. It was shown by Haagerup that, though free groups are non-amenable, they are weakly amenable. The finale will proceed by outlining a proof of this theorem.

MC 5403

Sabrina Lato, Department of Combinatorics & Optimization, University of Waterloo

"Perron, Frobenius, and some unexpected applications"

Spencer Whitehead, Department of Pure Mathematics, University of Waterloo

"Spin and Spinors"

We will define the groups Spin and Pin, the spinor representation, spin structures, and spinor bundles. As time permits we will look at some examples of spin structures and topological obstructions to spinnability. 

MC 5403

Yash Singh, Department of Pure Mathematics, University of Waterloo

"The Arithmetic of the Brauer-Manin Obstruction"

We study the Hasse principle on the existence of rational points on varieties and the Brauer-Manin obstruction which in some cases explains the failure of the Hasse principle.

This seminar will be held jointly online and in person:

• Room: MC 5403
• Zoom information: Meeting ID: 817 1030 9714; Passcode: 063438

Talk #1 (9:30am-10:45am): Catalina Quincosis Martínez, Department of Pure Mathematics, University of Waterloo

Benjamin Anderson-Sackaney, Department of Pure Mathematics, University of Waterloo

"Amenability Properties and Subobjects of Quantum Groups"

Nicole Kitt, Department of Pure Mathematics, University of Waterloo

"Crash course on the representation theory of complex semi-simple Lie algebras - Part 1"

Talk #1 (9:30am - 10:15 am): Prerecorded talk by Sven Hirsch, Duke University

"Spacetime harmonic functions and applications to relativity" (2021)

Talk #2 (10:30am - 11:30 am): Prerecorded talk by Vladimir Arnold, Steklov Mathematical Institute of Russian Academy of Sciences

"Statistics of the Morse theory of smooth functions" (2008)

Abstract: [translated from Russian]