Events

Moritz Weber, Saarland University

Quantum Mathematics, quantum symmetries and quantum information

Since the early days of the foundation of quantum mechanics, 100 years ago, it was clear that a new kind of mathematics was needed in order to capture the new physics. At that time, John von Neumann formulated his principles of quantum mechanics and one of the main features was noncommutativity - the fact, that two observables A and B need not to commute. This was the starting point of a systematic study of noncommuting operators which quickly emancipated from "just a physics tool" to an own branch in mathematics as such. More and more often, it is called quantum mathematics nowadays and it comprises C*-algebras (aka quantum
topology), von Neumann algebras (aka quantum measure theory), Connes’s noncommutative geometry (aka quantum differential geometry), quantum groups and many more. I will give a brief survey on quantum mathematics, and I will then focus on an introduction to quantum symmetries and their link to quantum information theory.

MC 5501

Alex Pawelko, University of Waterloo

Adiabatic Limits of Coassociative Fibrations

I will be going through Donaldson’s paper ”Adiabatic limits of co-associative KovalevLefschetz fibrations”.

MC 4058

Jacques Van Wyk, University of Waterloo

Generalised Complex Structures on Products of Lie Groups

Let \(M\) be an even-dimensional manifold, and let \(H\) be a closed three-form on \(M\). An \(H\)-twisted generalised complex structure on \(M\) is an endomorphism of \(TM \oplus T^*M\)which squares to −1, preserves the natural pseudometric of \(TM \oplus T^*M\), and whose \(i\)-eigenbundle is closed under the \(H\)-twisted Dorfman bracket. A natural question is given a fixed closed three-form \(H\) on \(M\), does there exist an \(H\)-twisted generalised complex structure on \(M\)? We explore this question for products of compact simple Lie groups. This is motivated by Marco Gualtieri’s result that any even-dimensional Lie group with a biinvariant metric admits a generalised complex structure.

MC 4058

Jiahui Huang, University of Waterloo

Motivic Integration on Artin Stacks

We discuss the twisted arc space of Artin stacks and necessary modifications to perform motivic integration on them.

MC 5403

Joey Lakerdas-Gayle, University of Waterloo

Sacks' Splitting Theorem on a tree

We will prove Sacks' Splitting Theorem following the method of Steffen Lempp which uses a dynamically constructed priority tree.

MC 5403

Beining Mu, University of Waterloo

Thickness Lemma and Infinite Injury Priority Argument

In this talk, I will present Strong Thickness Lemma, which states that every piecewise computable c.e. set has a thick subset which lies outside of an upper cone of a non-computable c.e. set, as an example of infinite injury priority argument. In addition, I will discuss how thickness lemma implies the lack of least upper bound for infinite ascending c.e. degrees.

MC 5403