Thu, 03 Dec 2020

16:00 - 16:45
Virtual

Algebras and games

Vern Paulsen
(Waterloo)
Further Information

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

There are many constructions that yield C*-algebras. For example, we build them from groups, quantum groups, dynamical systems, and graphs. In this talk we look at C*-algebras that arise from a certain type of game. It turns out that the properties of the underlying game gives us very strong information about existence of traces of various types on the game algebra. The recent solution of the Connes Embedding Problem arises from a game whose algebra has a trace but no hyperlinear trace.


Assumed knowledge: Familiarity with tensor products of Hilbert spaces, the algebra of a discrete group, and free products of groups.

Tue, 27 Oct 2020
15:30
Virtual

Further progress towards Hadwiger's conjecture

Luke Postle
(Waterloo)
Further Information

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

In 1943, Hadwiger conjectured that every graph with no Kt minor is $(t-1)$-colorable for every $t\geq 1$. In the 1980s, Kostochka and Thomason independently proved that every graph with no $K_t$ minor has average degree $O(t(\log t)^{1/2})$ and hence is $O(t(\log t)^{1/2)}$-colorable. Recently, Norin, Song and I showed that every graph with no $K_t$ minor is $O(t(\log t)^\beta)$-colorable for every $\beta > 1/4$, making the first improvement on the order of magnitude of the $O(t(\log t)^{1/2})$ bound. Here we show that every graph with no $K_t$ minor is $O(t (\log t)^\beta)$-colorable for every $\beta > 0$; more specifically, they are $O(t (\log \log t)^6)$-colorable.

Mon, 28 Nov 2016
14:15
L4

 Moduli spaces of generalized holomorphic bundles

Ruxandra Moraru
(Waterloo)
Abstract

Generalized holomorphic bundles are the analogues of holomorphic vector bundles in the generalized geometry setting. In this talk, I will discuss the deformation theory of generalized holomorphic bundles on generalized Kaehler manifolds. I will also give explicit examples of moduli spaces of generalized holomorphic bundles on Hopf surfaces and on Inoue surfaces. This is joint work with Shengda Hu and Mohamed El Alami

Tue, 04 Nov 2014
17:00
C1

Weak amenability of Fourier algebras of Lie groups

Mahya Ghandehari
(Waterloo)
Abstract

The Fourier algebra of a locally compact group was first defined by Eymard in 1964. Eymard showed that this algebra is in fact the space of all coefficient functions of the left regular representation equipped with pointwise operations. The Fourier algebra is a semi-simple commutative Banach algebra, and thus it admits no non-zero continuous derivation into itself. In this talk we study weak amenability, which is a weaker form of differentiability, for Fourier algebras. A commutative Banach algebra is called weakly amenable if it admits no non-zero continuous derivations into its dual space. The notion of weak amenability was first defined and studied for certain important examples by Bade, Curtis and Dales. 

 

In 1994, Johnson constructed a non-zero continuous derivation from the Fourier algebra of the rotation group in 3 dimensions into its dual. Subsequently, using the structure theory of Lie groups and Lie algebras, this result was extended to any non-Abelian, compact, connected group. Using techniques of non-commutative harmonic analysis, we prove that semi-simple connected Lie groups and 1-connected non-Abelian nilpotent Lie groups are not weak amenable by reducing the problem to two special cases: the $ax+b$ group and the 3-dimensional Heisenberg group. These are the first examples of classes of locally compact groups with non-weak amenable Fourier algebras which do not contain closed copies of the rotation group in 3 dimensions.

Mon, 25 Nov 2013

12:00 - 13:00
L5

A Kobayashi-Hitchin correspondence for generalized Kaehler manifolds

Ruxandra Moraru
(Waterloo)
Abstract

In this talk, we discuss an analogue of the Hermitian-Einstein equations for generalized Kaehler manifolds proposed by N. Hitchin. We explain in particular how these equations are equivalent to a notion of stability, and that there is a Kobayahsi-Hitchin-type of correspondence between solutions of these equations and stable objects. The correspondence holds even for non-Kaehler manifolds, as long as they are endowed with Gauduchon metrics (which is always the case for generalized Kaehler structures on 4-manifolds).

This is joint work with Shengda Hu and Reza Seyyedali.

Fri, 24 Feb 2012
14:15
DH 1st floor SR

Comparison between the Mean Variance Optimal and the Mean Quadratic Variation Optimal Trading Strategies

Peter Forsyth
(Waterloo)
Abstract

Algorithmic trade execution has become a standard technique

for institutional market players in recent years,

particularly in the equity market where electronic

trading is most prevalent. A trade execution algorithm

typically seeks to execute a trade decision optimally

upon receiving inputs from a human trader.

A common form of optimality criterion seeks to

strike a balance between minimizing pricing impact and

minimizing timing risk. For example, in the case of

selling a large number of shares, a fast liquidation will

cause the share price to drop, whereas a slow liquidation

will expose the seller to timing risk due to the

stochastic nature of the share price.

We compare optimal liquidation policies in continuous time in

the presence of trading impact using numerical solutions of

Hamilton Jacobi Bellman (HJB)partial differential equations

(PDE). In particular, we compare the time-consistent

mean-quadratic-variation strategy (Almgren and Chriss) with the

time-inconsistent (pre-commitment) mean-variance strategy.

The Almgren and Chriss strategy should be viewed as the

industry standard.

We show that the two different risk measures lead to very different

strategies and liquidation profiles.

In terms of the mean variance efficient frontier, the

original Almgren/Chriss strategy is signficently sub-optimal

compared to the (pre-commitment) mean-variance strategy.

This is joint work with Stephen Tse, Heath Windcliff and

Shannon Kennedy.

Tue, 10 May 2011

14:30 - 15:30
L3

Edge colouring multigraphs

Penny Haxell
(Waterloo)
Abstract

We highlight a technique for studying edge colourings of multigraphs, due to Tashkinov. This method is a sophisticated generalisation of the method of alternating paths, and builds upon earlier work by Kierstead and Goldberg. In particular we show how to apply it to a number of edge colouring problems, including the question of whether the class of multigraphs that attain equality in Vizing's classical bound can be characterised.

This talk represents joint work with Jessica McDonald.

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