Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
27 September 2018
14:00
Abstract

For a reductive group $ G $, Steinberg established a map from the Weyl group to nilpotent $ G $-orbits using momentmaps on double flag varieties.  In particular, in the case of the general linear group, he re-interpreted the Robinson-Schensted correspondence between the permutations and pairs of standard tableaux of the same shape in terms of product of complete flags.

We generalize his theory to the case of symmetric pairs $ (G, K) $, and obtained two different maps.  In the case where $ (G, K) = (\GL_{2n}, \GL_n \times \GL_n) $, one of the maps is a generalized Steinberg map, which induces a generalization of the RS correspondence for degenerate permutations.  The other is an exotic moment map, which maps degenerate permutations to signed Young diagrams, i.e., $ K $-orbits in the Cartan space $ (\lie{g}/\lie{k})^* $.

We explain geometric background of the theory and combinatorial procedures which produces the above mentioned maps.

This is an on-going joint work with Lucas Fresse.
 

8 October 2018
14:15
ELISA ALOS ALCALDE
Abstract

We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to describe the properties of the at-the-money implied volatility (ATMI) in terms of the Malliavin derivatives of the underlying process. More precisely, we study the short-time behaviour of the ATMI level and skew. As an application, we describe the short-term behavior of the ATMI of VIX and realized variance options in terms of the Hurst parameter of the model, and most importantly we describe the class of volatility processes that generate a positive skew for the VIX implied volatility. In addition, we find that our ATMI asymptotic formulae perform very well even for large maturities. Several numerical examples are provided to support our theoretical results.  

  • Stochastic Analysis Seminar
8 October 2018
14:15
Frances Kirwan
Abstract
When a complex reductive group acts linearly on a projective variety, the GIT quotient can be identified with an appropriate symplectic quotient. The aim of this talk is to discuss an analogue of this description for GIT quotients by suitable non-reductive actions. In general GIT for non-reductive linear algebraic group actions is much less well behaved than for reductive actions. However when the unipotent radical U of a linear algebraic group is graded, in the sense that a Levi subgroup has a central one-parameter subgroup which acts by conjugation on U with all weights strictly positive, then GIT for a linear action of the group on a projective variety has better properties than in the general case, and (at least under some additional conditions) we can ask for moment map descriptions of the quotients.
  • Geometry and Analysis Seminar
8 October 2018
15:45
Abstract

We study several important fine properties for the family of fractional Brownian motions with Hurst parameter H under the (p,r)-capacity on classical Wiener space introduced by Malliavin. We regard fractional Brownian motions as Wiener functionals via the integral representation discovered by Decreusefond and \"{U}st\"{u}nel, and show non differentiability, modulus of continuity, law of iterated Logarithm(LIL) and self-avoiding properties of fractional Brownian motion sample paths using Malliavin calculus as well as the tools developed in the previous work by Fukushima, Takeda and etc. for Brownian motion case.

 

  • Stochastic Analysis Seminar
9 October 2018
12:00
to
13:15
Chris White
Abstract

Non-abelian gauge theories underly particle physics, including collision processes at particle accelerators. Recently, quantum scattering probabilities in gauge theories have been shown to be closely related to their counterparts in gravity theories, by the so-called double copy. This suggests a deep relationship between two very different areas of physics, and may lead to new insights into quantum gravity, as well as novel computational methods. This talk will review the double copy for amplitudes, before discussing how it may be extended to describe exact classical solutions such as black holes. Finally, I will discuss hints that the double copy may extend beyond perturbation theory. 

9 October 2018
12:00
Lyuba V. Bozhilova
Abstract

Many protein interaction databases provide confidence scores based on the experimental evidence underpinning each in- teraction. The databases recommend that protein interac- tion networks (PINs) are built by thresholding on these scores. We demonstrate that varying the score threshold can re- sult in PINs with significantly different topologies. We ar- gue that if a node metric is to be useful for extracting bio- logical signal, it should induce similar node rankings across PINs obtained at different thresholds. We propose three measures—rank continuity, identifiability, and instability— to test for threshold robustness. We apply these to a set of twenty-five metrics of which we identify four: number of edges in the step-1 ego network, the leave-one-out dif- ference in average redundancy, average number of edges in the step-1 ego network, and natural connectivity, as robust across medium-high confidence thresholds. Our measures show good agreement across PINs from different species and data sources. However, analysis of synthetically gen- erated scored networks shows that robustness results are context-specific, and depend both on network topology and on how scores are placed across network edges. 

9 October 2018
14:15
to
15:30
Dima Pasechnik
Abstract

Abstract regular polytopes are finite quotients of Coxeter complexes
with string diagram, satisfying a natural intersection property, see
e.g. [MMS2002]. They arise in a number of geometric and group-theoretic
contexts. The first class of such objects, beyond the
well-understood examples coming from finite and affine Coxeter groups,
are locally toroidal cases, e.g.  extensions of quotients of the affine
F_4 complex [3,3,4,3].  In 1996 P.McMullen & E.Schulte constructed a
number of examples of locally toroidal abstract regular polytopes of
type [3,3,4,3,3], and conjectured completeness of their list. We
construct counterexamples to the conjecture using a Y-shaped
presentation for a subgroup of the Monster, and discuss various
related questions.
 

9 October 2018
16:00
Joel David Hamkins
Abstract

Abstract: The universal algorithm is a Turing machine program that can in principle enumerate any finite sequence of numbers, if run in the right model of PA, and furthermore, can always enumerate any desired extension of that sequence in a suitable end-extension of that model. The universal finite set is a set-theoretic analogue, a locally verifiable definition that can in principle define any finite set, in the right model of set theory, and can always define any desired finite extension of that set in a suitable top-extension of that model. Recent work has uncovered a $\Sigma_1$-definable version that works with respect to end-extensions. I shall give an account of all three results, which have a parallel form, and describe applications to the model theory of arithmetic and set theory. Post questions and commentary on my blog at http://jdh.hamkins.org/parallels-in-universality-oxford-math-logic-semin...

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