Tue, 12 Jun 2018

Decomposition spaces: theory and applications

Andrew Tonks

Decomposition (aka unital 2-Segal) spaces are simplicial ∞-groupoids with a certain exactness property: they take pushouts of active (end-point preserving) along inert (distance preserving) maps in the simplicial category Δ to pullbacks. They encode the information needed for an 'objective' generalisation of the notion of incidence (co)algebra of a poset, and motivating examples include the decomposition spaces for (derived) Hall algebras, the Connes-Kreimer algebra of trees and Schmitt's algebra of graphs. In this talk I will survey recent activity in this area, including some work in progress on a categorification of (Hopf) bialgebroids.
This is joint work with Imma Gálvez and Joachim Kock.

Thu, 24 Aug 2017

10:00 - 11:00

New varieties for algebras

Sibylle Schroll (Leicester)

Abstract: In this talk, we will introduce new affine algebraic varieties 
for algebras given by quiver and relations. Each variety contains a 
distinguished element in the form of a monomial algebra. The properties 
and characteristics of this monomial algebra govern those of all other 
algebras in the variety. We will show how amongst other things this gives 
rise to a new way to determine whether an algebra is quasi-hereditary. 
This is a report on joint work both with Ed Green and with Ed Green and 
Lutz Hille.

Tue, 26 Apr 2016

14:15 - 15:30

Multiserial and Special Multiserial Algebras

Sibylle Schroll

The class of multiserial algebras contains many well-studied examples of algebras such as the intensely-studied biserial and special biserial algebras. These, in turn, contain many of the tame algebras arising in the modular representation theory of finite groups such as tame blocks of finite groups and all tame blocks of Hecke algebras. However, unlike  biserial algebras which are of tame representation type, multiserial algebras are generally of wild representation type. We will show that despite this fact, we retain some control over their representation theory.

Mon, 20 Oct 2008
Oxford-Man Institute

Wiener-Hopf factorization as a general method for valuation of real and American options

Prof. Sergei Levendorskii
A new general approach to optimal stopping problems in L\'evy models, regime switching L\'evy models and L\'evy models with stochastic volatility and stochastic interest rate is developed. For perpetual options, explicit solutions are found, for options with finite time horizon, time discretization is used, and explicit solutions are derived for resulting sequences of perpetual options.

The main building block is the option to abandon a monotone payoff stream. The optimal exercise boundary is found using the operator form of the Wiener-Hopf method, which is standard in analysis, and interpretation of the factors as {\em expected present value operators} (EPV-operators) under supremum and infimum processes.

Other types of options are reduced to the option to abandon a monotone stream. For regime-switching models, an additional ingredient is an efficient iteration procedure.

L\'evy models with stochastic volatility and/or stochastic interest rate are reduced to regime switching models using discretization of the state space for additional factors. The efficiency of the method for 2 factor L\'evy models with jumps and for 3-factor Heston model with stochastic interest rate is demonstrated. The method is much faster than Monte-Carlo methods and can be a viable alternative to Monte Carlo method as a general method for 2-3 factor models.

Joint work of Svetlana Boyarchenko,University of Texas at Austin and Sergei Levendorski\v{i},

University of Leicester

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