Abstract: I will describe how the ADE preprojective algebras appear in
certain Conformal Field Theories, namely SU(2) WZW models, and explain
the generalisation to the SU(3) case, where 'almost CY3' algebras appear.
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.
Abstract: This is joint work with Ragnar-Olaf Buchweitz and Colin Ingalls.
The classical McKay correspondence relates the geometry of so-called
Kleinian surface singularities with the representation theory of finite
subgroups of SL(2,C). M. Auslander observed an algebraic version of this
correspondence: let G be a finite subgroup of SL(2,K) for a field K whose
characteristic does not divide the order of G. The group acts linearly on
the polynomial ring S=K[x,y] and then the so-called skew group algebra
A=G*S can be seen as an incarnation of the correspondence. In particular
A is isomorphic to the endomorphism ring of S over the corresponding
Kleinian surface singularity.
Our goal is to establish an analogous result when G in GL(n,K) is a finite
subgroup generated by reflections, assuming that the characteristic
of K does not divide the order of the group. Therefore we will consider a
quotient of the skew group ring A=S*G, where S is the polynomial ring in n
variables. We show that our construction yelds a generalization of
Auslander's result, and moreover, a noncommutative resolution of the
discriminant of the reflection group G.
Abstract: Joint work with Carlson, Grodal, Nakano. In this talk we will
present some recent results on an 'important' class of modular
representations for an 'important' class of finite groups. For the
convenience of the audience, we'll briefly review the notion of an
endotrivial module and present the main results pertaining endotrivial
modules and finite reductive groups which we use in our ongoing work.
I shall describe recent work with Srikanth Iyengar, Henning
Krause and Julia Pevtsova on the representation theory and cohomology
of finite group schemes and finite supergroup schemes. Particular emphasis
will be placed on the role of generic points, detection of projectivity
for modules, and detection modulo nilpotents for cohomology.
We discuss pathwise pricing-hedging dualities in continuous time and on a frictionless market consisting of finitely many risky assets with continuous price trajectories.
In this paper, we consider the pricing and hedging of a financial derivative for an insider trader, in a model-independent setting. In particular, we suppose that the insider wants to act in a way which is independent of any modelling assumptions, but that she observes market information in the form of the prices of vanilla call options on the asset. We also assume that both the insider’s information, which takes the form of a set of impossible paths, and the payoff of the derivative are time-invariant. This setup allows us to adapt recent work of Beiglboeck, Cox, and Huesmann [BCH16] to prove duality results and a monotonicity principle, which enables us to determine geometric properties of the optimal models. Moreover, we show that this setup is powerful, in that we are able to find analytic and numerical solutions to certain pricing and hedging problems. (Joint with B. Acciaio and M. Huesmann)
Rita Maria del Rio Chanona:
Global financial contagion on a Multiplex Network
We explore the global financial system, in particular the risk of global financial contagion through network theory. Although there is extensive literature on contagion in networks, we argue that it is important to consider different channels of contagion. Therefore we deem into the multilayer framework, where nodes are countries and each layer represents a different type of financial obligation. The multiplex network is built using data provided by collaborators in the IMF. We study contagion with a percolation model and conclude that financial shocks can be amplified considerably when the multilayer structure is taken into account.
Johannes Wiesel:
Robust Superhedging vs Robust Statistics
In this talk I try to reconcile the different understanding of robustness in mathematical finance and statistics. Motivated by recent advances in the estimation of risk measures, I present estimators for the superhedging price of a claim given a history of observed prices. I discuss weak efficiency and convergence speed of these estimators. Besides I explain how to apply classical notions of sensitivity for the estimation procedure. This talk is based on ongoing work with Jan Obloj.