Past

A new portfolio choice model in continuous time is formulated and solved, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as the decision variable. This formulation covers and leads to solutions to many existing and new models including expected utility maximisation, mean-variance, goal reaching, VaR and CVaR, Yaari's dual model, Lopes' SP/A model, and behavioural model under prospect theory.

The problem of Anderson localization in graphene

has generated a lot of renewed attention since graphene flakes

have been accessible to transport and spectroscopic probes.

The popularity of graphene derives from it realizing planar Dirac

fermions. I will show under what conditions disorder for

planar Dirac fermions does not result in localization but rather in a

metallic state that might be called a topological metal.

I will talk about recent work concerning the Onsager equation on metric

spaces. I will describe a framework for the study of equilibria of

melts of corpora -- bodies with finitely many

degrees of freedom, such as stick-and-ball models of molecules.

We introduce a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution for the BSDEs by using a penalization approach. Moreover, we show that under mild conditions the minimal solutions to these constrained BSDEs can be characterized as the unique viscosity solution of quasi-variational inequalities (QVIs), which leads to a probabilistic representation for solutions to QVIs. Such a representation in particular gives a new stochastic formula for value functions of a class of impulse control problems. As a direct consequence we obtain a numerical scheme for the solution of such QVIs via the simulation of the penalized BSDEs. This talk is based on joint work with I. Kharroubi, J. Ma and J. Zhang.

In this talk I will present recent results on ergodicity of Markov semigroups in large dimensional spaces including interacting Levy type systems as well as some R-D models.

Abstract: In this talk, I will give an overview of the new developments in the AdS_4/CFT_3 correspondence. I will present in detail an N=6 Chern-Simons-matter theory with gauge group U(N) x U(N) that is dual to N M2 branes in the orbifold C^4/Z_k. This theory can be derived from a construction involving D3 branes intersecting (p,q) fivebranes. I will also discuss various quantum mechanical aspects of this theory, including an enhancement of its supersymmetry algebra at Chern-Simons levels 1 and 2, and some novel phenomenon that arise in the U(N) x U(M) theory dual to configurations with N-M fractional branes. A generalization to N=3 CSM theories dual to AdS_4 x M_7, where M_7 is a 3-Sasakian 7-manifold, will be explained. The seminar will be based primarily on Aharony, Bergman, DJ, Maldacena; Aharony, Bergman, DJ; DJ, Tomasiello.

We prove existence of equilibrium in a continuous-time securities market in which the securities are potentially dynamically complete: the number of securities is at least one more than the number of independent sources of uncertainty. We prove that dynamic completeness of the candidate equilibrium price process follows from mild exogenous assumptions on the economic primitives of the model. Our result is universal, rather than generic: dynamic completeness of the candidate equilibrium price process and existence of equilibrium follow from the way information is revealed in a Brownian filtration, and from a mild exogenous nondegeneracy condition on the terminal security dividends. The nondegeneracy condition, which requires that finding one point at which a determinant of a Jacobian matrix of dividends is nonzero, is very easy to check. We find that the equilibrium prices, consumptions, and trading strategies are well-behaved functions of the stochastic process describing the evolution of information.

We prove that equilibria of discrete approximations converge to equilibria of the continuous-time economy

We show how the circle method with a suitably chosen Gaussian weight can be used to count unweighted zeros of polynomials. Tschinkel's problem asks for the density of solutions to Diophantine equations with S-unit and integral variables.

We consider the symmetric group S_n of degree n and an algebraically

closed field F of prime characteristic p.

As is well-known, many representation theoretical objects of S_n

possess concrete combinatorial descriptions such as the simple

FS_n-modules through their parametrization by the p-regular partitions of n,

or the blocks of FS_n through their characterization in terms of p-cores

and p-weights. In contrast, though closely related to blocks and their

defect groups, the vertices of the simple FS_n-modules are rather poorly

understood. Currently one is far from knowing what these vertices look

like in general and whether they could be characterized combinatorially

as well.

In this talk I will refer to some theoretical and computational

approaches towards the determination of vertices of simple FS_n-modules.

Moreover, I will present some results concerning the vertices of

certain classes of simple FS_n-modules such as the ones labelled by

hook partitions or two part partitions, and will state a series of

general open questions and conjectures.