Abstract: Dyadic models for the magnetohydrodynamics with Hall effect are derived in the way intermittency dimension enters the modeling naturally as a parameter. Existence of weak solutions, local strong solution, and global strong solution are obtained for suitable values of the intermittency dimension, respectively. Moreover, finite time blow-up can occur for positive solutions when the intermittency dimension is below a threshold.

]]>Abstract: Recently, Chatterjee and Diaconis showed that most bijections, if applied between steps of a Markov chain, cause the resulting chain to mix much faster. However, explicit examples of this speedup phenomenon are rare. I will discuss recent work studying such walks on finite fields where the bijection is algebraically defined, and give a near-linear mixing time. This work gives a large collection of examples where this speedup phenomenon occurs. These walks can be seen as a non-linear analogue of the Chung-Diaconis-Graham process, where the bijection is multiplication by a non-zero element of the finite field.

]]>Abstract: In this talk, we present a flexible technique to solve the continuous-time multi-asset/multi-option Kyle model under general assumptions on the distribution of the noise, and the distribution of the prior. The main insight is to postulate the pricing rule of the market maker at maturity as an optimal transport map. If the informed agent is risk averse, we show that our methodology yields to the existence of equilibrium by considering a system of backward quasilinear parabolic equation and a forward Fokker-Planck equation coupled via a transport type constraint at final time. Based on joint works with F. Cocquemas, A. Lioui and S. Bose.

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Abstract: TBA

Abstract: For various general random matrix models with integral entries we discuss the probability that the cokernels are isomorphic to a given finite abelian group, or when they are cyclic. We will show that these statistics are asymptotically universal, depending only on the symmetry class of the matrices.

Based on joint works with M. M. Wood.

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