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Relevant consequence relations021 (Ludwigstr. 31, 80539 München)

This paper, based on joint work with Badia, Behounek, and Cintula, concerns a generalisation of the Tarskian definition of consequence relation to accommodate relevant logics. In particular, these are non-monotone multiset consequence relations. In this course of the talk, I present some motivations for the central definitions (building on a picture of relevance as it concerns derivations in an axiomatic system), consider a range of examples, and study the properties of these consequence relations. The upshot is to capture the idea that relevant implication expresses the real consequence relation of these logics, and to study what these consequence relations must look like when studied from a more abstract perspective.

Continuous symmetry breaking and synchronization problemA027 (Theresienstraße 39, 80333 Mathematisches Institut, LMU)

In this talk, I will start by introducing spin systems on the lattice Z^d. I will then focus mainly on spin systems whose underlying symmetry is continuous (as opposed to the celebrated Ising model whose symmetry sigma->-sigma is discrete). The goal of this talk will be to explain a surprising link which appeared recently between these models in statistical physics and questions in Bayesian statistics / statistical reconstruction. I will introduce a new way to identify long-range-order in these spins systems with continuous symmetry (also called "symmetry breaking") which is based on the concept of "group synchronization" and relies in particular on a recent work by Abbe, Massoulié, Montanari, Sly and Srivastava (2018).

The talk will not require any background in statistical physics. This is a joint work with Thomas Spencer (IAS, Princeton).

The HYL model and random interlacements2.02.01 (Parkring 11, 85748 Garching-Hochbrück)

In this talk, we compute the thermodynamic limit of the loop-HYL model, an approximation to the Feynman representation of the hard-core Bose gas. We show that the excess density concentrates on the random interlacements, with a discontinuity at the critical point. Joint work with Matthew Dickson, LMU.

Convex stochastic optimizationA027 (Theresienstraße 39, 80333 Mathematisches Institut, LMU)

We study dynamic programming, duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in the 70s. We give a general formulation of the dynamic programming recursion and derive an explicit dual problem in terms of two dual variables, one of which is the shadow price of information while the other one gives the marginal cost of a perturbation much like in classical Lagrangian duality. Existence of primal solutions and the absence of duality gap are obtained without compactness or boundedness assumptions. In the context of financial mathematics, the relaxed assumptions are satisfied under the well-known no-arbitrage condition and the reasonable asymptotic elasticity condition of the utility function. We extend classical portfolio optimization duality theory to problems of optimal semi-static hedging. Besides financial mathematics, we obtain several new results in stochastic programming and stochastic optimal control.

LMU Christmas Workshop in Stochastics and Finance A 027 (Theresienstraße 39, 80333 München)

https://www.fm.mathematik.uni-muenchen.de/teaching/teaching_winter_term_2022_2023/seminars/christmas_workshop/index.html

Interacting diffusion on random graphs03.06.011 (Boltzmannstr. 3, 85748 Garching-Hochbrück)

In this talk we will talk about a class of particle system defined on top of random graphs that has the stochastic Kuramoto model as a particular example. We are interested on limit theorems for the empirical measure of the particles. In other words, we investigate the behavior of a typical particle proving law of large numbers and large deviations results. The graphs we consider include the Erdös-Rényi graph with different levels of sparsity.

"Into the wild: An invitation to turbulent completely integrable systems"A 027 (Theresienstraße 39, 80333 München)

The discovery of solitons and completely integrable partial differential equations (PDEs) provides a paradigm in mathematics and modern physics. Its impact on the development of PDEs in physics (both classical and quantum), pure analysis, and differential geometry can hardly be overrated. In this colloquium talk, I will give an introduction to a class of newly discovered completely integrable PDEs, which exhibit turbulent behavior, i.e., the degree of smoothness of solutions cannot be generally controlled by an infinite hierarchy of conservation laws and thus singularities can form. Indeed, these systems can be seen as infinite-dimensional continuum versions of classical so-called Calogero-Moser systems introduced by Francesco Calogero and Jürgen Moser in 1970s. Part of my talk is based on joint work with Patrick Gérard (Paris-Sud).

TBA2.02.01 (Parkring 11, 85748 Garching-Hochbrück)

TBA