Date/Time : 19 Apr 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Riccardo Brasca, Université Paris Cité

Workshop on Formal Proofs and Lean

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Date/Time : 17 Apr 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Riccardo Brasca, Université Paris Cité

Workshop on Formal Proofs and Lean

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Date/Time : 15 Apr 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Riccardo Brasca, Université Paris Cité

Workshop on Formal Proofs and Lean

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Date/Time : 06 Feb 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Ian Gleason, Universitat Bonn

The local Langlands correspondence, proposed by Langlands as the non-abelian analogue of local class field theory for non-Archimedean local fields, has been established for various reductive groups over the years. However, a construction in full generality was lacking until the recent proposal by Fargues and Scholze, who introduced semi-simplified Langlands parameters for every reductive group. Their construction employs Scholze’s theory of diamonds, a modern approach to p-adic analytic geometry. This talk begins by revisiting historical developments in number theory that led to the formulation of the local Langlands correspondence. Subsequently, we explore the relevance of p-adic analytic geometry to the study of the local Langlands program and the impact these innovative methods have on our comprehension of the local Langlands correspondence.

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Date/Time : 01 Feb 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Zhang Jiacheng, University of California, Berkeley

In this talk, we are going to talk about recent development on Stackelberg equilibrium and Mean Field Game. Stackelberg game has attracted recent interest modeling an asymmetric, general sum game between leaders and followers.

Firstly, we consider a discrete-time Stackelberg mean field game (SMFG) with one leader and an infinite number of homogeneous followers via optimization lense.We focus on a robust setting where the followers have bounded rationality and only aim at achieving some ε-Nash equilibrium (NE) while the leader wants to maximize her objective in the worst case scenario among all ε-NEs. We study the sensitivity analysis when the leader only has access to some perturbed model. We show that the value function is unstable with respect to the perturbation of the model and the leader needs to be more pessimistic and solve a relaxed problem to obtain a near optimal solution. The analysis is done by formulating this SMFG problem into an explicit minimax optimization problem and studying the sensitivity property using the optimization framework.

Second, we investigate the existence of an optimal policy to monitor a mean field system of agents managing a risky project under moral hazard with accidents modeled by L ́evy processes magnified by the law of the project. We provide a general method to find both a mean field equilibrium for the agents and the optimal compensation policy under general, sufficient and necessary assumptions on all the parameters. We formalize the problem as a bilevel optimization with the probabilistic version of a mean field game which can be reduced to a controlled McKean-Vlasov SDE with jumps. We apply our results to an optimal energy demand-response problem with a crowd of consumers subjected to power cut/shortage when the variability of the energy consumption is too high under endogenous or exogenous strains. In this example, we get an explicit solution to the mean field game and to the McKean-Vlasov equation with jumps.

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Date/Time : 31 Jan 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Matteo Mucciconi, University of Warwick

The deformed polynuclear growth is a growth process that generalizes the polynuclear growth studied in the context of KPZ universality class. In this talk, I will discuss the mathematical derivation of large time large deviations for the height function. Rare events, as functions of the time t, display distinct decay rates based on whether the height function grows significantly larger (upper tail) or smaller (lower tail) than the expected value. Upper tails exhibit an exponential decay with rate function which we determine explicitly. Conversely, the lower tails experience a more rapid decay and the rate function is given in terms of a variational problem.

Our analysis relies on two inputs. The first is a connection between the height function h and an important measure on the set of integer partitions, the Poissonized Plancherel measure, which stems from nontrivial applications of the celebrated Robinson-Schensted-Knuth correspondence. The second ingredient is the derivation of a priori convexity bounds for the rate function, which combines combinatorial and coupling arguments.

This is a joint work with S.Das (Chicago) and Y.Liao (Wisconsin-Madison).

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Date/Time : 29 Jan 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Jimmy He, Massachusetts Institute of Technology

Random growth models in 1+1 dimension capture the behavior of interfaces evolving in the presence of noise. These models are expected to exhibit universal behavior, but we are still far from proving such results even in relatively simple models. A key development which has led to recent progress is the discovery of exact formulas for certain models with rich algebraic structure, leading to asymptotic results. I will survey some of these results, with a focus on models where a single boundary wall is present, as well as applications to rates of convergence for a Markov chain.

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Date/Time : 22 Jan 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Yang Lei, Institute for Advanced Study

I will talk about recent progress in the study of quantitative equidistribution of unipotent orbits in homogeneous spaces, namely, effective versions of Ratner’s equidistribution theorem. I will sketch the main idea of my proof for unipotent orbits in SL(3,R)/SL(3,Z). The proof combines new ideas from harmonic analysis and incidence geometry. In particular, the quantitative behavior of unipotent orbits is closely related to a Kakeya model.

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Date/Time : 15 Jan 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Liu Jialin, Alibaba Group (U.S.) Inc, Damo Academy

AI and data science have demonstrated remarkable promise in enhancing optimization algorithms. Utilizing AI/ML techniques, we aim to complement and potentially enhance traditional optimization methods, offering improvements in aspects like computational speed and solution quality. Despite these advancements, a deep, systematic understanding of these methods remains underdeveloped. In this talk, the speaker will demonstrate through concrete examples how mathematical tools, particularly optimization theory, can be used to unravel the mysteries of these ‘black boxes’. The speaker will also discuss the development of interpretable and reliable AI models for optimization, grounded in these mathematical principles.

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