Title: Rectification of Coalgebras Abstract: There are two ways of talking about homotopy coherent algebras. One is to use model theoretic ideas: given a nice model category (C, W), one gets a right induced model structure on Alg(C). Second, one can use infinity category methods. Any nice model category (C, W) has an infinity categorical […]
Title: Transfer operators for the relative trace formula. Abstract: Transfer operators are operators between spaces of test measures on different groups, whose duals are supposed to realize the transfer of (stable) characters predicted by Langlands functoriality. I will explain how this concept generalizes to the setting of the relative trace formula, and present some formulas […]
Tittle: Partial regularity for Lipschitz solutions to the minimal surface system Abstract: The minimal surface system is the Euler-Lagrange system for the area functional of a high codimension graph and reduces to the minimal surface equation in the case that the codimension is one. Though the regularity theory for the minimal surface equation is well understood, […]
Title: Formalizing ∞-Category Theory in Lean
Title: The local theta correspondence and functoriality Abstract: In a letter to Howe, Langlands conjectured that the local theta correspondence is an instance of Langlands functoriality, e.g., it should preserve L-packets. Unfortunately, this was false. As a remedy, Adams conjectured that instead of L-packets, the local theta correspondence should preserve Arthur packets. Mœglin showed that […]
Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this talk, I will present a Krylov subspace based iterative method for solving linear inverse problems with general-form Tikhonov regularization term $x^top M x$ , where $M$ is a positive semidefinite matrix. An iterative […]
Title: Towards A-theory of orbifoldsAbstract: Waldhausen's A-theory of spaces — an extension of Quillen's higher algebraic K-theory of rings — is central to the study of moduli spaces of manifolds. In this talk, we will discuss a generalization of A-theory that takes as input an orbifold and which we expect to have rich geometric applications in analogy with the manifold setting. An orbifold is […]
Title: An Euler system of Heegner type Abstract: In this talk, I will present the result of Cornut in his paper "An Euler system of Heegner type" where he constructed the Kolyvagin Euler system associated with the spherical pair (SO(2n+1),U(n)) by reducing the local Horizontal norm relation to a divisibility result on integral Hecke module, […]
Topic: Formalizing ∞-Category Theory in Lean
Title: The Lawson-Osserman conjecture for the minimal surface systemAbstract: In their seminal work on the minimal surface system, Lawson and Osserman conjectured that Lipschitz graphs that are critical points of the area functional with respect to outer variations are also critical with respect to domain variations. We will discuss the proof of this conjecture for […]
Title: Relative Satake isomorphism and Euler systems Abstract: Starting from the inversion formula for the relative Satake isomorphism due to Sakellaridis, we observe a simple additional divisibility property. We will then explain how this gives a computation-free construction of Euler systems in some settings. This is joint work with Li Cai and Yangyu Fan.
Title: Towards the quantum exceptional series Abstract: Many Lie algebras fit into discrete families like GL(n), On, Spn. By work of Brauer, Deligne and others, the corresponding tensor categories fit into continuous familes GL(t) and OSp(t). A similar story holds for quantum groups, so we can speak of two parameter families GL(t)_q and OSp(t)_q. Thesetensor categories […]