Title: Canonical representations of surface groups.Abstract: For $Sigma_{g,n}$ a genus $g$ surface with $n$ punctures, we study the character variety parameterizing representations of $pi_1(Sigma_{g,n})$. This character variety has a natural action of […]
Title: Twisted GGP conjecture for unramified quadratic extensions Abstract: The twisted Gan--Gross--Prasad conjectures consider the restriction of representations from GL_n to a unitary group over a quadratic extension E/F. In […]
Title: Introduction to the trace formula. (Cont.)Abstract: In the first talk I presented some useful notions and translations in the theory of automorphic representations (Hecke operators and p-adic groups, locally […]
Title: A reintroduction to proofs Abstract: An introduction to proofs course aims to teach how to write proofs informally in the language of set theory and classical logic. In this […]
Title: Maximal Subellipticity Abstract: The theory of elliptic PDE stands apart from many other areas of PDE because sharp results are known for very general linear and fully nonlinear elliptic PDE. […]
Title: Pyknotic setsAbstract: In this talk, I will introduce the idea of Pyknotic/Condensed sets and how they can potentially be used to solve the problem of the category of topological […]
Title: On the cone conjecture for log Calabi-Yau threefolds.Abstract: Let $Y$ be a smooth projective threefold admitting a $K3$ fibration $f: Y rightarrow mathbb{P}^{1}$ with $-K_{Y} = f^{ast} mathcal{O}(1)$. Then the extremal […]
Title: Modularity of trianguline Galois representations Abstract: The Fontaine-Mazur conjecture (proved by Kisin and Emerton) says that (under certain technical hypotheses) a Galois representation rho: Gal_Q -> GL2(Qp) is modular […]
Title: Speculations on Computing with the Relative Trace FormulaAbstract: I will discuss and motivate the problem of computing statistics of automorphic representations. Many statistics have been computed previously using "explicit" forms […]
Title: A Generalization of the Geroch Conjecture with Arbitrary EndsThe Geroch conjecture (proven by Schoen-Yau and Gromov-Lawson) says that the torus T^n does not admit a metric of positive scalar […]
Title: Tannaka duality for algebraic 2-groupsAbstract: The Tannakian formalism is a web of statements which, in its most basic form, attempts to recover a group G from its symmetric monoidal […]