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 […]
Title: Pyknotic/condensed sets II Abstract: We will continue the discussion of pyknotic sets, and introduce the notion of condensed sets.
Title: Symmetries of Fano varieties.Abstract: A landmark result of Birkar, Prokhorov, and Shramov shows that automorphism groups of Fano (or more generally rationally connected) varieties over C of a fixed dimension are […]
Title: An introduction to Hopf Rings.Abstract: An old guy’s perspective on what homotopy theory used to be about and why complex cobordism has become central to the study.And, I’ll show […]
Title: Dirac geometryAbstract: Whatever it is that animates anima and breathes life into higher algebra, this something gives the homotopy groups of a commutative algebra in spectra the structure of […]
Title: Elliptic curves and modular forms.Abstract: If you’ve heard of Fermat’s last theorem, you might have heard that its proof involves some sophisticated geometric objects that seemingly have nothing to […]
Title: Condensed abelian groups IAbstract: We will talk about the categories of κ-condensed abelian groups with Grothendieck axioms and why they are the abelian category of the nicest possible sort.
Title: Relative trace formulae and progress on the mixed truncationAbstract: After a quick (re)introduction to relative trace formulae, we shall focus on the divergence issue in establishing them. We plan […]
Title: Skein theory and the geometric Langlands program.Abstract: Skein modules are certain families of vector spaces spanned by embedded links or graphs in a 3-manifold M, modulo certain local relations. […]