Talk, Babytop seminar, MIT
I defined the etale and pro-etale sites of rigid analytic spaces, and explained how when the base field contains the p-adic numbers that affinoid perfectoid objects form a basis for the pro-etale topology. I then went through some propositions about condensed pro-etale cohomology needed in this paper. Notes can be found here.
Talk, Mark Seminar, Harvard
I discussed the definition of the arc-topology on qcqs schemes, giving useful criteria for checking arc descent. I then explained arc and arc_p-descent of etale cohomology (which is what is used in the proof of the etale comparison theorem for prismatic cohomology). Notes can be found here.
Talk, Mark Seminar, Harvard
I talked about the basics of adic spaces and gave a quick introduction to perfectoid spaces, closely following the approach in Scholze’s thesis. I then explain some of the main ideas in Scholze’s proof of Faltings’ almost purity theorem. Notes can be found here.
Talk, Zygotop, Harvard
I gave a talk on the Beilinson fiber square, following the approach of Antieau-Mathew-Morrow-Nikolaus. I also talked on the applications of this result they give towards the p-adic variational Hodge conjecture, refining a result of Bloch-Esnault-Kerz. The notes can be found here.
Talk, Trivial notions, Harvard
I gave a talk on how the twistor line can be used to reformulate some statements in Hodge theory, presenting it in a form parallel to the role of the Fargues-Fontaine curve in p-adic Hodge theory. Notes are here.
Talk, Geometric Langlands Support Group, Harvard
I talked about how cohomology of shtukas can be assembled into a sheaf on a certain stack of local systems. It is now known that this sheaf and the cohomologies can also be produced via categorical traces (in the unramified setting), which amounts to what is called the trace conjecture. Following Gaitsgory’s argument, I sketch how the trace conjecture is true in a certain toy model. Notes are here
Talk, FLT Seminar, MIT
I presented in this seminar on the motivation for Serre’s conjecture on mod l Galois representations.
Talk, Non-Abelian Hodge theory seminar, Harvard
I presented on a result of Esnault and Groechenig that rigid flat connections have nilpotent p-curvature. Slides are here.
Talk, Geometric representation theory seminar, Harvard
I talked about the nearby cycles functor, and discussed the proof of Beilinson gluing. Notes are here.
Talk, Trivial notions seminar, Harvard
I talked about classical Honda-Tate theory, as well as recent developments that allow us to describe the full category of abelian varieties over a finite field rather than just the isogeny category. Notes are here.