Expository talks I’ve given

The following are notes from expository talks that I’ve given. They likely contain errors: use with caution!

Talks I’ve seen

The following are notes from talks that I’ve listened to. Any errors are mine: use with caution!

Derived structures in the Langlands Program

The following are notes from a study group on derived structures in the Langlands program from 2019, organized jointly with Pol van Hoften, Alice Pozzi, and Carl Wang–Erickson

DateGalois TrackSpeakerHecke TrackSpeaker
January 9Introduction IJames NewtonIntroduction IICarl Wang-Erickson
January 16Deformations of representations of Galois groupsMisja SteinmetzIntroduction to the cohomology of arithmetic groups, I: comparison with automorphic formsChris Williams
January 23The Taylor-Wiles methodFred DiamondIntroduction to the cohomology of arithmetic groups, II: Matsushima’s formulaJoaquin Rodrigues Jacinto
January 30The obstructed Taylor–Wiles method of Calegari–GeraghtyToby GeeDerived Hecke algebra, I: Definition of Derived Hecke algebraAlice Pozzi
February 6Homotopy background I: Simplicial objectsLorenzo la PortaDerived Hecke algebra, II: Satake isomorphism, Iwahori Hecke algebraRobert Kurinczuk
February 13Homotopy background II: Model categoriesChris BirkbeckDerived Hecke algebra in the Taylor-Wiles setting, IAndrew Graham
February 20Homotopy background III: Simplicial commutative ringsRaffael SingerDerived Hecke algebra in the Taylor-Wiles setting, II: Reciprocity lawDan Gulotta
February 27Derived deformation theory in generalDougal DavisThe conjecture and its complex realizationAlex Torzewski
March 6Derived Galois deformation problemsRebecca BellovinThe complex realization of the conjectureEran Assaf
March 13The derived deformation ring and patchingAshwin IyengarThe $p$-adic ($\ell \neq p$) realization of the conjectureAna Caraiani
March 20The derived deformation ring and the derived Hecke algebraPol van HoftenThe conjecture on weight one modular formsAlice Pozzi

$p$-adic local Langlands for $\mathrm{GL}_2(\mathbb{Q}_p)$

  Study group planPDFSee PDF
AbiMay 1, 2020Mod $p$ and integral $p$-adic representations of $\mathrm{GL}_n(\mathbb{Q}_p)$Notes[Eme1], [Her1], [New]
AshwinMay 8, 2020Irreducible smooth admissible mod $p$ representations of $\mathrm{GL}_n(F)$Notes[AHHV], [Bre], [GK], [Her2], [Her3]
AndyMay 15, 2020Ext groups between irreducible representationsTyped notes and written notes[Eme2], [Oll], [Paš1], [Vig]
AshvniMay 22, 2020Banach $L$-representationsSlides and handwritten proofs[Paš2]
PolMay 28, 2020Locally finite abelian categories [Gab]
AshwinJune 5, 2020Paškūnas’s deformation theoryNotes[Paš2]
SamJune 19, 2020Galois representations and $(\varphi,\Gamma)$-modulesNotes and Video (pw: 2g@0M%8#)[Ber]
WaqarJune 26, 2020Colmez’s Montréal Functor [Col]
AshwinJuly 31, 2020Deformation Theory for Supersingular RepresentationsNotes[Kis], [Paš1], [Paš2]


Notes from the Padova Summer School

In 2019 I attended the Padova school on Serre’s conjecture and the $p$-adic Langlands program. Here are some notes from the courses taught in the conference.