Lukas Kofler's homepage

Lukas Kofler

(under construction)

Welcome to my webpage! I am a second year PhD student at the University of Cambridge. I am funded through the Richard Metheringham Scholarship of the Worshipful Company of Cutlers and through the DPMMS.
My supervisor is Tony Scholl.

You can send me an email at lukas.kofler(at)maths(dot)cam(dot)ac(dot)uk. My office is E0.12.

Research

My research interests are algebraic number theory and the Langlands programme, especially (the reduction of) Shimura varieties and motives.

Currently I am trying to generalise the gerbe-theoretic formalism describing the reduction modulo p of a Shimura variety due to Langlands-Rapoport, using results of Kottwitz and Scholl.

Reading groups I've participated in

  • Easter 2022: Guillem Garcia Tarrach and I are organising a reading group on the Arthur-Selberg Trace Formula for GL2. We meet on Thursdays at 2:30pm.
  • Lent 2022: Further Developments in Deligne-Lusztig Theory
  • Lent 2022: p-adic Hodge theory (Oxford)
  • Michaelmas 2021: Cycles on Shimura varieties following this paper. I talked about Arakelov Theory and Arithmetic Intersection Theory.
  • Michaelmas 2021: Etale Cohomology (Oxford)
  • Summer 2021: Non-archimedean geometry (LSGNT). I talked about the Berkovich spectrum and affine line.
  • Lent and Easter 2021: Automorphy Lifting Theorems
  • Michaelmas 2020: Mazur's torsion paper
  • Summer 2020: Etale Cohomology
  • Other talks I've given

  • Cambridge Number Theory Mini Conference: The Langlands-Rapoport Conjecture
  • Cambridge Number Theory Seminar: A Deuring Criterion for Abelian Varieties
  • Conferences and workshops I've been to or will go to

  • JNT Biennial Conference (Cetraro)
  • Motives and Arithmetic Groups (Strasbourg)
  • Other notes

  • I wrote my Smith-Knight Rayleigh-Knight Prize Essay on Plectic Hodge Structures and Equivariant Sheaves.
  • A note on the Langlands-Rapoport Conjecture for a modular curve: matching isogeny classes with admissible gerbe homomorphisms
  • My Part III essay on the Grunwald-Wang Theorem.