University of Chicago

Department of Mathematics

5734 S University Ave

Chicago, IL 60637

E-mail: nick [at] math [dot] uchicago [dot] edu

**About me**

I am interested in algebraic geometry and topology, particularly in algebraic geometric and homotopical structures arising from topological quantum field theory and representation theory.

**Writing**

Volume I: Correspondences and duality

Volume II: Deformations, Lie theory and formal geometry

- The cyclic Deligne conjecture and Calabi-Yau structures (joint with C. Brav)
- Connections on moduli spaces and infinitesimal Hecke modifications
- Derived Mackey functors and C_{p^n}-equivariant cohomology (joint with D. Ayala and A. Mazel-Gee)
- Automorphic functions as the trace of Frobenius (joint with D. Arinkin, D. Gaitsgory, D. Kazhdan, S. Raskin, and Y. Varshavsky)
- Duality for automorphic sheaves with nilpotent singular support (joint with D. Arinkin, D. Gaitsgory, D. Kazhdan, S. Raskin, and Y. Varshavsky)
- The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support (joint with D. Arinkin, D. Gaitsgory, D. Kazhdan, S. Raskin, and Y. Varshavsky)
- A toy model for the Drinfeld-Lafforgue shtuka construction (joint with D. Gaitsgory, D. Kazhdan, and Y. Varshavsky)
- Stratified noncommutative geometry (joint with D. Ayala and A. Mazel-Gee)
- A naive approach to cyclotomic spectra (joint with D. Ayala and A. Mazel-Gee)
- Factorization homology of enriched ∞-categories (joint with D. Ayala and A. Mazel-Gee)
- Geometry of the cyclotomic trace (joint with D. Ayala and A. Mazel-Gee)
- Gaiotto's Lagrangian subvarieties via derived symplectic geometry (joint with V. Ginzburg)
- Factorization homology I: Higher categories (joint with D. Ayala and J. Francis)
- A stratified homotopy hypothesis (joint with D. Ayala and J. Francis)
- Crystals and D-modules (joint with D. Gaitsgory)
- DG Indschemes (joint with D. Gaitsgory)
- Modules Over a Chiral Algebra

**Notes/Talks**

Introduction to Chiral Algebras (Notes from 2009 Graduate Geometric Representation Theory Seminar)