Karol Koziol

I am a postdoctoral assistant professor in the mathematics department at The University of Michigan. I am interested in various aspects of the (local) Langlands Program, specifically representation theory of p-adic reductive groups, associated Hecke algebras, and Galois representations.

My research is partially supported by NSF grant DMS-2101836.

I am currently (Fall 2021) on the job market.

Previously, I was
• a postdoctoral fellow at The University of Alberta, working with Manish Patnaik;
• an NSF Postdoctoral Fellow at The University of Toronto, with sponsor Florian Herzig;
• an EPDI Postdoctoral Fellow at the Institut des Hautes Études Scientifiques and the Max Planck Institute for Mathematics;
• a graduate student at Columbia University under the supervision of Rachel Ollivier;
• an undergrad at NYU.

Organization

MANTIS 2021

RTG Representation Theory

Representations of p-adic groups and Langlands correspondences

POINT: New Developments in Number Theory

Cross Atlantic Representation Theory and Other topics ONline (CARTOON) Conference

RTG Seminar on Number Theory

Publications and Preprints

Functorial properties of pro-p-Iwahori cohomology
J. London Math. Soc. (2) 104 (2021) 1572-1614. Journal

On the existence of admissible supersingular representations of p-adic reductive groups (with Florian Herzig and Marie-France Vignéras, and an appendix by Sug Woo Shin)
Forum of Mathematics, Sigma 8 (2020), e2. Journal

Serre weight conjectures for p-adic unitary groups of rank 2 (with Stefano Morra)
To appear in Algebra & Number Theory

The first pro-p-Iwahori cohomology of mod-p principal series for p-adic GL_n
Trans. Amer. Math. Soc. 372 (2019), 1237-1288. Journal

Hecke module structure on first and top pro-p-Iwahori cohomology
Acta Arithmetica 186 (2018), 349-376. Journal

Irreducible admissible mod-p representations of metaplectic groups (with Laura Peskin)
Manuscripta Math. 155 (2018), no. 3-4, 539-577. Journal

Homological dimension of simple pro-p-Iwahori--Hecke modules
Math. Res. Lett. 26 (2019), no. 3, 769-804. Journal

Pro-p-Iwahori invariants for SL₂ and L-packets of Hecke modules
International Mathematics Research Notices (2016), no. 4, 1090-1125. Journal

A Classification of the Irreducible mod-p Representations of U(1,1)(Q_p²/Q_p)
Annales de l'Institut Fourier 66 (2016), no. 4, 1545-1582. Journal

Hecke Modules and Supersingular Representations of U(2,1) (with Peng Xu)
Representation Theory 19 (2015), 56-93. Journal

Notes

p-modular Representations of p-adic Groups - Notes for a minicourse given by Florian Herzig at IMS Singapore, April 2013
DG Hecke modules - Notes about Schneider's derived equivalence
On mod p orientation characters (with David Schwein) - Short note proving that the mod p orientation character is trivial

REU Supervision

Summer 2020: Alex Wang - Extensions of irreducible representations of quaternion algebras
Summer 2021: Drew Keisling and Dylan Pentland - Extensions of mod p representations of division algebras over non-Archimedean local fields (co-advised with Tasho Kaletha)

Teaching

Current Teaching:

Math 214