Karol Koziol

I am an assistant professor in the Mathematics Department at Baruch College, City University of New York. 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-2310225.

Previously, I was
• a postdoctoral assistant professor at The University of Michigan, supervised by Stephen DeBacker;
• 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.

Here is a 2-adic version of me.

Publications and Preprints

Parahoric Hecke Ext-algebras in characteristic p (with Rachel Ollivier and Jacob Stockton)
includes the appendix "On mod p orientation characters" joint with David Schwein
Preprint
Derived Satake morphisms for p-small weights in characteristic p (with Cédric Pépin)
Preprint
Gelfand-Kirillov dimension for mod p representations of p-adic unitary groups of rank 2 (with Stefano Morra)
Preprint
Derived right adjoints of parabolic induction: an example
Pacific J. Math. 321 (2022), no. 2, 345–358. Journal

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)
Algebra & Number Theory 16 (2022), no. 9, 2005–2097. Journal

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

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)
Summer 2022: Gahl Shemy - Modular principal series representation of GL₂ over finite rings (co-advised with Charlotte Chan)

Teaching

Current Teaching:

Organization

Ongoing:
Baruch Distinguished Lecture Series

Past Organization