## Karol Koziol

I am a postdoctoral fellow in the mathematics department at The University of Alberta, working with Manish Patnaik. 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.

Previously, I was

• 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.

### Publications and Preprints

- Serre weight
conjectures for
*p*-adic unitary groups of rank 2 (with Stefano Morra)

Preprint

- Supersingular
representations of rank 1 groups

Preprint

- The first pro-
*p*-Iwahori cohomology of mod-*p*principal series for*p*-adic GL_{n}

To appear in Transactions of the AMS 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

To appear in Math. Res. Letters

- Pro-
*p*-Iwahori invariants for SL_{2}and*L*-packets of Hecke modules

(previously titled "Restriction of pro-*p*-Iwahori-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

### Seminar

Schedule for Number Theory/Representation Theory Seminar### Teaching

**University of Alberta:**

Fall 2018: MATH100 - Calculus I

**University of Toronto:**

Summer 2017: MAT224 - Linear Algebra II

Winter 2017: MAT224 - Linear Algebra II

Fall 2016: MAT223 - Linear Algebra
I

© 2018 Karol Koziol

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Viklund