Karol Koziol

Education

Ph.D., Mathematics, Columbia University New York United States

M.Phil., Mathematics, Columbia University New York United States

M.A., Mathematics, Columbia University New York United States

B.A., Mathematics, New York University New York United States

Journal Articles

(2022). Serre weight conjectures for p-adic unitary groups of rank 2. Algebra & Number Theory,

(2022). Derived right adjoints of parabolic induction: an example. Pacific Journal of Mathematics,

(2021). Functorial properties of pro-p-Iwahori cohomology. Journal of the London Mathematical Society, Second Series, 104(no. 4). 1572 - 1614.

(2020). On the existence of admissible supersingular representations of p-adic reductive groups. Forum of Mathematics, Sigma, 8(e2).

(2019). Homological dimension of simple pro-p-Iwahori–Hecke modules. Mathematical Research Letters, 26(no. 3). 769 - 804.

(2019). The first pro-p-Iwahori cohomology of mod-p principal series for p-adic GL_n. Transactions of the American Mathematical Society, 372. 1237 - 1288.

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

(2018). Irreducible admissible mod-p representations of metaplectic groups. manuscripta mathematica, 155(no. 3-4). 539 - 577.

(2016). Pro-p-Iwahori Invariants for SL_2 and L-Packets of Hecke Modules. International Mathematics Research Notices , 2016(no. 4). 1090 - 1125.

(2016). A Classification of the Irreducible mod-p Representations of U(1,1)(Q_{p^2}/Q_p). Annales de l'Institut Fourier, 66(no. 4). 1545 - 1582.

(2015). Hecke modules and supersingular representations of U(2, 1). Representation Theory, 19. 56 - 93.

Presentations

Koziol, K. Iwahori–Hecke algebras and the mod-p Langlands program. Introduction to p-adic Langlands program. IIT JammuIn Progress.

Koziol, K. Poincare duality for modular representations of p-adic groupsand Hecke algebras. Automorphic Forms and Representation Theory Seminar. West Lafayette, IN: Purdue University.

Koziol, K. Local-Global Compatibility. RTG Seminar on Number Theory. Ann Arbor, MI: University of Michigan.

Koziol, K. Poincare duality for modular representations of p-adic groups and Hecke algebras. Joint Columbia-CUNY-NYU Number Theory Seminar. New York, NY: Columbia-CUNY-NYU.

Koziol, K. Derived Hecke algebras for p-adic groups. RTG Seminar on Number Theory. Ann Arbor, MI: University of Michigan.

Koziol, K. Supersingular representations of p-adic reductive groups. Number Theory Seminar. Boston, MA: Harvard University.

Koziol, K. Supersingular representations of p-adic reductive groups. New Developments in Number Theory, hosted by POINT. Online: POINT (People Online In Number Theory).

Koziol, K. An introduction to the Langlands program. Topology, Analysis & Geometry Seminar. Mount Pleasant, MI: Central Michigan University.

Koziol, K. Serre weight conjectures for unitary groups. Algebra, Combinatorics, and Geometry Seminar. Pittsburgh, PA: University of Pittsburgh.

Koziol, K. Some functorial constructions for pro-p-Iwahori cohomology. Algebra and Number Theory Seminar. Tucson, AZ: University of Arizona.

Koziol, K. Serre weight conjectures for unitary groups. Number Theory Seminar. Evanston, IL: Northwestern University.

Koziol, K. The p-adic Local Langlands Correspondence for GL_2(Q_p). RTG Seminar on Number Theory. Ann Arbor, MI: University of Michigan.

Koziol, K. Approaches to the mod-p Langlands program. N/A (Job interview presentation). Dublin, Ireland: Trinity College Dublin.

Koziol, K. Serre weight conjectures for unitary groups. Number Theory Seminar. Vancouver, BC: University of British Columbia.

Koziol, K. Serre weight conjectures for unitary groups. Number Theory/Representation Theory Seminar. Edmonton, AB: University of Alberta.

Koziol, K. Some calculations with higher pro-p-Iwahori cohomology. Number Theory Seminar. Los Angeles, CA: UCLA.

Koziol, K. Some calculations with higher pro-p-Iwahori cohomology. Number Theory Seminar. Pasadena, CA: California Institute of Technology.

Koziol, K. Some calculations with higher pro-p-Iwahori cohomology. Number Theory Seminar. San Diego, CA: UC San Diego.

Koziol, K. Some calculations with higher pro-p-Iwahori cohomology. Séminaire de Géométrie Algébrique. Montpellier, France: Universite Montpellier 2.

Koziol, K. Projective dimensions of simple Iwahori-Hecke modules in characteristic p. Number/Representation Theory Seminar. Toronto, ON: University of Toronto.

Koziol, K. Some calculations with higher pro-p-Iwahori cohomology. Number/Representation Theory Seminar. Toronto, ON: University of Toronto.

Koziol, K. L-packets of Hecke modules in characteristic p. Number/Representation Theory Seminar. Toronto, ON: University of Toronto.

Koziol, K. Hecke algebras in Number Theory. Postdoc Seminar. Toronto, ON: University of Toronto.

Koziol, K. Introduction to Theta functions. Postdoc Seminar. Toronto, ON: University of Toronto.

Koziol, K. Trees, apartments, and buildings: an introduction to p-adic city planning. Postdoc Seminar. Toronto, ON: University of Toronto.

Koziol, K. Towards a Langlands correspondence for Hecke modules of type A_n in characteristic p. Number Theory Seminar. Vancouver, BC: University of British Columbia.

Koziol, K. Projective dimensions of simple Iwahori-Hecke modules in characteristic p. Séminaire de Théorie des Nombres. Montpellier, France: Universite Montpellier 2.

Koziol, K. Projective dimensions of simple Iwahori-Hecke modules in characteristic p. Mittagsseminar zur Arithmetik. Munster, Germany: Universitat Munster.

Koziol, K. The mod-p Local Langlands Program and Iwahori-Hecke algebras. Oberseminar. Bonn, Germany: Max Planck Institute for Mathematics.

Koziol, K. Projective dimensions of simple Iwahori-Hecke modules in characteristic p. Séminaire Groupes Réductifs et Formes Automorphes,. Paris, France: Institut de Mathématiques de Jussieu.

Koziol, K. The mod-p Local Langlands Program and Iwahori-Hecke algebras. Postdoc Seminar. Bures-sur-Yvette, France: Institut des Hautes Études Scientifiques.

Koziol, K. L-packets of Hecke modules in characteristic p. Arithmetic Geometry Seminar. Hamilton, ON: McMaster University.

Koziol, K. Towards a Langlands correspondence for Hecke modules of SL_n in characteristic p. Princeton/IAS Junior Faculty Number Theory Seminar. Princeton, NJ: Princeton University.

Koziol, K. Towards a Langlands correspondence for Hecke modules of SL_n in characteristic p. Group, Lie and Number Theory Seminar. Ann Arbor, MI: University of Michigan.

Koziol, K. Towards a Langlands correspondence for Hecke modules of SL_n in characteristic p. Representation Theory Seminar. New York, NY: CUNY Graduate Center.

Koziol, K. Towards a Langlands correspondence for Hecke modules of type A_n in characteristic p. Séminaire Groupes Réductifs et Formes Automorphes. Paris, France: Institut de Mathématiques de Jussieu.

Koziol, K. Towards a Langlands correspondence for Hecke modules of type A_n in characteristic p. Séminaire de Théorie des Nombres. Montpellier, France: Universite Montpellier 2.

Koziol, K. Poincare duality for modular representations of p-adic groups and Hecke algebras. Journées Arithmétiques du LAGA. Paris, France: Université Sorbonne Paris Nord (Paris XIII).

Koziol, K. Poincare duality for modular representations of p-adic groups and Hecke algebras. AMS Sectional Meeting. Denver, CO: University of Denver/American Mathematical Society.

Koziol, K. Derived second adjointness in characteristic p. Midwest Representation Theory Conference. Ann Arbor, MI: University of Michigan.

Koziol, K. Poincare duality for modular representations of p-adic groups and Hecke algebras. Mathematical Congress of the Americas. Buenos Aires, Argentina: Mathematical Council of the Americas.

Koziol, K. Iwahori–Hecke algebras in the (mod p) Local Langlands program. Nonassociative Algebras and Geometry. Norris Point, NL: Atlantic Association for Research in the Mathematical Sciences.

Koziol, K. Serre weight conjectures for unitary groups. Padova school on Serre conjectures and the p-adic Langlands program. Padova, Italy: Università di Padova.

Koziol, K. Serre weight conjectures for unitary groups. Alberta Number Theory Days XI. Banff, AB: Banff International Research Station.

Koziol, K. Serre weight conjectures for unitary groups. AMS Sectional Meeting. Ann Arbor, MI: University of Michigan/American Mathematical Society.

Koziol, K. Some calculations with higher pro-p-Iwahori cohomology. Upstate Number Theory Conference. Buffalo, NY: University of Buffalo.

Koziol, K. Projective dimensions of simple Iwahori-Hecke modules in characteristic p. AMS Sectional Meeting. Bloomington, IN: University of Indiana/American Mathematical Society.

Koziol, K. On Schneider's derived equivalence. Geometric methods in the mod p local Langlands correspondence. Pisa, Italy: Centro di Ricerca Matematica Ennio De Giorgi.

Koziol, K. Towards a Langlands correspondence for Hecke modules of type A_n in characteristic p. Conference on Modular Iwahori-Hecke Algebras. Berlin, Germany: Humboldt-Universität zu Berlin.

Koziol, K. Towards a Langlands correspondence for Hecke modules of type A_n in characteristic p. Local Langlands Conjecture and Galois Representations. Mumbai, India: Tata Institute of Fundamental Research, School of Mathematics.

Koziol, K. Towards a Langlands correspondence for Hecke modules of SLn in characteristic p. AMS Sectional Meeting. Philadelphia, PA: Temple University/American Mathematical Society.

Koziol, K. Towards a Langlands correspondence for Hecke modules of SL_n in characteristic p. Hecke algebras in Number Theory and Categorification. New York, NY: Columbia University.

Koziol, K. Supersingular representations of U(2,1). Modular Representation Theory of Finite and p-adic Groups. Singapore: National University of Singapore.

Koziol, K. Poincaré duality for representations and Hecke modules in characteristic p. Midwest Arithmetic Geometry and Number Theory Series. Ann Arbor: University of Michigan.

Koziol, K. An introduction to the mod p Langlands Program. Southern Illinois University Mathematics Colloquium. Southern Illinois University

Koziol, K. Derived K-invariants and the derived Satake transform. Philadelphia Area Number Theory Seminar.

Koziol, K. Derived K-invariants and the derived Satake transform. Representation Theory, L-functions, and Arithmetic. University of Pittsburgh

Koziol, K. Derived K-invariants and the derived Satake transform. Hecke Algebras as a Unifying Theme. University of British Columbia

Koziol, K. Derived K-invariants and the derived Satake transform. CMS Summer Meeting. University of Ottawa

Koziol, K. Poincare duality for modular representations of p-adic groups and Hecke algebras. Number Theory Seminar. State College, PA: The Pennsylvania State University.

Koziol, K. Derived K-invariants and the derived Satake transform. Automorphic Forms and Representation Theory Seminar. Purdue University

Koziol, K. Iwahori–Hecke algebras and the mod-p Langlands program. 4-part lectures series. Paris, France: Université Sorbonne Paris Nord (Paris XIII).

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