Jessica Fintzen

If you are not a mathematician, but are curious what I am working on, I invite you to watch this short (3 minutes) movie in which I introduce myself and my PhD thesis to a broad audience.
More recently I have given a one hour public talk in German for non-mathematicians which provides an introduction to my research. A recording can be found here (unfortunately the video itself is rather small).

Papers and Preprints

• Reduction to depth zero for tame p-adic groups via Hecke algebra isomorphisms. With Jeffrey Adler, Manish Mishra and Kazuma Ohara. If you open the link in your browser or save this and the next paper in the same folder, then the hyperlinks between them should work (at least using, e.g., Adobe Acrobat).


• Structure of Hecke algebras arising from types. With Jeffrey Adler, Manish Mishra and Kazuma Ohara. If you open the link in your browser or save this and the above paper in the same folder, then the hyperlinks between them should work (at least using, e.g., Adobe Acrobat).


• Supercuspidal representations: construction, classification, and characters.


• Representations of p-adic groups. To appear in Current Developments in Mathematics.


• Supercuspidal representations in non-defining characteristics. To appear in Journal of Algebra, Special Volume in the Memory of Jacques Tits.


• A twisted Yu construction, Harish-Chandra characters, and endoscopy. With Tasho Kaletha and Loren Spice. Duke Mathematical Journal 172 (2023), pp. 2241-2301
  


• Congruences of algebraic automorphic forms and supercuspidal representations. With Sug Woo Shin. Cambridge Journal of Mathematics (CJM) 9 (2021), no. 2, pp. 351-429.


• On the construction of tame supercuspidal representations. Compositio Mathematica 157 (2021), no. 12, pp. 2733–2746.


• Tame cuspidal representations in non-defining characteristics. Michigan Mathematical Journal, Special Volume in Honor of Gopal Prasad, vol. 72 (2022), pp. 331–342.


• Types for tame p-adic groups. Annals of Mathematics 193 no. 1 (2021), pp. 303-346.


• Tame tori in p-adic groups and good semisimple elements. International Mathematics Research Notices (IMRN) 2021, no. 19, pp. 14882–14904.


• On Kostant Sections and Topological Nilpotence. With Jeffrey D. Adler and Sandeep Varma. Journal of the London Mathematical Society 97 no. 2 (2018), pp. 325-351.


• On the Moy-Prasad filtration. Journal of the European Mathematical Society (JEMS) 23 (2021), no. 12, pp. 4009–4063. (This paper is based on my PhD thesis On the Moy-Prasad filtration and stable vectors, which is available in original formatting and my own formatting. However, I strongly recommend to read the above preprint. It is the most recent version and also contains indices.)


• Differential operators and families of automorphic forms on unitary groups of arbitrary signature. With Ellen Eischen, Elena Mantovan and Ila Varma. Documenta Mathematica 23 (2018), pp. 445-495.


• Stable vectors in Moy-Prasad filtrations. With Beth Romano. Compositio Mathematica, Vol. 153, Issue 2 (2017), pp. 358-372.


• p-adic q-expansion principles on unitary Shimura varieties. With Ana Caraiani, Ellen Eischen, Elena Mantovan and Ila Varma. Directions in Number Theory (2016), Springer, pp. 197-244.


• Reflection subgroups of odd-angled Coxeter groups. With Anna Felikson and Pavel Tumarkin. J. Combin. Theory A 126 (2014), pp. 92-127.


• Cyclotomic polynomial coefficients a(n,k) with n and k in prescribed residue classes. Journal of Number Theory 131 (2011), pp. 1852-1863.

A copyright form asked me to mention that the published versions of the above articles differ from the versions on this homepage / the arxiv.

Research Poster

• Stable vectors in the Moy-Prasad filtration. Poster about my research for a general math audience presented at the AWM Research Symposium 2015 at the University of Maryland, College Park.

Selected Videos

• Cours Peccot International (Topic: Representations of p-adic groups). Four two-hour lectures at Collège de France (the first lecture is an overview aimed at a general math audience), Paris, January-February 2024.


• Representations of p-adic groups and Hecke algebras. Workshop on p-adic Arithmetic Geometry, Princeton, USA, November 2023.


• Von Symmetrien alltäglicher Objekte zu ungelösten Problemen in der reinen Mathematik. Public talk for non-mathematicians in German, Bonn, Germany, August 2023.


• Representations of p-adic groups and applications. Talk in the Joint IAS / Princeton University Number Theory Seminar, Princeton, USA, October 2020 (online).


• Representations of p-adic groups for non-experts. A short (15 minutes) talk about my research for a general math audience, Princeton, USA, October 2020 (online).


• Representations of p-adic groups and applications. Talk during the Workshop on Serre weights conjectures and geometry of Shimura varieties, Montreal, Canada, September 2020 (online).


• From representations of p-adic groups to congruences of automorphic forms. Talk during the workshop Modularity and Moduli Spaces, Oaxaca, Mexico, October 2019.


• Representations of p-adic groups. Research talk during the Padova school on Serre conjectures and the p-adic Langlands program, Padova, Italy, May 2019.


• Representations of p-adic groups (Research talk). Talk during the Workshop on Representation Theory and Analysis on Locally Symmetric Spaces, Princeton, USA, March 2018.


• Representations of p-adic groups (IAS Members' Seminar). A one hour talk about my research for a general math audience, Princeton, USA, February 2018.


• Representations of p-adic groups (Short talk). A short (15 minutes) talk about my research for a general math audience, Princeton, USA, September 2017.


• Kostant Sections and Topological Nilpotence. Talk during the conference on representation theory of p-adic groups in Pune, India, July 2017.

Address:
Universität Bonn
Mathematisches Institut
Prof. Dr. Jessica Fintzen
Endenicher Allee 60
53115 Bonn
Germany

Email:
lastname@math.uni-bonn.de