Anna Medvedovsky

Anna Medvedovsky

Anna Medvedovsky

Postdoc, Boston University.

Research interests: mod-p and p-adic phenomena in modular forms, Hecke algebras, and Galois representations.

Previously, I was a postdoc at the Max-Planck-Institut für Mathematik. I completed my Ph.D. in 2015 from Brandeis University under the supervision of Joël Bellaïche.

Curriculum vitae
Updated January 2021.

Research

Big images of Galois pseudorepresentations. Joint with Andrea Conti and Jaclyn Lang. Under revision at Math. Annalen.

Newforms mod p in squarefree level, with applications to Monsky’s Hecke-stable filtration. Joint with Shaunak Deo, and with an appendix by Alexandru Ghitza. Transactions of the AMS, Series B 6 (2019), 245–273.

Mod-2 dihedral Galois representations of prime conductor. Joint with Kiran Kedlaya. Proceedings of the Thirteenth Algorithmic Number Theory Symposium. Open Book Series 2 (2019) 325–342.
- Kiran Kedlaya's slides at ANTS-XIII.

Modular forms modulo 3 of level one.
- Paper draft: An explicit universal Galois representation on the mod-3 Hecke algebra.
- Speed talk slides: A universal Galois representation attached to modular forms mod 3.
- Data: A convenient basis for the space of mod-3 modular forms of level one, adapted, in the spirit of Nicolas and Serre, to T₇–2 and T₂.

Nilpotence order growth of recursion operators in characteristic p. Algebra and Number Theory 12 (2018) no. 3, 693–722.

Poster slides on this project. An overview. Some pretty pictures.

Lower bounds on dimensions of mod-p Hecke algebras: The nilpotence method. Ph.D. dissertation. Not short.
- The proof of the key technical result (which had an error) has been corrected and appears in Nilpotence order growth of recursion operators in characteristic p, above.
- Data: Hecke recursion polynomials in level one mod small primes.

Teaching

Fall 2021. BU MA 541: undergraduate algebra I