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Reading Seminar in Number Theory
(2019-2022)

Contact:

Department of Mathematics,
Dartmouth College,
Hanover, New Hampshire
03755

Eran.Assaf@Dartmouth.edu

Eran Assaf

I have moved to MIT.

Research:

My latest interest is computing modular forms, in various settings, with applications to equations of modular curves (classical modular forms), the paramodular conjecture and understanding endoscopy in the Langlands program (orthogonal forms). I am interested in algebraic number theory, representation theory and the interplay between them. In particular, the $p$-adic Langlands programme and Shimura Varieties.

Papers and preprints:

• A database of paramodular forms from quinary orthogonal modular forms, with Watson Ladd, Gustavo Rama and Gonzalo Tornaría. Contemporary Mathematics, Volume 796, 2024, Pages 285-312.


• A database of basic numerical invariants of Hilbert modular surfaces, with Angelica Babei, Ben Breen, Edgar Costa, Juanita Duque-Rosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Sam Schiavone and John Voight. Contemporary Mathematics, Volume 796, 2024, Pages 243-259.


• On smooth plane models for modular curves of Shimura type, with Samuele Anni and Elisa Lorenzo García. Research in Number Theory 9:21, Springer, 2023.


• Definite orthogonal modular forms: Computations, Excursions and Discoveries, with Dan Fretwell, Colin Ingalls, Adam Logan, Spencer Secord and John Voight. Research in Number Theory 8:70, Springer, 2022.


• An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process, with Jeremiah Buckley and Naomi Feldheim. Probability Theory and Related Fields, Springer, 2023.


• Computing classical modular forms for arbitrary congruence subgroups. Arithmetic Geometry, Number Theory and Computation, Simons Symposia, Springer, 2022, pp. 43-104.


• Existence of invariant norms in $p$-adic representations of $GL_2(F)$ of large weights. Journal of Number Theory, Volume 224, 2021, Pages 95-141.


• Kirillov models and the Breuil-Schneider conjecture for $GL_2(F)$, with David Kazhdan and Ehud de Shalit. arXiv preprint.


• Pay for a sliding Bloom filter and get counting, distinct elements, and entropy for Free, with Ran Ben Basat, Gil Eizinger and Roy Friedman. IEEE INFOCOM 2018 - IEEE Conference on Computer Communications.


• Counting distinct elements over sliding windows, with Ran Ben Basat, Gil Eizinger, Roy Friedman and Yaron Kassner. SYSTOR 2017 Proceedings of the 10th ACM International Systems and Storage Conference.


• Characterization of regular Diophantine quadruples, with Shay Gueron. Elemente der Mathematik 2001.

Teaching:

• Fall 2021 - Math 9, Dartmouth College.


• Winter 2021 - Math 3, Dartmouth College.

Code Packages:

• Modular symbols to arbitrary congruence subgroups.


• Algebraic modular forms.

PhD Thesis

Existence of Invariant Norms in p-adic Representations of Reductive Groups

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