David Marcil

Picture of me

One of the rare time I dressed nicely.

Email : dmarcil [at] uoregon.edu (CV)

I am currently a Paul Olum Postdoctoral Scholar at the University of Oregon. My mentor is Ellen Eischen. Previously, I completed my Ph.D. in Mathematics at Columbia University under the supervision of Michael Harris.

My main research interest is algebraic number theory with an emphasis on automorphic representations, Hida theory and p-adic L-functions.

Publications

Constructing vector-valued automorphic forms on unitary groups, Documenta Mathematica, to appear.
arxiv:2408.05198 (PDF)
  With Thomas L. Browning, Pavel Čoupek, Ellen Eischen, Claire Frechette, Serin Hong, and Si Ying Lee.

Numerical verification of a conjecture of Harris and Venkatesh, Journal of Number Theory, Volume 221, April 2021, p.484-495.
https://doi.org/10.1016/j.jnt.2020.09.003 (PDF)

ORCID iD icon https://orcid.org/0000-0001-6667-0320

Preprints

September 2024. p-adic L-functions for P-ordinary Hida families on unitary groups, arxiv:2409.03783 (PDF)
  This paper contains and refines the content of both arxiv:2310.09110 and arXiv:2311.05466 below

November 2023. p-adic zeta integrals on unitary groups via Bushnell-Kutzko types, arxiv:2311.05466 (PDF)

October 2023. Bushnell-Kutzko types for P-ordinary automorphic representations on unitary groups, arxiv:2310.09110 (PDF)

Seminars

Spring 2023 : Eigenvarieties, families of Galois representations and p-adic L-functions
Spring 2022 : p-adic Automorphic Forms on Shimura Varieties
Summer 2021 : Higher Hida Theory
Spring 2021 : p-adic Modular Forms and p-adic L-functions

Teaching

Fall 2025 : Calculus I and Calculus II
Summer 2023 : Calculus III
Spring 2022 : College Algebra and Analytic Geometry (Pre-Calculus)

Invited Research Talks

The talks below were mostly all modeled after the following set of notes (PDF)
November 18th, 2024. University of Michigan. Group, Lie, and Number Theory seminar, 60 minutes : p-adic L-functions for P-ordinary Hida families on unitary groups.

November 14th, 2024. University of California, Santa Barbara. Seminar on Geometry and Arithmetic, 90 minutes : p-adic L-functions for P-ordinary Hida families on unitary groups.

November 6th, 2024. University of Utah. Representation Theory / Number Theory Seminar, 60 minutes : p-adic L-functions for P-ordinary Hida families on unitary groups.

October 24th, 2024. Princeton University. PU/IAS Number Theory seminar, 60 minutes : p-adic L-functions for P-ordinary Hida families on unitary groups.

October 22nd, 2024. Massachusetts Institute of Technology. MIT Number Theory seminar, 60 minutes : p-adic L-functions for P-ordinary Hida families on unitary groups.

October 19th, 2024. University of Albany. AMS Fall Eastern Sectional Meeting, 50 minutes : p-adic L-functions for P-ordinary Hida families on unitary groups. (Slides)

October 6th, 2024. Universite Laval. Quebec-Maine Number Theory conference, 20 minutes : p-adic L-functions for P-ordinary Hida families on unitary groups. (Slides)

April 4th, 2024. Purdue University. Automorphic Forms and Representation Theory Seminar, 60 minutes : p-adic L-functions for P-ordinary Hida families on unitary groups.

February 11th, 2024. Johns Hopkins University. Junior Number Theory Days, 45 minutes : p-adic L-functions for Pordinary Hida families of automorphic representations on unitary groups.

December 7th, 2023. Princeton University. Monodromy and Its Applications (Pre-workshop for Junior Researchers), 10 minutes : Eisenstein measures for P-ordinary representations on unitary groups.

Undergraduate Research Experiences

D. Marcil, Modules supersinguliers et valeurs speciales de fonctions L sur corps quadratiques imaginaires , 2018. (PDF)
Description : This is my final report from my research with Henri Darmon during the summer of 2018, funded by an Undergraduate Science Research Award from the Natural Science and Engineering Research Council of Canada (NSERC USRA) held at McGill University.

D. Marcil, Resolution of singularities on Elkies' models of towers of modular curves , 2017. (PDF)
Description : This is my final report from my research with Eyal Goren and Jan Vonk during the summer of 2017, funded by an Science Undergraduate Research Award (SURA) held at McGill University.