Nate Harman


Affiliation: Institute for Advanced Study
Pronouns: He/him

Email: nharman [at] math [dot] ias [dot] edu

I am currently a member at the Institute for Advanced Study. I received my PhD from MIT in 2017, my thesis was titled "Deligne Categories and Representation Stability in Positive Characteristic", and my PhD advisor was Pavel Etingof. I am interested in stability phenomena in representation theory, tensor categories in positive characteristic, representations of infinite rank arithmetic groups, applications of model theory to representation theory, and problems in algebraic combinatorics arising from representation theory. The picture is of me teaching a mini-course on non-euclidean geometry to high school students at MathILy in 2014.

Recent papers and preprints:

"On Quadratic Representations of S_n" an appendix to "Modular functions and resolvent problems" by Farb, Kisin, and Wolfson, December 2019 arXiv

"Effective and Infinite-Rank Superrigidity in the Context of Representation Stability" February 2019 arXiv

"Classification of simple algebras in Deligne category Rep(S_t)" with Daniil Kalinov, to appear in Journal of Algebra arXiv

"Representations of monomial matrices and restriction from GLn to Sn" April 2018, arXiv

"Virtual Specht stability for FI-modules in positive characteristic", Journal of Algebra, Volume 488, 15 October 2017, Pages 29-41 - arXiv

"Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups", with Georgia Benkart and Tom Halverson,
Journal of Algebraic Combinatorics August 2017, Volume 46, Issue 1, pp 77–108 - arXiv

"Counting SET-free sets", Annals of Combinatorics, September 2018, Volume 22, Issue 3, pp 575–582 - arXiv

"Quantum integer valued polynomials", with Sam Hopkins, Journal of Algebraic Combinatorics, March 2017, Volume 45, Issue 2, pp 601–628 - arXiv

"Deligne categories as limits in rank and characteristic" (2016) - arXiv

"p-adic dimensions in symmetric tensor categories in characteristic p", with Pavel Etingof and Victor Ostrik, Quantum Topology, Volume 9, Issue 1, 2018, pp. 119–140 - arXiv

"Stability and periodicity in the modular representation theory of symmetric groups" (2015) - arXiv

"Generators for the representation rings of certain wreath products", Journal of Algebra, Volume 445, January 2016, Pages 125-135 - arXiv

Programs I have been affiliated with:

Math Circles of Chicago
MathILy and MathILy-Er
Research Science Institute (RSI)
Budapest Semesters in Mathematics