Alex(ander) Sherman

Greetings! I am a mathematician working in the field of representation theory. Currently, I'm a lecturer at UNSW in the School of Mathematics and Statistics. Previously, I did postdocs at the University of Sydney with Kevin Coulembier and at Ben Gurion-University of the Negev with Inna Entova-Aizenbud.

In research I like to find down-to-earth connections between representation theory and geometry. My main expertise lies in super representation theory and supergeometry, although lately I've been thinking more about mod p representation theory, including modular representation theory and exotic tensor categories.

Teaching

In term 2 of 2025 I will be lecturing the Linear Algebra stream of MATH1241.

Activities I organize

Preprints and publications:

(all links lead to arXiv version)

Towards the Green correspondence for supergroups, with I. Entova-Aizenbud and V. Serganova
A remarkable functor on G-modules, joint with J. Baine, A. Romanov, T. Fell, and G. Williamson
Homogeneous spaces in tensor categories, joint with Kevin Coulembier
Sylow theorems for supergroups, joint with Vera Serganova and Dmitry Vaintrob
The Cartan-Helgason theorem for supersymmetric spaces: spherical weights for Kac-Moody superalgebras International Mathematics Research Notices, Volume 2025, Issue 13, July 2025
A queer Kac-Moody construction, joint with Lior Silberberg.
It takes two spectral sequences, joint with Inna Entova-Aizenbud and Vera Serganova. Accepted to Journal of Algebra, special issue in memory of Georgia Benkart.
Localization theorem for homological vector fields, joint with Vera Serganova. Communications in Mathematical Physics, Vol. 405, no. 39.
Ghost distributions on supersymmetric spaces II: basic classical superalgebras, International Mathematics Research Notices, Volume 2024, Issue 5, March 2024, Pages 3706–3747
Splitting quasireductive supergroups and volumes of supergrassmannians, joint with Vera Serganova. Accepted for publication in Algebraic Geometry and Physics.
On the Grothendieck ring of a quasireductive Lie superalgebra, joint with Maria Gorelik and Vera Serganova. Accepted for publication in Algebra and Number Theory.
On the Duflo-Serganova functor for the queer Lie superalgebra, joint with Maria Gorelik. Advances in Mathematics, Vol. 441, April 2024.
On symmetries of the Duflo-Serganova functor. Accepted for publication in the Israel Journal of Mathematics.
The Duflo-Serganova functor, vingt ans après, joint with Maria Gorelik, Crystal Hoyt, and Vera Serganova. Journal of the Indian Institute of Science, Vol. 102 (2022): 961-1000.
Ghost distributions on supersymmetric spaces I: Koszul induced superspaces, branching, and the full ghost centre. Accepted for publication in Transformation Groups.
Two geometric proofs of the classification of algebraic supergroups with semisimple representation theory.
Layers of the coradical filtration. Journal of Algebra, Vol. 632, no. 15 (2023): 102-116.
Iwasawa decomposition for Lie superalgebras. Journal of Lie Theory, Vol. 32 (2022): 973-996.
Spherical supervarieties. Annales de L'institut Fourier, Tome 71, no 4, p. 1449-1492 (2021).
Indecomposable spherical representations of Lie superalgebras. Journal of Algebra, Volume 547, 1 April 2020, Pages 262-311
Spherical and symmetric supervarieties (PhD thesis).
From Fields-MITACS REU (2012): Omitting types and AF algebras; joint with Kevin Carlson, Enoch Cheung, Ilijas Farah, Alexander Gerhardt-Bourke, Bradd Hart, Leanne Mezuman and Nigel Sequeira : Journal for Mathematical Logic, 53, pages 157–169 (2014)

Honours and HDR students

If you are interested in working on a project with me, please send me an email and we can have a chat. I have a number of projects connected to representation theory, algebraic geometry, and tensor categories that are suitable for students.

Recently organized activities

I organized, with Sam Jeralds, a course on Kazhdan-Lusztig equivalences in semester 2 at the University of Sydney. See website here!
I organized, with Nate Harman, a special session on Representation theory and tensor categories at the joint AustMS-NZMS-AMS meeting in Auckland, NZ 2024.
I helped organize the University of Sydney Algebra Seminar.
With Harini Desiraju, I organize Shut Up and Write in the Quad. See scnews for details.

Magma Mondays, organized jointly with Bregje Pauwels in the second semester of 2023.
Tensor categories and their modules: a course organized jointly with Anna Romanov in the first semester of 2024.

Email address: My name is Alexander Sherman. My email is the last 6 letters of my first name, followed by the first 5 letters of my last name, at gmail.