Research

I am interested in representation theory and its connections to algebraic geometry and combinatorics. In particular, I enjoy thinking about (double affine, affine, quiver...) Hecke algebras and their connections to Hilbert schemes and the combinatorics appearing in Lie representation theory.

Papers

[7] (jt. wt. Eugene Gorsky and Monica Vazirani) Hilbert schemes on singular curves via the Dunkl-Opdam subalgebra. arXiv

[6] (jt. wt. Pavel Etingof, Vasily Krylov and Ivan Losev) Representations with minimal support for quantized Gieseker varieties. Submitted.   arXiv

[5] Harish-Chandra bimodules for type A rational Cherednik algebras. Submitted.   arXiv

[4] (jt. wt. Chris Bowman and Emily Norton) Characteristic-free bases and BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras. Submitted.   arXiv

[3] Harish-Chandra bimodules over rational Cherednik algebras. Adv. Math. 317 2017, pp. 299-349.   arXiv   journal

[2] (jt. wt. Joseph Mastromatteo, Chris Holston and Sergio López-Permouth) An alternative perspective on projectivity of modules. Glasg. Math. J. 57 (01) 2015, pp. 83-99.   .pdf   arXiv   journal

[1] (jt. wt. Sergio López-Permouth) Characterizing rings in terms of the extent of the extent of the injectivity and projectivity of their modules. J. Algebra 362 2012, pp. 56-69.   arxiv   journal

Not intended for publication: Harish-Chandra bimodules for quantizations of type A Kleinian singularities. After writing this paper, I found a much easier proof of the main result (which has a gap here in Prop. 5.2 anyways) that is now written in Section 5 of [3] above. However, some other results here may be of independent interest. .pdf


Expository texts.

D-modules on flag varieties and localization of g-modules. Notes for the MIT-NEU Graduate Seminar on Quantum Cohomology and Representation theory, Fall 2013.

Rational Cherednik algebras of type A. Notes for the MIT-NEU Graduate Seminar on Quantum Cohomology and Representation Theory, Spring 2014.

Cluster algebras and Quantum affine algebras. Notes for a talk given for the course "Cluster algebras", taught by Dylan Rupel, Spring 2014.

Introduction to type A categorical Kac-Moody actions. Notes for the MIT-NEU Graduate Seminar on Hecke algebras and Affine Hecke algebras. Fall 2014.

Introduction to Geometric Invariant Theory. Notes for the MIT-NEU Graduate Student Seminar on moduli of sheaves on K3 surfaces. Spring 2016.

Notes on Tannakian Categories. Notes for a talk given for the course "Differential equations and Quantum groups", taught by Valerio Toledano Laredo, Spring 2016.

D-modules and the Riemann-Hilbert correspondence. Notes for the MIT-NEU Graduate Student Seminar on Hodge Modules, Fall 2016.

Double affine Hecke algebras. Notes for the MIT-NEU Graduate Student Seminar on Double affine Hecke algebras and elliptic Hall algebras, Spring 2017.


Videos

In March 2015, I was teaching assistant to Ivan Losev in a Masterclass on Quantized quiver varieties at QGM, Aarhus. As a teaching assistant, I gave some of the lectures. Here are videos of them.

In June 2019, I gave a 1-hour expository talk on the basics of the representation theory of rational Cherednik algebras during a Summer school on Geometric representation theory and Low-dimensional topology at ICMS, Edinburgh. Here is a video of it.