Siddharth Venkatesh


About

I am a Hedrick Assistant Adjunct Professor in the math department at UCLA. My postdoctoral mentor is Raphael Rouquier. My research interests are in representation theory, algebraic geometry and category theory. My PHD thesis involved the study of group schemes and Lie algebras in symmetric tensor categories in positive characteristic, with the case of the Verlinde category being of particular interest.I am also working on problems related to D-modules on quiver varieties. Here is my CV .


Education

Ph.D. in Mathematics, Massachusetts Institute of Technology, 2019, under Pavel Etingof .

B.A. in Mathematics with highest honors, University of California, Berkeley, 2014.


Teaching

Fall 2019: I will be teaching Math 32A (multivariable calculus) Lectures 3 and 5. Here is the course outline .

Syllabus for Lecture 3.

Syllabus for Lecture 5.

Homework 1: Link to pdf.


Research Papers (abstracts)

General Linear groups in the Verlinde Category (in preparation)

$D$-modules on the cyclic quiver and representations of the cyclotomic rational Cherednik algebra (in preparation, link to work in progress )

Harish-Chandra pairs in the Verlinde category in positive characteristic (arXiv )

Computations in symmetric fusion categories in characteristic $p$ (with P. Etingof and V. Ostrik), Int. Math. Res. Not. (2017). (arXiv)

Hilbert basis theorem and finite generation of invariants in symmetric tensor categories in positive characteristic, Int. Math. Res. Not. (2016). (arXiv)

Semigroup Conjectures for Central Semidirect Product of $\mathbb{R}^n$ with $\mathbb{R}^m$ (with K. Lui and V. Nitica), Topology Proc. (2015). (arXiv)


Seminars I helped organize

Graduate seminar on étale cohomology, MIT Spring 2016

Graduate seminar on $D$-modules and perverse sheaves, MIT Fall 2015


Expository Seminar Talks

Hodge-Riemann bilinear relations for Soergel bimodules , MIT-NEU Graduate seminar on the category $\mathcal{O}$ and Soergel bimodules (Fall 2017)

Etale cohomology of curves , MIT graduate seminar on etale cohomolgy (Spring 2017)

Quot Schemes , MIT-NEU graduate seminar on the moduli of sheaves on K3 surfaces (Spring 2016)

On Atiyah and Segal's "Equivariant K-Theory and Completion" , Kan Seminar (Fall 2015)

On Thom's "Quelques Propriétés" , Kan Seminar (Fall 2015)

Introduction to perverse sheaves , MIT graduate seminar on D-modules and perverse sheaves

Constructible sheaves on stratified spaces , MIT graduate seminar on D-modules and perverse sheaves

Introduction to intersection homology , MIT graduate seminar on D-modules and perverse sheaves

Kazhdan-Lusztig Cells , MIT-NEU Graduate seminar on quiver varieties (Spring 2015)

Affine Hecke algebras and their cyclotomic quotients , MIT-NEU graduate seminar on Hecke algebras and affine Hecke algebras (Fall 2014)


Research papers of students I've mentored

Laura Pierson PRIMES-USA 2016 , Stability properties of signatures of $S_{n}$-representations (project won 6th place at Regeneron STS 2017).

Mrudul Thatte UROP+ 2016 , Stability properties of signatures of $GL_{N}$-representations

Yutao Liu UROP+ 2016 , Minimal cell structures for $G-CW$ complexes

Saarik Kalia UROP+ 2015 , Signatures of representations of cyclotomic Hecke algebras and rational Cherednik algebras

Girishwar Venkat PRIMES-USA 2015 , Signatures of representations of cyclotomic Hecke algebras and rational Cherednik algebras


Programs I have been affiliated with

PRIMES

RSI

SPUR

UROP


Contact

Department of Mathematics
Massachusetts Institute of Technology
Building 2
77 Massachusetts Avenue
Cambridge, MA-02139
sidnv [at] mit [dot] edu