Research Interests
My research lies at the intersection of representation theory, algebraic geometry, and quantum algebra. I am currently thinking about asymptotics of quantum groups, and the quantum analogues of the wonderful compactification, the Vinberg semigroup, and related objects. Another research direction concerns the interaction between group-valued Hamiltonian reduction and Azumaya phenomena that occur at quantization at root of unity. Of particular interest are multiplicative quiver varieties as instances of the general framework of Frobenius quantum moment maps. I am also interested in deformations of category O for rational Cherednik algebras and relations to sheaves on moment graphs.
My advisor is David Ben-Zvi.
Publications
I. Ganev. Quanitzations of multiplicative hypertoric varieties at a root of unity. Submitted. Preprint: arXiv:1412.7211.
I. Ganev. The wonderful compactification for quantum groups. Ph.D thesis. In preparation.
Seminars, workshops, and programs
Special program on Geometric Representation Theory, MSRI, Fall 2014.
Working group on The Geometric Satake Equivalence, MSRI, Fall 2014.
Workshop on Yangians and Quantum Loop Algebras, near Austin, May 2014.
Learning seminar on Categorical Representation Theory related topics, UT Austin, Spring 2012 and part of Summer 2012.
Talks and lecture notes
Here are a few talks I have presented:
- The wonderful compactification for quantum groups.
University of Virginia, November 2015.
Geometric and Categorical Representation Theory Conference (link), Mooloolaba, Australia, December 2015. (Slides)
- The wonderful compactification.
Ben-Zvi seminar, UT Austin, September 2015.
GRASP seminar, UC Berkeley, May 2015.
- Multiplicative quiver varieties and their quantizations.
University of Oxford, March 2015.
- The symmetric monoidal structure on the Satake category.
Working group on the Geometric Satake Equivalence, MSRI, November 2014.
- Quantum multiplicative hypertoric varieties at a root of unity.
Various places, 2014-2015.
- The derived category of constructible sheaves. (with Robin Walters, Notes)
Summer school on Quiver Hecke algebras (link).
Institut d'Études Scientifiques de Cargèse Corsica, June 2014.
- Quasi-bialgebras and associators. (Notes)
Workshop on quantization and formality (link), UT Austin, June 2014.
- An introduction to character sheaves. (Notes)
Student Geometry Seminar, October 2013.
- Unipotent characters of finite groups of Lie type. (Notes)
Student Geometry Seminar, April 2013.
- Deformation theory. (Notes)
Ben-Zvi Seminar, March 2013.
- Geometric realizations of affine Hecke algebras.
RTG Geometry and Topology Current Literature Seminar, January 2013.
- An overview of Springer theory.
Student Geometry Seminar, November 2012. (Notes)
Ben-Zvi Seminar, October 2012. (Two lectures, notes from part 2)
- Tannaka duality for affine group schemes. (Notes)
Candidacy Talk, September 2012
- Representations of finite groups. (Notes)
Categorical Representation Theory Workshop (link)
Eugene, Oregon, August 2012
- Young tableaux, symmetric polynomials, and representations. (Notes)
Undergraduate Math Club, February 2012. A video can be found here.
Writings
In addition to the notes above, here are other things I have written, some of which are relatively informal:
- Torus-valued moment maps. (pdf)
- Quantum Hamiltonian reduction. (pdf)
- Real and quaternionic representations of finite groups. (pdf)
- SU(2) as a double cover of SO(3) and related topics. (pdf)
- Undergraduate project: Groups of square-free order. (pdf)
- A research paper from when I worked in a biology lab.
Teaching
I am a TA for M427J Differential Equations with Linear Algebra (Fall 2015).
I was a TA for M408M Multivariable Calculus (Fall 2013) and M408C Differential and Integral Calculus (Fall 2012).