**Email:**
mim2 (at) illinois.edu
**[OR]**
mim2 (at) math.uiuc.edu

**Mailing Address:** 250 Altgeld Hall, 1409 West Green Street,
Urbana, IL 61801

**Campus Mail:** Department of Mathematics, MC-382

**Seminars:** **AG & Related Seminars**

**Background:**

- Doctor of Philosophy (Ph.D.) in Mathematics at the University of Illinois at Urbana-Champaign

- Master of Arts (M.A.) in Mathematics at the University of Georgia

- Master of Philosophy (M.Phil.) in Mathematics at the University of Birmingham, England

- Bachelor of Science (B.S.) in Mathematics
and Physics
at the University of Georgia

- From Atlanta, GA

**Research Interests:**

**KLR-algebras**. My research interests primarily lie in representation theory. More specifically, I have studied generalized Grothendieck-Springer resolutions (i.e., universal quiver flags) through quiver representations, the nilpotent cone, almost-commuting varieties, and generalizations and applications of invariant theory. Quiver flag varieties and filtered quiver varieties (these are isomorphic to fibers of natural projection maps from generalized Grothendieck-Springer resolution to each factor) are closely related to KLR-algebras, quiver Hecke algebras, q-Schur algebras and categorification of quantum groups; my research interests are studying representations of these algebras using combinatorial and geometric techniques.**Integrable systems**. I am also interested in t-deformations of certain solutions to various integrable systems. Currently, my collaborators (D. Addabbo and B. Turmunkh) and I are systematically studying and relating t-deformation of q-characters of quantum affine algebras (which are related to deformed T-systems constructed by Nakajima using quiver varieties) to quantum cluster algebras (which are a different realization of deformed Q-systems). We are interested in combinatorial, algebraic, and geometric constructions of these solutions.**Applications**. Third aspect of my research interests lies in applications of representation theory, e.g., fast Fourier transforms (FFT) for homogeneous spaces of groups (algebras, monoids, etc), connections between FFT and (binary) codes, high dimensional data sets of images and shapes.

- On fast Fourier transform for partially ordered subgroup chains of the symmetric group, with A. Wu. In progress.

- On classification of iterated wreath products of finite groups, with A. Wu. In preparation.

- Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence, with A. Wu, preprint, 2014.

- Generalized iterated wreath products of cyclic groups and rooted trees correspondence, with A. Wu, preprint, 2014.

- On Nakajima's deformation of q-characters (tentative title), with D. Addabbo and B. Turmunkh. In preparation.

- On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution, IDEALS,
Dissertation, 2014.

- Suggestions to study affine and GIT quotients of the extended Grothendieck-Springer resolution,
preprint, 2014.

- Semi-invariants of filtered quiver representations with at most two pathways,
preprint, 2014.

- The regularity of the cotangent bundle of the Grothendieck-Springer resolution, paper, 2013.

- The regular semisimple locus of the affine quotient of the cotangent bundle of the Grothendieck-Springer resolution,
preprint, 2012.

- On Kostant's theorem for Lie algebra cohomology, (with UGA VIGRE Algebra Group), Contemporary Mathematics, 478 (2009),
39-60.

- Nonstandard approach to Hausdorff measure theory and an analysis of some sets of dimension less than 1, British Library,
Thesis, 2005.

- Examples relating to Green's conjecture in low characteristics and genera, with T. Estu, J. Manning, Z. Michaels, W. Rulla, J. Pasko, N. Wijesinghe, accepted upon revision, Experimental Mathematics, 2004.

- May 2014, Alexandria, VA. [slides]
- April 2014, University of California, Berkeley, CA. [slides]
- April 2014, Doctoral defense, University of Illinois, Urbana, IL. [slides]
- April 2014, University of Texas, Austin, TX.
- December 2013, Lexington, MA. [slides]
- January 2013, Mathematical Sciences Research Institute (MSRI), Berkeley, CA.

Department
of Mathematics 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Telephone: (217) 333-3350 Fax: (217) 333-9576 Email: office@math.uiuc.edu Last modified on: |