# Monica Vazirani

**Professor****Representation theory, combinatorics**

Ph.D., 1999, University of California, Berkeley**Refereed publications:** Via Math Reviews

**Web Page: ** http://www.math.ucdavis.edu/~vazirani/

Email: vazirani@math.ucdavis.edu

Office: MSB 3224

Phone: 530-754-0498

### Research

Professor Monica Vazirani studies combinatorial representation theory. Representation theory is the study of symmetry. As such, it gives us the tools to solve problems about any system that exhibits symmetry, and so has wide applications in other areas of mathematics, as well as in chemistry, physics, and computer science. Her area of expertise is the representation theory of Hecke algebras and Khovanov-Lauda-Rouquier (KLR) algebras. Hecke algebras arise naturally in many areas of mathematics and physics, such as quantum groups, quantum field theory, statistical mechanics, and knot theory. KLR algebras were invented to categorify quantum groups, and have connections to quantum 3-manifold invariants. She studies their irreducible representations, which are the most basic objects whose symmetries are encoded in these algebras.

### Selected Publications

**[1]** A. Lauda, and M. Vazirani, "Crystals from categorified quantum groups," *Advances in Mathematics*, **228**(2):803-861, 2011.
Full Text here.

**[2]** E. Rains and M. Vazirani, "Vanishing Integrals of Macdonald, Koornwinder polynomials," *Transformation Groups*, **12**(4):725-759, 2007. Full Text here.

**[3]** M. Vazirani, M. Grigni, L. Schulman, and U. Vazirani, "Quantum Mechanical Algorithms for the Nonabelian Hidden Subgroup Problem," *Combinatorica*, **24**(1): 137-154, 2004,
Full Text here.

**[4]** M. Vazirani, "Filtrations on the Mackey Decomposition for Cyclotomic Hecke Algebras," *Journal of Algebra*, **252**(2): 205-227, 2002,
Full Text here.

**[5]** M. Vazirani and I. Grojnowski, "Strong multiplicity one theorem for affine Hecke algebras of type A," *Transformation Groups*, **6**(2): 143-155, 2001,
Full Text here.

*Last updated: 2011-09-07*