# RESEARCH: Algebra

Algebra at USC is very broadly conceived. The expertise of the faculty covers a broad swathe of the field, including group theory, Hopf algebras, representation theory, homological methods, aspects of abstract algebraic geometry, arithmetic algebraic geometry, and algebraic methods of mathematical physics.

###### Faculty

- Asok, Aravind (Algebraic Geometry)
- Friedlander, Eric (Algebraic Geometry, Algebraic K-Theory, Representation Theory)
- Guralnick, Robert (Finite Groups, Representation Theory, Curves, Galois Theory, and Linear Algebra)
- Kamienny, Sheldon (Arithmetic Geometry, Modular Forms, Abelian Varieties)
- Lanski, Charles (Non-Commutative Ring Theory)
- Lauda, Aaron (Categorification, representation theory, and low-dimensional topology)
- Malikov, Fedor (Mathematical Physics, Representation Theory)
- Montgomery, Susan (Noncommutative Algebras, Hopf Algebras and their

Representation Theory)

###### Post Docs and Visitors

- Ayala, David
- Iovanov, Miodrag (Hopf algebras and coalgebras)
- Jedwab, Andrea (Representation theory of Hopf algebras)
- Ross, Joe (Algebraic Geometry)
- Williams, T. Benedict (Homotopy theory, Algebraic Geometry)

###### Current Graduate Students

- Chebotarov, Dmytro (advisor Malikov)
- Bilal, Taylan (advisor Friedlander)
- Cheung, Matthew (advisor Kamienny)
- Courter, Rebecca (advisor Montgomery)
- Ericksen, Adam (advisor Asok)
- Pavelescu, Andrei (advisor Guralnick)
- Sobaje, Paul (advisor Friedlander)
- Timmer, Joe (advisor Friedlander)
- Zhong, Changlong (advisor Geisser)

###### Recent Ph.D.'s Awarded with Thesis Title

- Keilberg, Marc, 2010 ``Higher indicators for some groups and their doubles"
- Chu, Chenghao, 2008 (Northwestern) ``Representing Cohomology Theories
- in the Triangulated Category of Motives''
- DiMuro, Joseph, 2008 ``On Prime Power Elements of GL_d(q) Acting

Irreducibly on Large Subspaces'' - Guest, Simon, 2008 ``A Solvable Version of the Baer-Suzuki Theorem''
- Jedwab, Andrea, 2008 ``Representations of Finite-Dimensional Hopf

Algebras'' - Voineagu, Mircea, 2007 (Northwestern) ``Semi-Topological K-Theory of

Certain Projective Varieties'' - Han, Yongho, 2006 ``Commuting Triples of Matrices''
- Heller, Jeremiah, 2006 (Northwestern) ``Semi-Topological Cobordism for

Complex Varieties''