# 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, algebraic K-theory, and algebraic methods of mathematical physics.

###### Tenured and Tenure-Track Faculty

- Assaf, Sami (Algebraic combinatorics, combinatorial representation theory, algebraic geometry, probability)
- Asok, Aravind (Algebraic Geometry)
- Friedlander, Eric (Algebraic Geometry, Algebraic K-Theory, representation theory)
- Guralnick, Robert (Finite and algebraic 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 (Non-commutative algebras, Hopf algebras and their representation)

###### Post-Docs

- Appel, Andrea (Representation theory, quantum groups, classical and quantum integrable systems)
- Drew, Bradley (Algebraic geometry)
- Dominic Searles (combinatorics and algebraic geometry)
- Alexander Soibelman (algebraic geometry and representation theory)
- Guangbin Zhuang (Homological aspects of non-commutative algebra)

###### Current Graduate Students

- Abram, Mike (advisor: Lauda)
- Egilmez, Ilknur (advisor: Lauda)
- Ejder, Oslem (coadvisors: Friedlander and Kamienny)
- Gerhardt, Spencer (advisor: Guralnick)
- Kantarci, Ezgy (advisor: Assaf)
- Kleen, Viktor (advisor: Asok)
- Lamberto, Lafitte (advisor: Lauda)
- Oguz, Can (advisor: Lauda)
- Tucker, Henry (advisor: Montgomery)
- Wintner, Mose (advisor: Asok)

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

- Burton Newman, 2015 "Growth of torsion in quadratic extensions of quadratic cyclotomic fields"
- Jian Wang, 2015 "On the torsion structure of elliptic curves over cubic number fields"
- Jared Warner, 2015 “Springer isomorphisms and the variety of elementary subalgebras”
- Joseph Timmer 2014 "Indicators of bismash products arising from factorizations of the symmetric group"
- Taylan Bilal 2013 "Computations for bivariant cycle cohomology"
- Adam Ericksen 2013 "The geometry of motivic spheres"
- Rebecca Courter 2012 "Computing higher indicators for the double of a symmetric group"
- Andrei Pavelescu 2012 "On the proportion of derangements in primitive permutation groups"
- Dmytro Chebotarov 2011 "Classification of transitive vertex algebroids"
- Paul Sobaje 2011 "Blocks of finite group schemes"
- Chonglong Zhong 2011 "Comparison of dualizing complexes"
- Keilberg, Marc, 2010 "Higher indicators for some groups and their doubles"

###### Recent Post-Docs and Visitors

- Jincheng Dong (Hopf algebras)
- Murfet, Daniel (Algebraic geometry, topological field theory)
- Sobaje, Paul (Modular representations of algebraic groups)