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
- Asok, Aravind (Algebraic geometry, algebraic K-theory, homotopy theory)
- Assaf, Sami (Algebraic combinatorics, combinatorial representation theory, algebraic geometry, probability)
- Friedlander, Eric (Algebraic geometry, algebraic K-theory, representation theory)
- Guralnick, Robert (Finite and algebraic groups, representation theory, curves, Galois theory, and linear algebra)
- 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)
- Panova, Greta (Algebraic combinatorics, computational complexity, statistical mechanics and probability)
- Williams, Harold (representation theory, algebraic geometry, symplectic geometry)
Post-Docs
Current Graduate Students
- Armon, Sam (advisor Assaf)
- Bowling, Grant (advisor Assaf)
- Ebert, Mark (advisor: Lauda)
- Ehrhard, Henry (advisor Assaf)
- Jiang, Wenhan (advisor: Asok)
- Orlinsky, Kayla (advisor: Montgomery)
- Qiu, Ye (advisor Assaf)
Recent Ph.D.’s Awarded with Thesis Title
- Balcik, Irmak (2022), “Growth of torsion of elliptic curves over noncyclotomic imaginary quadratic fields of class number 1”
- Kagey, Peter (2022), “Permutations, Statistics, and Switches”
- Siegel, Max (2022) “(p,q)-adic Analysis and the Collatz Conjecture”
- Port, Alex (2021), “Motivic Cohomology of BG_2”
- Quijada, Danjoseph (2021) “A Pieri rule for key polynomials”
- Eilidh McKemmie (2020)
- Viktor Kleen (2019), `Some Stable Spliings in Motivic Homotopy Theory”
- Nicolle Sandoval Gonzalez (2019), “Categorical operators and crystal structures on the ring of symmetric functions”
- Donner, Matthew (2018), “Regular unipotents in finite maximal subgroups of classical groups”
- Egilmez, Ilknur (2018) “DG Structures on Categorified Quantum Groups”
- Oguz, Ezgi Kantarci (2018) “Advances in the Combinatorics of Shifted Tableaux”
- Ozan Oguz, Can (2018) “Center and Trace of the Twisted Heisenberg Category”
- Ejder, Oslem (2017) “Torsion subgroups of elliptic curves in elementary abelian 2-extensions and monodromy of Fermat surfaces.”
- Gerhardt, Spencer (2017) “Topological generation of algebraic groups “
- Lamberto, Lafitte (2016) “A categorified braid group action”
- Tucker, Henry (2016) “Frobenius-Schur indicators for near-group and Haagerup-Izumi fusion categories”
- Abram, Mike (2015) “Symmetries of categorified quantum groups”
- Newman, Burton (2015) “Growth of torsion in quadratic extensions of quadratic cyclotomic fields”
- Wang, Jian (2015) “On the torsion structure of elliptic curves over cubic number fields”
- Warner, Jared (2015) “Springer isomorphisms and the variety of elementary subalgebras”
Recent Post-Docs and Visitors
- Jay Taylor (group theory)
- Brendan Pawlowski(algebraic combinatorics)
- Andy Manion (low-dimensional topology, representation theory)
- Nivedita Bhaskhar (algebraic groups)
- Alexander Soibelman (algebraic geometry and representation theory)
- Dominic Searles (combinatorics and algebraic geometry)
- Appel, Andrea (Representation theory, quantum groups, classical and quantum integrable systems)
- Drew, Bradley (Algebraic geometry)
- Jincheng Dong (Hopf algebras)
- Daniel Murfet (Algebraic geometry, topological field theory)
- Paul Sobaje(Modular representations of algebraic groups)
- Guangbin Zhuang (Homological aspects of non-commutative algebra)
Retired Faculty
- Kamienny, Sheldon (Arithmetic geometry, modular forms, abelian varieties)
- Lanski, Charles (Non-commutative ring theory)