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)




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&nbsp(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