{"id":178,"date":"2023-01-14T16:06:35","date_gmt":"2023-01-15T00:06:35","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mathematics\/?page_id=178"},"modified":"2025-09-19T15:13:57","modified_gmt":"2025-09-19T22:13:57","slug":"research-algebra","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mathematics\/research-algebra\/","title":{"rendered":"Algebra"},"content":{"rendered":"\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>Algebra at USC is very broadly conceived. The expertise of the faculty covers a broad swathe of the field, including representation theory, group theory, algebraic geometry, algebraic combinatorics, algebraic K-theory, and connections to mathematical physics.<\/p>\n<h4>Tenured and Tenure-Track Faculty<\/h4>\n<ul>\n<li><a href=\"https:\/\/dornsife.usc.edu\/profile\/aravind-asok\/\">Asok, Aravind<\/a> (algebraic geometry, algebraic K-theory, homotopy theory)<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/samihassaf\">Assaf, Sami<\/a> (algebraic combinatorics, combinatorial representation theory, algebraic geometry, probability)<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/ericmfriedlander\/\">Friedlander, Eric<\/a> (algebraic geometry, algebraic K-theory, representation theory)<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/profile\/robert-guralnick\">Guralnick, Robert<\/a> (finite and algebraic groups, representation theory, curves, Galois theory, linear algebra)<\/li>\n<li><a href=\"https:\/\/sites.google.com\/view\/lauda-home\/home\">Lauda, Aaron<\/a> (categorification, representation theory, low-dimensional topology, quantum computation)<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/profile\/fedor-malikov\">Malikov, Fedor<\/a> (mathematical physics, representation theory)<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/susan-montgomery\/\">Montgomery, Susan<\/a> (non-commutative algebras, Hopf algebras, representation theory)<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/negron\">Negron, Cris<\/a> (tensor categories, quantum groups, representation theory, mathematical physics)<\/li>\n<li><a href=\"https:\/\/sites.google.com\/usc.edu\/gpanova\/home\">Panova, Greta<\/a> (algebraic combinatorics, computational complexity, statistical mechanics, probability)<\/li>\n<li><a href=\"https:\/\/www.hwilliams.net\/\">Williams, Harold<\/a> (representation theory, algebraic geometry, symplectic geometry, mathematical physics)<\/li>\n<\/ul>\n<h4>Post-Docs<\/h4>\n<ul>\n<li>Daniele Garzoni (finite groups, algebraic groups, Galois theory)<\/li>\n<li>Czenky, Agustina (tensor categories, representation theory, quantum algebra)<\/li>\n<li>Biman Roy (algebraic geometry, homotopy theory)<\/li>\n<li>Gagnon, Lucas (combinatorics, representation theory, geometry)<\/li>\n<\/ul>\n<h4>Current Graduate Students<\/h4>\n<ul>\n<li>Somaiya, Yash (Asok)<\/li>\n<li>Yang, Fan (Asok)<\/li>\n<li>Qiu, Ye (Assaf)<\/li>\n<li>Kim Sung, Hyun (Lauda)<\/li>\n<li>Jernej Grlj (Lauda)<\/li>\n<li>Filippo Iulianelli (Lauda) (physics)<\/li>\n<li>Roman, Vlad (Guralnick)<\/li>\n<li>Sajan, Anna (Negron)<\/li>\n<li>Zhang Qiyu, (Negron)<\/li>\n<li>Wen, Jiayi (Panova)<\/li>\n<li>Liu, Tianle (Williams)<\/li>\n<li>Cetin, Baran (Williams)<\/li>\n<\/ul>\n<h4>Recent Ph.D.&#8217;s<\/h4>\n<ul>\n<li>Liu, Haoyang (2025) (Asok), &#8220;Splitting of some projective varieties in motivic stable homotopy category&#8221;<\/li>\n<li>Armon, Samuel (2025) (Assaf), &#8220;Atoms, Kohnert&#8217;s Rule, and Science Fiction&#8221;<\/li>\n<li>Bose, Jishnu (2025) (Williams), &#8220;Picard Group Actions on Constructible Sheaves via Contact Isotopies&#8221;<\/li>\n<li>Peng, Tina (2025) (Williams), &#8220;Koszul-perverse sheaves and the A_2^(1) dual canonical basis&#8221;<\/li>\n<li>Jiang, Wenhan (2024) (Asok), &#8220;Chow-Witt Rings of Toric Surfaces&#8221;<\/li>\n<li>Uskuplu, Elif (2024) (Lauda), \u201cFormalizing Two-Level Type Theory with Cofibrant ExoNat&#8221;<\/li>\n<li>Zhao, Chenchen (2024) (Panova), &#8220;On the Kronecker product of Schur functions&#8221;<\/li>\n<li>Bowling, Grant (2023) (Assaf), &#8220;Characters of Flagged Schur Modules and Compatible Slides&#8221;<\/li>\n<li>Ehrhard, Henry (2023) (Assaf), &#8220;Colors, Kohnert&#8217;s Rule, and Flagged Kostka Coefficients&#8221;<\/li>\n<li>Orlinsky, Kayla (2023) (Montgomery), &#8220;An Indicator Formula for a Semi-Simple Hopf Algebra&#8221;<\/li>\n<li>Ebert, Mark (2023) (Lauda), \u201cThe Structure and Higher Representation Theory of Odd Categorified sl_2&#8243;<\/li>\n<li>Wang, Shiyun (2023) (Panova), &#8220;Applications of Symmetric and Quasisymmetric functions&#8221;<\/li>\n<li>Balcik, Irmak (2022), &#8220;Growth of torsion of elliptic curves over noncyclotomic imaginary quadratic fields of class number 1&#8221;<\/li>\n<li>Kagey, Peter (2022), &#8220;Permutations, Statistics, and Switches&#8221;<\/li>\n<li>Siegel, Max (2022) &#8220;(p,q)-adic Analysis and the Collatz Conjecture&#8221;<\/li>\n<li>Port, Alex (2021), &#8220;Motivic Cohomology of BG_2&#8221;<\/li>\n<li>Quijada, Danjoseph (2021) &#8220;A Pieri rule for key polynomials&#8221;<\/li>\n<li>Eilidh McKemmie (2020)<\/li>\n<li>Viktor Kleen (2019), `Some Stable Splittings in Motivic Homotopy Theory&#8221;<\/li>\n<li>Nicolle Sandoval Gonzalez (2019), &#8220;Categorical operators and crystal structures on the ring of symmetric functions&#8221;<\/li>\n<li>Donner, Matthew (2018), &#8220;Regular unipotents in finite maximal subgroups of classical groups&#8221;<\/li>\n<li>Egilmez, Ilknur (2018) &#8220;DG Structures on Categorified Quantum Groups&#8221;<\/li>\n<li>Oguz, Ezgi Kantarci (2018) &#8220;Advances in the Combinatorics of Shifted Tableaux&#8221;<\/li>\n<li>Ozan Oguz, Can (2018) &#8220;Center and Trace of the Twisted Heisenberg Category&#8221;<\/li>\n<li>Ejder, Oslem (2017) &#8220;Torsion subgroups of elliptic curves in elementary abelian 2-extensions and monodromy of Fermat surfaces.&#8221;<\/li>\n<li>Gerhardt, Spencer (2017) &#8220;Topological generation of algebraic groups &#8220;<\/li>\n<li>Lamberto, Lafitte (2016) &#8220;A categorified braid group action&#8221;<\/li>\n<li>Tucker, Henry (2016) &#8220;Frobenius-Schur indicators for near-group and Haagerup-Izumi fusion categories&#8221;<\/li>\n<li>Abram, Mike (2015) &#8220;Symmetries of categorified quantum groups&#8221;<\/li>\n<li>Newman, Burton (2015) &#8220;Growth of torsion in quadratic extensions of quadratic cyclotomic fields&#8221;<\/li>\n<li>Wang, Jian (2015) &#8220;On the torsion structure of elliptic curves over cubic number fields&#8221;<\/li>\n<li>Warner, Jared (2015) &#8220;Springer isomorphisms and the variety of elementary subalgebras&#8221;<\/li>\n<\/ul>\n<h4>Recent Post-Docs and Visitors<\/h4>\n<ul>\n<li>Jay Taylor (group theory)<\/li>\n<li>Brendan Pawlowski (algebraic combinatorics)<\/li>\n<li><a href=\"https:\/\/sites.google.com\/usc.edu\/manion\/home\">Andy Manion<\/a> (low-dimensional topology, representation theory)<\/li>\n<li><a href=\"https:\/\/nivbhaskhar.github.io\/\">Nivedita Bhaskhar<\/a>\u00a0(algebraic groups)<\/li>\n<li>Alexander Soibelman (algebraic geometry and representation theory)<\/li>\n<li>Dominic Searles (combinatorics and algebraic geometry)<\/li>\n<li>Appel, Andrea (representation theory, quantum groups, classical and quantum integrable systems)<\/li>\n<li>Drew, Bradley (algebraic geometry)<\/li>\n<li>Jincheng Dong (Hopf algebras)<\/li>\n<li><a title=\"Daniel Murfet\" href=\"http:\/\/therisingsea.org\" target=\"_blank\" rel=\"noopener\">Daniel Murfet<\/a> (algebraic geometry, topological field theory)<\/li>\n<li>Paul Sobaje (modular representations of algebraic groups)<\/li>\n<li>Guangbin Zhuang (homological aspects of non-commutative algebra)<\/li>\n<\/ul>\n<h4>Retired Faculty<\/h4>\n<ul>\n<li><a href=\"https:\/\/dornsife.usc.edu\/profile\/sheldon-kamienny\/\">Kamienny, Sheldon<\/a> (Arithmetic geometry, modular forms, abelian varieties)<\/li>\n<\/ul>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":279,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-178","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ 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