Cris Negrón

Cris Negrón is an Assistant Professor in the Department of Mathematics at the University of Southern California (USC), within the Dornsife College of Letters, Arts and Sciences. His research focuses on quantum groups, representation theory, mathematical physics, and related areas such as cohomology theories and algebraic geometry. He organizes the USC Algebra Seminar, which explores topics including algebra, representation theory, algebraic geometry, homotopy theory, and mathematical physics.

Education:

• PhD in Mathematics from the University of Washington (advisor: James Zhang)
• Postdoctoral positions at Louisiana State University, MIT, Hausdorff Institute (Bonn), and MSRI (Berkeley)
• Previous faculty position at the University of North Carolina (2019-2021)

Research Interests:

Negrón investigates quantum algebra structures, including small quantum groups and their cohomological properties. His work bridges representation theory, Hopf algebras, and geometric methods, with applications to mathematical physics and topological quantum field theories. Key themes include support theories for Hopf algebras, quantum group modularity, and logarithmic vertex operator algebras.

Recent Work Trends:

His papers emphasize modularity in quantum groups, support varieties, and cohomological structures. Notable contributions include studies on quantum Frobenius maps, Springer resolutions, and Drinfeld doubles of infinitesimal group schemes. Collaborations with experts like Julia Pevtsova and Eric Friedlander highlight his engagement with cutting-edge problems in representation theory.

Grants & Funding:

• NSF CAREER Grant (DMS-2239698)
• Simons Collaboration Grant (999367)

Teaching & Service:

In Fall 2024, he teaches Math 430. He actively participates in academic travel, presenting at institutions like MIT, Banff International Research Station, and conferences in Europe and North America. His leadership in organizing the Algebra Seminar reflects his commitment to fostering interdisciplinary dialogue.

Labs/Teams:

Engaged with USC’s mathematics research community, contributing to collaborative projects on quantum algebra and representation theory through seminars and workshops.