Cris Negrón
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Office: KAP 444C, USC
Email: cnegron_at_usc.edu
I am currently an Associate Professor at the University of Southern California, department of mathematics.
-- Mathematical interests
Quantum groups, representation theory, mathematical physics, and related topics.
-- Upcoming workshop
From June 1-5, this summer, we are hosting a "new structures in low-dimensional topology" workshop at AIM (in Pasadena CA). This is a grad-focused workshop meant to introduce participants to a wide array of topics within low-dimensional topology, from direct topological methods to more algebraic approaches. See more information, and the application, here.
-- Teaching Spring 2026
Math 510 B, Grad Algebra. Course website here.
-- Algebra Seminar
Schedule here.
-- Papers and preprints
Currently supported by NSF CAREER Grant No. DMS-2239698 and Simons Collaboration Grant No. 999367.
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(w/ A. Czenky) Cochain valued TQFTs from nonsemisimple modular tensor categories. submitted. (pdf)
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Quantum Frobenius and modularity for quantum groups at arbitrary roots of 1. J. Reine Angew. Math. to appear. (pdf)
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Revisiting the Steinberg representation at arbitrary roots of 1. Represent. Theory 2025. (pdf)
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(w/ J. Pevtsova) The half-quantum flag variety and representations for small quantum groups. Transform. Groups 2025. (pdf)
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(w/ J. Pevtsova) The Springer resolution and support theory for quantum groups. draft. (pdf)
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(w/ E. Friedlander) Support theory for Drinfeld doubles of some infinitesimal group schemes. Algebra Number Theory. 2023. (pdf)
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(w/ T. Gannon) Quantum SL(2) and logarithmic vertex operator algebras at (p,1)-central charge. J. Eur. Math. Soc. 2024. (pdf)
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(w/ J. Pevtsova) Hypersurface support and prime ideal spectra for stable categories. Ann. K-theory 2022. (pdf)
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(w/ J. Pevtsova) Hypersurface support for noncommutative complete intersections. Nagoya Math. J. 2022. (pdf)
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Finite generation of cohomology for Drinfeld doubles of finite group schemes. Selecta Math. 2021. (pdf)
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(w/ J. Pevtsova) Support for integrable Hopf algebras via noncommutative hypersurfaces. Int. Math. Res. Not. 2021. (pdf)
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(w/ P. Etingof) Pointed Hopf actions on central simple division algebras.
Transform. Groups. 2022. (pdf)
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Log-modular quantum groups at even roots of unity and the quantum Frobenius I. Comm. Math. Phys. 2021. (pdf)
- (w/ J. Plavnik) Cohomology of finite tensor categories: duality and Drinfeld centers. Trans. Amer. Math. Soc. 2022. (pdf)
- (w/ T. Schedler + appendices by P. Etingof and P. Belmans) The Hochschild cohomology ring of a global quotient orbifold. Adv. Math. 2020. (pdf)
- (w/ S. Witherspoon and Y. Volkov) A∞-coderivations and the Gerstenhaber bracket on Hochschild cohomology. J. Noncommut. Geom. 2020. (pdf)
- (w/ E. Friedlander) Cohomology for Drinfeld doubles of some infinitesimal group schemes. Algebra Number Theory 2018. (pdf)
- Twists for quantum Borel algebras. J. Algebra 2018. (pdf)
- Small quantum groups associated to Belavin-Drinfeld triples. Trans. Amer. Math. Soc. 2019. (pdf)
- (w/ S.
Witherspoon) The Gerstenhaber bracket as a Schouten bracket for
polynomial rings extended by finite groups. Proc. Lond. Math. Soc. 2017. (pdf)
- (w/ R. Ng) Gauge invariants from the powers of antipodes. Pacific J. Math. 2017. (pdf)
- Braided Hochschild cohomology and Hopf actions. J. Noncommut. Geom. 2019. (pdf)
- The cup product on Hochschild cohomology via twisting cochains
and applications to Koszul rings. J. Pure Appl. Algebra 2017. (pdf)
- The derived Picard group of an affine Azumaya algebra. Selecta Math. 2017.
(pdf)
- (w/ S.
Witherspoon) An alternate approach to the Lie bracket on Hochschild
cohomology. Homology Homotopy Appl. 2016. (pdf)
- Spectral sequences for the cohomology rings of a smash product. J. Algebra 2015. (pdf)
Works ordered according to when they were written.
-- Other writings
- Kerodon remix part I: ∞-category basics for algebraists. (pdf)
- Kerodon remix part II: Cocartesian fibrations, limits and colimits, and Yoneda embedding. (In progress)
- Kerodon remix part III: A small study of the derived ∞-category. (pdf)
Remark: These documents are still in development, to varying degrees. I'll probably edit them into 2026 (at least), after which point they may become some kind of book. Certainly all of the texts above are full of typos. So, I don't really need to know about those kinds of things. However, I would be happy to receive any comments concerning errors, misstatements, sections which might be confusing, historical remarks, etc. etc., all of which can be sent to me via email.
In my own estimations, Part I is in ok shape, Part III is probably serviceable, though it could use some work, and Part II is simply incomplete.
-- Travel Scheduled
| Location | Date |
| Orsay France | Sept 27-Oct 11, 2025 |
| Banff, CA | Jan 25-30 |
| Simons Center NY | Mar 25-30 |
| Riverside, California | Apr 2 |
| LSU, Baton Rouge | May 18-29 |
| Bonn, Germany | Aug 12-21 |
| SLMath, Berkeley | Sept |
-- Short Biography
I completed my undergrad work at the University of Virginia, then attended the University of Washington for grad school. At UW I worked under my advisor James Zhang. I did postdoc work at Louisiana State University, the Massachusetts Institute of Technology, the Hausdorff Institute at Bonn, and the Mathematical Science Research Institute at Berkeley. I was previously an assistant professor at the University of North Carolina (2019-2021).