Cris Negrón
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Office: KAP 444C, USC
Email: cnegron_at_usc.edu
I am currently an Assistant Professor at the University of Southern California, department of mathematics.
 Mathematical interests
Quantum groups, representation theory, mathematical physics, and related topics.
 Teaching Fall 2024
Math 513 Lie Theory, DMC 207 1212:50 pm. HW problems etc here.
 Algebra Seminar
Schedule here.
 Papers and preprints
Currently supported by NSF Grant No. DMS2149817, NSF CAREER Grant No. DMS2239698 and Simons Collaboration Grant No. 999367.

Quantum Frobenius and modularity for quantum groups at arbitrary roots of 1. submitted. (pdf)

Revisiting the Steinberg representation at arbitrary roots of 1. submitted. (pdf)

(w/ J. Pevtsova) The halfquantum flag variety and representations for small quantum groups. submitted. (pdf)

(w/ J. Pevtsova) The Springer resolution and support theory for quantum groups. draft. (pdf)

(w/ E. Friedlander) Support theory for Drinfeld doubles of some infinitesimal group schemes. Algebra Number Theory. to appear. (pdf)

(w/ T. Gannon) Quantum SL(2) and logarithmic vertex operator algebras at (p,1)central charge. J. Eur. Math. Soc. to appear. (pdf)

(w/ J. Pevtsova) Hypersurface support and prime ideal spectra for stable categories. Ann. Ktheory 2022. (pdf)

(w/ J. Pevtsova) Hypersurface support for noncommutative complete intersections. Nagoya Math. J. 2022. (pdf)

Finite generation of cohomology for Drinfeld doubles of finite group schemes. Selecta Math. 2021. (pdf)

(w/ J. Pevtsova) Support for integrable Hopf algebras via noncommutative hypersurfaces. Int. Math. Res. Not. 2021. (pdf)

(w/ P. Etingof) Pointed Hopf actions on central simple division algebras.
Transform. Groups. 2022. (pdf)

Logmodular 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_\inftycoderivations 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 BelavinDrinfeld 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)
 Travel Scheduled
Location  Date 
Simons Center NY  March 3031, 2023 
AMS Sectional SF  May 45, 2023 
Simons Center NY  Nov, 2023 
JMM San Francisco  Jan 5 

IPAM, Los Angeles  Jan 812 

Simons Center NY  March 2628 
AMS Sectional SF  May 45 
ICMS, Edinburgh  June 1721 
Renyi Institute, Budapest  July 114 
MSRI  July 15Aug 9 
USC  Aug 911 
Berkeley  Oct 8 
Melboourne  Nov 2229 
 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 (20192021).