Casimir Kothari

Email: ckothari (at) uchicago (dot) edu.

I am a sixth year graduate student at the University of Chicago interested in algebraic geometry and number theory. My advisor is Matthew Emerton.
My graduate studies were supported by an NSF Graduate Research Fellowship. Previously, I was an undergraduate at Princeton University.

Research

• Dieudonné theory for n-smooth group schemes, with Joshua Mundinger. Submitted. [pdf] [arXiv] [Informal talk notes] [Companion Note]
  
  
• Duality of differential operators and algebraic de Rham cohomology, with Caleb Ji, Oliver Li, Svetlana Makarova, Shubhankar Sahai,
  and Sridhar Venkatesh. [pdf] [arXiv]
  
  
• Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic p. To appear in Journal de Théorie des Nombres
  de Bordeaux. [pdf] [arXiv]
  
  
• The Explicit Sato-Tate Conjecture For Primes In Arithmetic Progressions, with Trajan Hammonds, Noah Luntzlara, Steven J. Miller,
  Jesse Thorner, and Hunter Wieman. International Journal of Number Theory, Vol. 17, No. 08, pp. 1905-1923 (2021). [pdf] [arXiv]

Talk Notes

• Group Schemes over the Integers and Galois Representations
  
• Dieudonné theory for n-smooth group schemes
  
• Group Schemes and Dieudonné Theory
  
• The Moduli Stack of Displays [video]
  
• Modular Curves and Shimura Varieties
  
• Revisiting Failure of Hodge Symmetry in Characteristic p
  
• Motivating Witt Vectors and Delta Rings
  
• Differential Forms in Positive Characteristic and the Cartier Isomorphism

Other Notes

• Explicit Presentations for the Moduli Stack of n-smooth Group Schemes
  
• The Hodge Numbers of Projective Hypersurfaces