Ritvik Ramkumar

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I am currently a sixth-year PhD student at UC Berkeley in the Department of Mathematics. My advisor is David Eisenbud and I am primarily interested in Algebraic Geometry (with a view toward Commutative Algebra). Prior to that, I was an undergraduate student at the University of Waterloo.

Starting in the fall, I will be an H. C. Wang Assistant Professor at Cornell University in the Department of Mathematics.

Research

  1. A local study of the fiber-full scheme (with Yairon Cid-Ruiz) [submitted | arXiv]

  2. Rational singularities of nested Hilbert schemes (with Alessio Sammartano) [submitted | arXiv]

  3. The fiber-full scheme (with Yairon Cid-Ruiz) [submitted | arXiv | Video]

  4. On the tangent space to the Hilbert scheme of points in P^3 (with Alessio Sammartano), Transactions of the American Mathematical Society [to appear | arXiv | Video 1 | Video 2]

  5. The Hilbert scheme of a pair of linear spaces, Mathematische Zeitschrift 300: 493-540 (2022) [Journal | arXiv]

  6. On the smoothness of lexicographic points on Hilbert schemes (with Alessio Sammartano), Journal of Pure and Applied Algebra 226: Article 106872 (2022) [Journal | arXiv]

  7. Hilbert schemes with few Borel-fixed points [submitted | arXiv]

  8. Embeddings of quotient division algebras of rings of differential operators (with Jason P. Bell, Colin Ingalls) , Israel Journal of Mathematics 219: 411-430 (2017) [Journal | arXiv]

  9. A Hilbert scheme of radius two [arXiv]

Software

  • GKMVarieties - A Macaulay2 package for computations with GKM varieties and moment graphs (with Chris Eur)

Contact

Office: 1075 Evans Hall

Email: ritvik [at] berkeley [dot] edu