# Ritvik Ramkumar

I am 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 University of Waterloo.

## Research

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

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

3. A Hilbert scheme of radius two [submitted | arXiv]

4. The Hilbert scheme of a pair of linear spaces, Mathematische Zeitschrift, to appear [Journal | arXiv]

5. On the smoothness of lexicographic points on Hilbert schemes (with Alessio Sammartano), Journal of Pure and Applied Algebra, to appear [Journal | arXiv]

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

7. On the tangent space to the Hilbert scheme of points in P^3 (with Alessio Sammartano) [submitted | arXiv | Video]

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]

## 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