Department of Mathematics
Columbia University
Office: Room 506, Mathematics Hall
Email: akashs [at] math [dot] columbia [dot] edu
I am a Ritt Assistant Professor at Columbia University. My research interests are in algebraic geometry, number theory and algebraic complexity theory. I received my PhD in 2019 from Princeton University under the supervision of János Kollár. Previously, I completed my Bachelor's and Master's studies at Chennai Mathematical Institute, India.
Here is my Curriculum Vitae .
My research work is in algebraic geometry and its applications to number theory, algebraic complexity theory and combinatorics. I use the minimal model program (MMP) to prove results about birational geometry of algebraic varieties and apply these results to study arithmetic and geometric problems about rational points and rational curves on Fano varieties. I am also interested in algebraic geometric problems motivated by algebraic complexity theory. My research has focused on proving dimension bounds on Sylvester-Gallai configurations using algebraic geometric techniques, which have far-reaching applications to the Polynomial Identity Testing (PIT) problem in theoretical computer science. Here are some of my papers:
1. Radical Sylvester-Gallai Theorem for Tuples of Quadratics (with A. Garg , R. Oliviera , and S. Peleg ). CCC 2023 .
2. Radical Sylvester-Gallai Theorem for Cubics (with R. Oliviera ), FOCS 2022 .
3. Robust Radical Sylvester-Gallai Theorem for Quadratics (with A. Garg and R. Oliviera ), SoCG 2022 .
4. Geometric consistency of Manin's Conjecture (with B. Lehmann and S. Tanimoto ) Compositio Math. 158 (2022), 1375-1427.
5. Manin's Conjecture and the Fujita invariant of finite covers. Algebra & Number Theory 15 (2021), 2071–2087.
6. Manin's b-constant in families. Algebra & Number Theory 13(8): 1893-1905 (2019).
7. Counterexamples to Mercat's conjecture, Archiv der Mathematik 106, 439-444 (2016).
1. Calculus I, Columbia University, Fall 2019, Fall 2020, Fall 2021, Fall 2022.
2. Algebraic Curves, Columbia University, Spring 2020, Summer 2021, Spring 2022.
3. Multivariable Calculus, Princeton University, Fall 2016.