Research

Ongoing projects:

1. Weak Brill-Noether theory: With Howard Nuer.

2. Exceptional collections on some surfaces of general type: With Alexey Elagin.

3. Non-commutative Minimal Model Program for surfaces: With Hannah Dell and Alekos Robotis.

4. Stability manifold of projective bundles over curves: With Nicolás Vilches.

Papers: 

1. (With Pat Lank, Kabeer Manali Rahul) Integral transforms on singularity categories for Noetherian schemes (arxiv), accepted in the Michigan Mathematical Journal.

2. (With Sean M. Edwards, Neelarnab Raha) Nef cones of Hilbert schemes of points on some rank K3 surfaces (arxiv).

3. Stability conditions on product-quotient surfaces (in preparation).

4. Stability conditions on Calabi-Yau threefolds of type A. (In preparation)

Grants/Awards:

1. Travel grant from the University of South Carolina, 2026.

2. Recipient of the Simons Dissertation Fellowship in Mathematics, 2025.

3. Received the Heilbronn Institute for Mathematical Research (HIMR) Grant, 2025, jointly with Hannah Dell, Sam Johnston, and Patrick Kennedy-Hunt.

Activities: 

1. We organized a special session on “Derived Categories, Stability Conditions, and Homological Mirror Symmetry” at the AMS 2026 Spring Eastern Sectional Meeting at Boston College, March 28-29, 2026.

2. In the Spring of 2025, we ran an online learning seminar on Quantum cohomology. Here's the website.

3. In the Spring of 2024, we organized an online learning seminar on Stacks.

4. In the Fall of 2023, Sayan (UGA) and I arranged a reading group on Deformation theory. Here is the webpage.

5. In the Fall of 2023 I arranged a learning seminar on the "New outlook of MMP". Find more on this webpage.

Talks: 

1. Oct, 2026: Student Algebraic Geometry Seminar, University of Michigan. 

2. Sep, 2026: CAAG Seminar, University of Minnesota. 

3. Sep, 2026: Algebraic Geometry Seminar, University of California, Santa Barbara (online).

4. Sep, 2026: Algebraic Geometry Seminar, Centre for Mathematical Sciences, University of Cambridge. 

5. Sep, 2026: Algebraic Geometry Seminar, School of Mathematical and Physical Sciences, University of Sheffield 

6. At the Special Session on Geometry of Moduli Spaces at Boston College.

7. At the Derived FRG workshop: Hyperkähler Varieties, Derived Categories, and Moduli Spaces. 

8. 10/09/2023: Moduli problems in Algebraic Geometry, at AGCANT Student Seminar at the University of South Carolina.

9. 10/02/2023: Stability conditions, at AGCANT Student Seminar at the University of South Carolina.

10. 03/22/2023: Mori Dream Surfaces, at AG & CA Student Seminar at the University of South Carolina.

11. 03/16/2023: Mori Dream Spaces, at AG & CA Student Seminar at the University of South Carolina.

Conferences attended:

1. Georgia Algebraic Geometry Symposium 2025 at UGA.

2. Derived FRG 2025 - Hyperkähler Varieties, Derived Categories, and Moduli Spaces at Columbia University.

3. Algebraic Geometry Northeastern Section 2024 at Dartmouth College.

4. Introduction to the Theory of Algebraic Curves, at SLMath, July 8-19, 2024.

5. Algebraic Geometry Northeastern Section 2024 at Boston College.

6. Introductory Workshop: Noncommutative Algebraic Geometry at SLMath, Feb 5-9, 2024.

7. Algebraic Geometry Northeastern Section 2023 at UPenn.

8. Georgia Algebraic Geometry Symposium 2023 at UGA.