I study symplectic geometry through Kontsevich's homological mirror symmetry conjecture. I research Fukaya categories of Landau-Ginzburg models.

Papers

1. Homological mirror symmetry for theta divisors (slides)
   With Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu, 55 pages. Talks by Chiu-Chu Melissa Liu, Haniya Azam, Heather Lee.

2. Global SYZ mirror symmetry for genus two curves and Voronoi decompositions (slides)
   With Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu, 24 pages. Talk here and by Heather Lee here. Shorter notes here.

3. Semi-orthogonal decompositions in Fukaya-Seidel mirrors to blowups of abelian varieties, arXiv:2508.06379
   With Sara Venkatesh (2025), 33 pages

4. Global SYZ mirror symmetry and homological mirror symmetry for principally polarized abelian varieties,  arXiv:2503.20948
   With Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu (2025), 52 pages

5. On fiber and base decompositions in the Fukaya category of a symplectic Landau-Ginzburg model, arXiv:2312.00973
   With Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu (2023), 16 pages

6. Fukaya category on a symplectic manifold with a B-field, arXiv:2311.04143
   With Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu, 19 pages, under revision for Mathematical Research Letters (2025)

7. A mirror into the higher dimensional world (pdf)
   SCGP newsletter, Volume XVII (2022), pp 12-16

8. Historical context as an inclusive practice
   Contribution to Dr. Pamela E. Harris and Dr. Aris Winger's book 2 in their series, Practices and Policies: Advocating for Students of Color in Mathematics (2021), pp 28-55. Panel recording here.

9. Action-angle and complex coordinates on toric manifolds (pdf)
   With Haniya Azam and Heather Lee. In Research Directions in Symplectic and Contact Geometry and Topology, Eds. Bahar Acu, Catherine Cannizzo, Dusa McDuff, Ziva Myer, Yu Pan, Lisa Traynor. Association for Women in Mathematics Series, vol. 27, Springer International Publishing (2021), pp 159–216

10. Categorical mirror symmetry on cohomology for a complex genus 2 curve (pdf)
    Advances in Mathematics, 375 (2020), pp 107392. Talks here and here while Long-Time Visitor at the Fields Institute, Fall 2019.

11. Kähler-Einstein Metrics on Fano Manifolds (pdf)
    Cambridge University Part III essay, Master of Mathematics (2012)

12. Z2-actions by Symplectic Automorphisms of a Torus (pdf)
    Joint with Alexander Leaf and Nina Sakharova. Project in Penn State REU (2011)

13. X-Ray Variability: Quasi-periodic Oscillations (pdf)
    Project in NASA internship (2010)

14. Carmichael's Totient Conjecture and Fermat Primes (pdf)
    UMBC Review, volume 9, pp 160-173 (2008)

Student Projects

Masters

• Blythe Davis, Open book decompositions and surgery on contact 3-manifolds, Stony Brook, Spring 2021

Undergraduate

• Ofelia Flores Rodriguez, Respiratory Diseases Among Residents Living Near Dairy Farms, UC Berkeley, MPS Scholars, Summer 2024

• Lauren Aycott and Adán Javier Ortiz, A Quantitative Approach to Disseminating Impacts of Dismantling Affirmative Action, UC Berkeley, MPS Scholars, Summer 2024