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

Papers

• 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)

• Fukaya category on a symplectic manifold with a B-field, arXiv:2311.04143
  With Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu (2023)

• Homological mirror symmetry for theta divisors, in preparation, (slides)
  With Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu. Talks by Chiu-Chu Melissa Liu, Haniya Azam, Heather Lee.

• Global homological mirror symmetry for genus two curves, in preparation
  With Haniya Azam, Heather Lee, Chiu-Chu Melissa Liu. Talk here and by Heather Lee here. Shorter notes here.

• Semi-orthogonal decompositions in Fukaya-Seidel mirrors to blowups of abelian varieties (preprint, JMM 2024 slides)
  With Sara Venkatesh.

• A mirror into the higher dimensional world (pdf)
  SCGP newsletter, Volume XVII (2022), p12-16

• 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), p28-55. Panel recording here.

• 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)

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

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

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

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

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

Notes & lectures

• Geometry of Landau-Ginzburg Models and Homological Mirror Symmetry, Latam-ICTP Physics Without Frontiers, Math & HEP Seminars, Sept 22, 2023

• Floer Homology Fundamentals at Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Summer School

• SYZ for hypersurfaces in toric varieties - talk in Seminar on Mirror Symmetry, Spring 2016

• The Fukaya category and mirror of the genus 2 curve  - talk in Seminar on Mirror Symmetry, Fall 2015

• Qualifying exam syllabus