Curiouser and curiouser!

I’m a PhD student in Mathematics at Brown University. My advisor is Melody Chan.

My current research interest is to study enumerative and intersection problems in algebraic geometry and arithmetic geometry, using techniques from combinatorics and representation theory.

Prior to Brown, I was a Lang Fellow at Yale 2017-2019 where I got my master’s degree in math and had spent wonderful four years of undergrad at Harvey Mudd College studying math, CS and music.

Research

In Preparation

  • Relative Bott-Samelson Varieties
    We recall the definition of relative Bott-Samelson varieties, and prove that product of two relative Bott-Samelson schemes is a resolution of singularities of relative Richardson varieties defined with respect to versal flags. This reflects the nature that local geometry of relative Richardson varieties is completely governed by the two intersecting relative degeneracy loci, studied by Chan and Pflueger in 2019. Along the way, we generalize results regarding local geometry of intersection of degeneracy loci with respect to versal flags, defined by Chan and Pflueger, to general Lie types. We then present geometric and cohomological results about relative Bott-Samelson varieties and their products analogous to Brion's notes on flag varieties in type A. Such construction yields an application to resolution of singularities of Brill-Noether variteies with imposed ramification in the two-pointed case. See work by Chan, Osserman and Pflueger in 2018.

Preprints

  • Chow ring of Heavy/Light Hassett Spaces via Tropical Geometry
    (with Siddarth Kannan and Dagan Karp, 2019)
    Heavy/light Hassett spaces are moduli space of rational curves with weighted marked points that satisfy a “heavy/light” and a stability condition. We present a computation of the Chow ring of such spaces via Tropical Geometry. Our computation weaves together many beautiful combinatorial gadgets that appear in algebraic geometry. The starting point of our computation is to view these spaces as tropical compactifications of hyperplane arrangement complements, using work by Cavalieri-Hampe-Markwig-Ranganathan. Then the computation of the Chow ring then reduces to intersection theory on the toric variety of the Bergman fan of a graphic matroid. In particular, this reduction allows us to bijectively correspond divisors of the related toric variety to trees with stable weighted rays, thereby computing the final Chow ring combinatorially.

Undergrad Senior Thesis

Travel

Upcoming Travel

  • AMS Spring Eastern Sectional Meeting, Medford, MA, March 21-22, 2020
  • Women in Algebraic Geometry, ICERM, Providence, RI, July 27-31, 2020
  • Semester program in Combinatorial Algebraic Geometry, ICERM, Providence, RI, Spring 2021

Past Travel

  • Facets of Algebraic Geometry, University of Michigan, October 18-20, 2019
  • AGNES Fall 2019, Boston College, Sep 20-22, 2019
  • MSRI Summer Graduate School: Toric Varieties, Taipei, July 29-August 10, 2019
  • Ideals, Varieties, Applications (Celebrating the Influence of David Cox), Amherst, June 10-14, 2019
  • AGNES Spring 2019, Amherst, Mar 22 - 24, 2019
  • AGNES Fall 2018, Brown University, Sep 21 - 23, 2018
  • MSRI Summer Graduate School: Séminaire de mathématiques supérieures (SMS) 2018 on Derived Geometry and Higher Categorical Structures in Geometry and Physics, Fields Institute, June 10-22, 2018
  • Arizona Winter School, University of Arizona, March 3-8, 2018
  • MSRI Enumerative Geometry Beyond Numbers Workshops, Berkeley, Jan 18-27, 2018
  • BATMOBYLE Fall 2017, Yale University, Nov 27, 2017
  • AGNES Fall 2017, Northeastern University, Oct 13-15, 2017
  • Western Algebraic Geometry Symposium Fall 2016, Colorado State University, Oct 15-16, 2016
  • Student Tropical Alegbraic Geometry Seminar, Yale University, June 3-6, 2016

Misc