Curiouser and curiouser!
I’m a PhD student in Mathematics at Brown University. I’m fortunate to be advised by Melody Chan.
My current research interest is to study enumerative and intersection problems in algebraic geometry and arithmetic, using techniques from combinatorics and representation theory.
Prior to Brown, I was a Lang Fellow at Yale where I received my M.Sc. in math and had spent wonderful four years of undergrad at Harvey Mudd College studying math and music.
I also enjoyed computing and AI. With that, I was lucky to work with amazing research scientists at Google Research during undergrad.
Click on the four icons below my pic for cv, email, github and google scholar, up to a permutation.
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
- Tropical Derivation of Cohomology Ring of Heavy/Light Hassett Spaces
Harvey Mudd College Senior thesis, 2017. For new development on the same topic, see a preprint above under a similar title.
Teaching
Canada/USA Mathcamp
- Mathcamp 2018: Algebraic Number Theory
- Mathcamp 2018: Modular Forms
- Mathcamp 2018: Rational Points on Elliptic Curves
- Mathcamp 2018: Introduction to Geometric Group Theory (Trees!)
- Mathcamp 2019: Introduction to Group Theory
- Mathcamp 2019: Young Tableaux and Combinatorics
- Mathcamp 2019: Young Tableaux and Probability (with Andrew Lin)
I felt at home and had tons of fun at Mathcamp 2018 and 2019.
See below for my class notes.
Misc
- In Spring 2020, I'm organizing The 7th AMS Annual Graduate Student Conference with Sam Freedman.
- Since Spring 2019, I've been organizing Brown Directed Reading Program with Kyle Ferendo and Jiahua Zou.
- I loved teaching and living at Canada/USA Mathcamp.
- I'm on the Diversity and Inclusion Committee of the math department at Brown. Let us know how we can improve!
- I am an alum of Summer Science Program '12, where we stayed up and looked at stars, scorpius and saturn till 3AM for 6 weeks in a New Mexico desert.
- I use Dvorak keyboard layout, which feels much comfier than QWERTY for typing English, and helps with my hand strains.
- I support Access Fund, protecting America's climbing.