I am a PhD student in the University of Washington math department studying algebraic geometry with Sándor Kovács.

Research

My research focuses on singularities coming from the minimal model program and moduli of varieties. Particular interests include:

• applications of intersection theory and Hodge theory,

• positive-characteristic behavior, and

• infinitesimal deformations of MMP singularities

Preprints

• Higher direct images of logarithmic structure sheaves, in preparation
• Thrifty rational resolutions in arbitrary characteristic (general exam paper)

Talks

• Higher direct images of logarithmic structure sheaves, University of Washington Algebra and Algebraic Geometry Seminar (October 27, 2020)
• Du Bois Singularities in Families (joint work with Takumi Murayama), AMS Fall Eastern Sectional Meeting Special Session on Algebraic Singularities in Arbitrary Characteristic (October 3, 2020)
• Logarithmic Chow-to-Hodge cycle maps, MSRI Graduate Student Seminar (Spring 2019)
• The Cohomology of a Smooth Hypersurface, University of Washington Graduate Student 1, 2, 3 Seminar following the last section of these notes (Fall 2018)
• The cone of curves, University of Washington Graduate Student MMP Seminar (Winter 2017)
• The K-theory of finite fields, University of Washington Graduate Student 1, 2, 3 Seminar (Spring 2016)
• Survey of Linear Stochastic Bandits, MSRI Mathematics of Machine Learning Summer School (Summer 2019)

Notes

• Some notes I wrote while learning local Grothendieck Duality, mostly following the classic (Hartshorne, 1966).

  1. Hartshorne, R. (1966). Residues and Duality; Lecture Notes of a Seminar on the Work of A. Grothendieck, given at Harvard 1963/64. Springer-Verlag.

Axioms

I believe in Federico Ardila’s axioms:

• Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

• Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

• Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

• Axiom 4. Every student deserves to be treated with dignity and respect.

Acknowledgments

During the spring of 2019 I was in residence at the Mathematical Sciences Research Institute in Berkeley, California, supported by the National Science Foundation under Grant No. 1440140. During the academic year of 2018-2019 I was supported by the University of Washington Department of Mathematics Graduate Research Fellowship.