I am a recent PhD in mathematics at University of Illinois Chicago.

Research:

PhD Thesis: Tilt Stability and Wall-Crossings for Curves in P3 and Cone of Divisors of Curves with High Genera, Mar 2023

- Examined the parametrization spaces for all curves in projective space to understand its local geometry

- Classification of space curves, especially singular curves, is extremely important for rigid motion in robotics 

• Programmed functions to compute Chern characteristics of curves using Python

• Programmed functions to compute expected dimension of parametrization space of curves of given characteristics

• Modeled cones in the plane to understand sub-geometric objects in the parametrization space of curves

• Generalized result on when curves of a given degree and genus can be represented with “nice” sequences of matrices

Higher Rank Brill-Noether Theory on P2, Int. Math. Res. Not, Dec 2022 (joint with Ben Gould and Yeqin Liu) (pdf)

- Generalization of when a curve can be embedded into projective space, studied extensively in classical algebraic geometry

- Laid groundwork for when vector bundles (coherent sheaves) over P2 have unexpected cohomological dimensions

• Received research assistantship from UIC for this collaborative work ($6,600)

• Programmed functions to compute characteristic classes of vector bundles using Python

• Programmed graphs depicting fractal curves on the plane using MATLAB

• Published in International Mathematics Research Notices after peer-review

• Presented the result in UIC Graduate Algebraic Geometry Seminar and GTA: Philadelphia at Temple University

Master’s Thesis: Tensor Categories, Z+ Rings, and Grothendieck Rings, May 2018 (pdf)

- Expository work on understanding the notion of tensor products in category theory

• Computed generators of matrix rings using Python

• Computed Koszul complexes, which are sequences given by matrices using Python

• Contacted by peers at UC Davis for usage as learning material 

An Infinite Family of Almost Unknotted θ4 Graphs, in preparation (joint with Hans Chaumont, Erica Flapan, Kenji Kozai, and Sarah Rundell)

- Classification of knots via mirror image symmetry

- Knot theory has wide applications and is integral to the study of genetic materials in biology and medical sciences

• Research Grant by National Science Foundation ($5,000)

• Programmed graphic representations of knots using Python and SnapPy

Homophonic Quotients of Linguistic Free Groups: German, Korean, and Turkish, Involve, 2019 (joint with Herbert Gangl and Gizem Karaali) (pdf)

- Measured how “rigid” pronunciations are for languages

- Languages with fewer possible pronunciations for each character in their alphabets have more complex group structure

• Computed free groups generated by homophonic equivalence on three languages

Undergraduate Thesis (Mathematics): Predicting Irrational Outcomes in Game Theory

- Examined irrational outcomes via usage of error terms in computing mixed equilibria 

• Took arbitrarily small spheres around the mixed equilibria to iterate probabilistic variance from the rational choice

• Gathered experimental data from students at Pomona College and compared with predicted variance from Nash equilibrium

Senior Project (Economics): Monetary Incentives and Willingness to Participate

- A documented phenomenon in behavioral economics is that people respond worse to small monetary incentives than none

- The project was an empirical study on such phenomenon, where questionnaires were collected from students at Pomona College

• Using R and STATA, ran logistic regression to find where monetary compensation incentivizes more than charitability

• Chosen as outstanding senior project and presented in front of the graduating class in the economics department