Dorian Lee
(Legal Name: Woo Hyung Lee)
Email: wlee213@uic.edu, dorianlee2790@gmail.com
851 S. Morgan St. 721
University of Illinois at Chicago
Dorian Lee
(Legal Name: Woo Hyung Lee)
Email: wlee213@uic.edu, dorianlee2790@gmail.com
851 S. Morgan St. 721
University of Illinois at Chicago
I studied algebraic geometry, and my advisor is Izzet Coskun.
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