UROP+ Papers
2020
Jordan Benson,
The Balmer Spectrum of Stable Module Categories Over Finite Group Schemes
Mentor: Adela Zhang
Krit Boonsiriseth,
The Maximum Number of $k$-gons in the Zone of a Pseudoline
Mentor: Pakawut Jiradilok
David Darrow,
A Convergence Rate for Extended-Source Internal DLA in the Plane,
Scaling Limits of Fluctuations of Extended-Source Internal DLA
Mentor: Pu Yu
Kaarel Hänni,
Asymptotics of Descent Functions
Mentor: Pakawut Jiradilok
Alina Harbuzova,
Sum-Product Estimates for Well-Spaced Sets
Mentor: Shengwen Gan
Junyao Peng,
A Homomorphism Between Elliptic Hall Algebra and $K$-theoretic Algebra of Surfaces
Mentor: Yu Zhao
Peter Rowley,
Perverse Sheaves and Quiver Representations
Mentor: Timothy Ngotiaoco
Tristan Shin,
On The Space of Planar Branched Polymers with Fixed Tangency Graph
Mentor: Vishal Patil
Naveen Venkat,
Contact Graphs for Disk Packing in the Plane
Mentor: Vishal Patil
Julian Wellman,
Higher Bruhat Orders for any Weyl Group
Mentor: James Tao
Chris Xu,
Homotopy Groups of the Fibers of the Chromatic Resolution of Determinant Twists of $Q(\ell)$
Mentor: Robert Burklund
2019
David Anthony Bau,
Comparing Two Braid Group Actions on Derived Categories of Flag Varieties and Projective Space
Mentor: Pablo Boixeda Alvarez
Yiran Cai,
The Maximal Divided Power Extension of the Spherical Cherednik Algebras for $\mathbb{Z}/p\mathbb{Z}$
Mentor: Daniil Kalinov
Anlong Chua,
Mod 2 Prismatic Cohomology of BSpin(n)
Mentor: Dmitry Kubrak
Maxwell Fishelson,
Packing Perfect Matchings in Random Graphs at the Optimal Threshold
Mentor: Vishesh Jain
Marisa Gaetz,
Dual Pairs in Complex Reductive Groups
Mentor: Lucas Mason-Brown
Kevin Ren,
On Constant Terms of Eisenstein Series
Mentor: Yongyi Chen
Zhuofan Xie,
On a Sharp Sobolev Inequality with Remainder Term
Mentor: Lingxian Zhang
2018
Kevin Beuchot,
Derived Functors for Hom and Tensor Product: The Wrong Way to do It
Mentor: Gurbir Dhillon
Korina Digalaki,
Irreducible Components and Dimension of the Spaltenstein Variety in Type A
Mentor: Pablo Boixeda Alvarez
Juan Carlos Ortiz,
The Steenrod Square on Khovanov Homologies
Mentor: Piotr Suwara
Sandeep Silwal,
Spectral Methods for Testing Clusters in Graphs
Mentor: Jonathan Tidor
Christopher Xu,
An Upper Bound For Signatures Of Irreducible, Self-dual
$\mathfrak{gl}$(n,$\mathbb{C}$)-representations
Mentor: Daniil Kalinov
Zixuan Xu,
Almost Conservation Laws for KdV and Cubic NLS
Mentor: Ricardo Grande Izquierdo
Avi Zeff,
Tate's thesis and arithmetic zeta functions
Mentor: Chun Hong Lo
2017
Christian Altamirano,
A Problem In Algebraic Number Theory
Mentor: Atticus Christensen
Anlong Chua,
p-Curvature Map of SL2 Opers on Elliptic and Hyperelliptic Curves
Mentor: Pablo Boixeda Alvarez
Zachary J. Farr,
Investigating Determinants Of Some Combinatorial Hard Lefschetz Isomorphisms
Mentor: Christian Gaetz
Bernardo Antonio Hernandez Adame,
Solitons of Curve Shortening Flow and Vortex Filament Equation
Mentor: Jiewon Park
Sung Gi Park,
On GKM Description of the Equivariant Cohomology of Flag Varieties and Affine Springer Fibers
Mentor: Pablo Boixeda Alvarez
Oron Propp,
Constructing Explicit K3 Spectra
Mentor: Hood Chatham
Stephen Yearwood,
A Correlated Approach to the Hamburger-Cheeseburger Theorem
Mentor: Minjae Park
Avi Zeff,
Counting points parametrized by infinitely many polynomial conditions
Mentor: Soohyun Park
YiYu Zhang,
An introduction to equivariant cohomology and the equivariant first Chern class
Mentor: Jiewon Park
2016
Attilio Castano,
Universal Homotopy Theories
Mentor: Pablo Boixeda
Siqi Chen,
Robustness of SDPs for Partial Recovery of Clustering Subgaussian Mixtures
Mentor: Amelia Perry
Carlos Cortez,
Approximation Of Smooth Surfaces By Polyhedral Surfaces with Hidden Vertices
Mentor: Aleksandr Berdnikov
Dimakis Panagiotis,
On The Non Negativity Of A Special Class Of Generalized Littlewood Richardson Coefficients
Mentor: Dongkwan Kim
Yuchen Fu,
The Conley-Zehnder Index of Brownian Paths on Sp(2,R)
Mentor: Umut Varolgunes
Yuzhou Gu,
Nilpotent Orbits: Geometry And Combinatorics
Mentor: Konstantin Tolmachov
Zachary Izzo,
Probability Measures on Representations of Unitary Groups
Mentor: Christopher Ryba
Kritkorn Karntikoon,
Energy Minimization Of Repelling Particles On A Toric Grid
Mentor: Dongkwan Kim
Yutao Liu,
Minimal Cell Structures for G-CW Complexes
Mentor: Siddharth Venkatesh
Panagiotis Lolas,
Asymptotics At The Edge Of Multilevel Discrete β-ensembles
Mentor: Evgeni Dimitrov
Eli Sadovnik,
A Central Limit Theorem for Fluctuations of Internal Diffusion-Limited Aggregation with Multiple Sources
Mentor: Ricardo Grande Izquierdo
Mark Sellke,
An Introduction to Imaginary Geometry
Mentor: Andrew Ahn
Mrudul Thatte,
Signatures of GLn Multiplicity Spaces
Mentor: Siddharth Venkatesh
Jianqiao Xia,
Classification of Formal Duality with an Example in Sphere Packing
Mentor: Soohyun Park
2015
Lara Booth,
“Maximal Products Of Su(2) In Compact Lie Groups”
Mentor: Daniel Thompson
Arkadiy Frasinich,
“The Image of Weyl Group Translations in Hecke Algebras”
Mentor: Konstantin Tolmachov
George Friedlander,
“On the Fixed Points of Unipotent Action on Flag
Varieties and Its Relation to Pairs Of Young Tableaux”
Mentor: Nate Harman
Saarik Kalia,
“Computing Signatures for Representations of
the Hecke and Cherednik Algebras”
Mentor: Siddharth Venkatesh
Semon Rezchikov,
“Diff-invariant relations on open manifolds”
Mentor: Konstantin Tolmachov
Bertrand Stone,
“Asymptotic Recursive Line Complexity Behavior of
Polynomial Cellular Automata”
Mentor: Chiheon Kim
Simon Zheng,
“The Vertex Isoperimetric Problem on Kneser Graphs”
Mentor: Brandon Tran
2014
Jiacheng Feng,
“Portfolio Selection with Mandatory Bequest”
Mentor: Menglu Wang
Yajit Jain,
“Bredon Equivariant Homology of Representation Spheres”
Mentor: Eva Belmont
James Rowan,
“Oscillating tableaux and a superanalogue of the Robinson-Schensted-Knuth correspondence”
Mentor: Cesar Cuenca
Yair Shenfeld,
“Tug-of-war Games with Spatial and Temporal Dependence in Noisy Environments”
Mentor: Cheng Mao
Cheng Mao, Xin Sun and Tianyou Zhou,
“Inventory accumulation with k products”
Mentor: Cheng Mao