UROP+ Papers

2024

Howard Beck and Kyle Roke	Chromatic blueshift conjecture: the simple case and an algebraic analogue	Mentor: Tristan Yang
Owen Conoly	Irreducible Components and Dimension of the Springer Fiber of a Hook-Type Slodowy Slice	Mentor: Haoshuo Fu
Mikaela Finlay	Learning Dynamics of Particle Systems	Mentor: Harry James Walden
Abhinav Goel	Strichartz Estimates for One Dimensional Stochastic Schrodinger Equation with Potential	Mentor: Josh Messing
Oluyinka Lindblad	Curve Shortening Flow in the Hyperbolic Plane	Mentor: Alexander McWeeney
Maximus Lu	Combinatorial Results in Partition Theory	Mentor: Ryota Inagaki
Holden Mui	Coalescence Probabilities Of Cycle Products	Mentor: Oriol Sole Pi
Jaedon Whyte	Critical Points for the Gaussian Isoperimetric Problem in $\mathbb{R}^{2}$	Mentor: Michael Law
Isaac Zhu	Knizhnik-Zamolodchikov Equations In Deligne Categories	Mentor: Ivan Motorin

2023

Sophie Vulpe	A Survey of Time-Frequency Decomposition	Mentor: Sarah Greer
Kenta Suzuki	Kazhdan-Lusztig Polynomials On Subregular Affine Weyl Group Elements In Type B	Mentor: Vasily Krylov
Daniel Xia	The Hidden Subgroup Problem for Non-Abelian Groups	Mentor: Henry Ma
Mohit Hulse	The asymptotic size of Selmer groups over function fields	Mentor: Gefei Dang
Roni A Edwin	The Fractal Uncertainty Principle (FUP)	Mentor: Alain Kangabire
Allen Lin	Exploring Gaps in Arithmetic Sequences	Mentor: Alexander Ortiz
Omar Abdelghani	SO(N) lattice Gauge Theory in the large N Limit	Mentor: Ron Nissim
Erick Padilla	Weyl-Kac Character Formulas for Lie Superalgebras	Mentor: Ivan Motorin
Pedro A Suarez	To find a pairs of knots (K, J) such that K has smooth 4-ball genus equal to one, and Fintushel-Stern surgery on the 0-trace of K with companion J is diffeomorphic to the 0-trace of some third knot K0	Mentor: Charles Stine
Fedir Yudin	Fine Mixed Subdivisions of a Dilated Triangle	Mentor: Yannick Yao
Zhao Yu Ma	Enumerating singular curves in linear systems on surfaces.	Mentor: José Guzman

2022

Omar Abdelghani	SO(N) lattice Gauge Theory in the large N Limit	Mentor: Ron Nissim
Roni A Edwin	The Fractal Uncertainty Principle (FUP)	Mentor: Alain Kangabire
Mohit Hulse	The asymptotic size of Selmer groups over function fields	Mentor: Gefei Dang
Allen Lin	Exploring Gaps in Arithmetic Sequences	Mentor: Alexander Ortiz
Zhao Yu Ma	Enumerating singular curves in linear systems on surfaces.	Mentor: José Guzman
Erick Padilla	Weyl-Kac Character Formulas for Lie Superalgebras	Mentor: Ivan Motorin
Pedro A Suarez	To find a pairs of knots (K, J) such that K has smooth 4-ball genus equal to one, and Fintushel-Stern surgery on the 0-trace of K with companion J is diffeomorphic to the 0-trace of some third knot K0	Mentor: Charles Stine
Kenta Suzuki	Kazhdan-Lusztig Polynomials on Subregular Affine Weyl Group Elements in Type B	Mentor: Vasily Krylov
Sophie Vulpe	UROP+: A Survey of Time-Frequency Decomposition	Mentor: Sarah Greer
Fedir Yudin	Fine Mixed Subdivisions of a Dilated Triangle	Mentor: Yannick Yao
Daniel Xia	The Hidden Subgroup Problem for Non-Abelian Groups	Mentor: Henry Ma

UROP+ Papers

2021

Keita Allen	Complexity Analysis of Computation of Homotopy Groups of Spheres	Mentor: Robert Burklund
Ibrahim Suat Evren	On Hypercontractivity on the Symmetric Group	Mentor: Ashwin Sah
Jeffery Li	An Exploration into Local Sparse Spanning Graph Algorithms	Mentor: Aaron Berger
Kerri Lu	Learning Mixtures of Elliptical Distributions	Mentor: Cole Franks
Andrew Weinfeld	Lifting L-polynomials of Smooth Plane Quartics	Mentor: David Jongwon Lee
Andrew Yao	Limits of Probability Measures With General Coefficients	Mentor: Matthew Nicoletti

2020

Aruzhan Amanbayeva	Convex Hull of Parking Functions of Length $n$	Mentor: Danielle Wang
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 GL_n 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