UROP+ Papers


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
Archana Mohandas TBA Mentor: Tang-Kai Lee
Sam Packman TBA Mentor: Alexander McWeeney
Erick Padilla Weyl-Kac Character Formulas for Lie Superalgebras Mentor: Ivan Motorin
Adam W Rothbaum TBA Mentor: Lior Alon
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


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


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


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


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


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


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


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


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