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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


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