Past SPUR Projects

2023 Topics

Serena An and Holden Mui Flip Graphs on Self-Complementary Ideals of Chain Products Mentor: Elisabeth Bullock
Saba Lepsveridz and Yihang "Kimi" Sun Size of the largest Sum-Free Subset of [n]^3 Mentor: Mehtaab Sawhney
Maxim Q Li and Misheel Otgonbayar On constructing solutions to S-unit equations in Q∞,l Mentor: Minh-Tam Trinh
Elaine Liu Modeling International Trade Tariffs Mentor: George Stepaniants
Isaac Lopez and Daniel Santiago Positive Mass Theorems for Asymptotically Euclidean Smooth Metric Measure Spaces Mentor: Michael Law
Isabel McGuigan and Katherine Pan Bipartite and Euclidean Gallai-Ramsey Theory Mentor: Zixuan Xu
Nathan S Sheffield and Divya P Shyamal Matching Algorithms in the Sparse Stochastic Block Model Mentor: Anna Brandenberger and Byron Chin
Atticus Wang On The Analytic Langlands Correspondence for PGL_2 In Genus 0 with Wild Ramification Mentor: Daniil Kliuev

2022 Topics

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Carlos Alvarado and Ayodeji Linblad Dynamical Stability of Translators Under Mean Curvature Flow Mentor: Tang-Kai Lee
Evgeniya Artemova and Christina Yu Lower Bounds on the Discrete Newton’s Algorithm for the Submodular Line Search Problem Mentor: Yuchong Pan
Merrick Cai Decomposition of Frobenius Pushforwards of Line Bundles on Wonderful Compactifications Mentor: Vasily Krylov
Paige Dote Exceptional Set Estimates For Orthogonal and Radial Projections In $\mathbb{R}^n$ Mentor: Shengwen Gan
Shu Ge Extension of $K_4$-Intersecting Families of Graphs Mentor: Nitya Mani
Milan Haiman Irreducibility of Generalized Permutohedra, Supermnodular Functions, and Balanced Multisets Mentor: Yuan Yao
Sanjay Raman Multiplication Kernels for the Analytic Langlands Program in Genus Zero Mentor: Danill Kliuev
Kenta Suzuki Gelfand-Kirillov Dimension of Representations of $GL_n$ Over a Non-Archimedean Local Field Mentor: Hao Peng
Andrew Yao Densities for Elliptic Curves over Global Function Fields Mentor: Hao Peng
Honglin Zhu Maximum Overlap Area of a Convex Polyhedron and a Convex Polygon Under Translation Mentor: Hyuk Jun Kweon

2021 Topics

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Enrico Colón Split-multiplicity-free flagged Schur polynomials Mentor: Yibo Gao
Preston Cranford and Peter Rowley Finding Bounded Simplicial Sets with Finite Homology Mentor: Robert Burklund
Dain Kim and Anqi Li Cubic Goldreich-Levin Mentor: Jonathan Tidor
Daishi Kiyohara A new approach to the upper estimate of lattice points on a curve via $\mathscr{l}^2$ decoupling Mentor: Feng Gui
Jacob Lerma and Jeffery Opoku-Mensah Positivity of the mass using p—harmonic functions on asymptotically flat 3-manifolds Mentor: Julius Baldauf
Yuyuan Luo Explicit Construction of the Hecke Character Associated to Certain CM Elliptic Curves Mentor: Gefei Dang
Alan Peng Convolution-exact perverse sheaves on the affine flag variety Mentor: Calder Morton-Ferguson
Amanda Ledesma Vanegas A Reduced Swift-Hohenberg Style Model for Vegetation Patterns in Drylands Mentor: Davis Evans and Alasdair Hastewell
Frank Wang Toward explicit Hilbert series of quasi-invariant polynomials in characteristic $p$ and $q$-deformed quasi-invariants Mentor: Calder Morton-Ferguson

2020 Topics

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Elisabeth Bullock and Katie Gravel Higher Secondary Polytopes for Two-Dimensional Zonotopes Mentor: Alexey Balitskiy
Kevin Chang A v1-banded vanishing line for the mod 2 Moore Spectrum Mentor: Robert Burklund
Korina Digalaki Deformed Airy Kernels in Height Function Fluctuations of the Stochastic Six-Vertex Model Mentor: Roger Van Peski
Aparna Ajit Gupte and Kerri Lu Fine-Grained Complexity of Sparse Linear Regression Mentor: Frederic Koehler
Christina Meng On Configuration Spaces of Higher-Dimensional Analogues of Genus g Surfaces Mentor: Araminta Gwynne
Dylan Pentland Filtrations on Block Subalgebras of Reduced Universal Enveloping Algebras Mentor: Andrei Ionov
Kevin Ren Incidence estimates for $α$-dimensional tubes and $β$-dimensional balls in $\mathbb{R}^2$ Mentor: Yuqiu Fu
Carl Schildkraut and William Zhao Relating Counts in Different Characteristics for Steiner’s Conic Problem Mentor: Chun Hong Lo
Calvin Yost-Wolff A Geometric RSK Correspondence and Relative Positions Within Springer Fibers Mentor: Oron Propp
Hung-Hsun Hans Yu Joints of Varieties Mentor: Jonathan Tidor

2019 Topics

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Kevin Beuchot Castellanos Lifting to $\mathbb{Z}/p^2\mathbb{Z}$ and Splittings of the de Rham Complex Mentor: Robert Burklund
Andrew Gu Arithmetic of Weighted Catalan Numbers Mentor: Yibo Gao
Kaarel Haenni Wilf-equivalence in Weyl Groups and Signed Permutations Mentor: Yibo Gao
Alexandra Hoey and Wanyi Xiao A Combinatorial Proof for a Generalized Reciprocity Theorem Mentor: Pakawut Jiradilok
Miles Johnson and Natalie Stewart Some Graphical Realizations of Two-Row Specht Modules of Iwahori-Hecke Algebras of the Symmetric Group Mentor: Oron Propp
Nelson Niu and Lillian Zhang A Multiplicity-free Macdonald Identity Mentor: Gurbir Dhillon
Qiuyu Ren On the Union of Essentially Distinct $\delta$-tubes Mentor: Yuqiu Fu
Douglas Stryker Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at -$\infty$ Mentor: Ao Sun
Christopher Xu Traces of CM Values of Certain Weak Maass Forms Mentor: Yongyi Chen
Yuan Yao and Shengtong Zhang Equiangular Lines with a Fixed Angle Mentor: Jonathan Tidor

2018 Topics

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Julius Baldauf-Lenschen Sharp entropy bounds for plane curves and dynamics of the curve shortening flow Mentor: Ao Sun
Sanath Devalapurkar Uncompleting E-theory and Johnson-Wilson theory at height 2 Mentor: Robert Burklund
Juan Gil and Joshua Amaniampong Uniform generation of w-free strings and H-free subgraphs with partial rejection sampling Mentor: Jake Wellens
Calvin Hsu Quantitative decay for nonlinear wave equations Mentor: Ruoxuan Yang
Laura Koemmpel and Olga Medrano How graph structure and connectivity affects the propagation of cooperation in a network Mentor: Ashwin Narayan
Deven Jay Lahoti Torsion subspaces of complex Lie groups Mentor: Gurbir Dhillon
Junyao Peng Counting shellings of complete bipartite graphs and trees Mentor: Yibo Gao
Nikhil Reddy Generalizing auxeticity to aperiodic networks Mentor: Vishal Patil
Dhruv Rohatgi Biclique partitions and off-diagonal ordered Ramsey numbers Mentor: Jake Wellens
Julian Wellman Flips in reduced plabic graphs Mentor: Alexey Balitskiy
Yunkun Zhou The Sidorenko problem for directed graphs in tournaments Mentor: Jonathan Tidor

2017 Topics

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Brian Chen The Suboptimality of Asymmetric Recursive Reconstruction Algorithms Mentor: Ashwin Narayan
Panagiotis Dimakis On a Connection between Affine Springer Fibers and L-U Decomposable Matrices Mentor: Guangyi Yue
Alonso Espinosa Domínguez On Kakeya-type Problems For Hyperplanes in $\mathbb{R}$d Mentor: Paxton Turner
Hyo Won Kim and Christopher Maldonado On Graphs and the Gotsman-Linial Conjecture for $d = 2$ Mentor: Jake Lee Wellens
Justin Lim Building Forests in Maker-Breaker Games: Upper and Lower Bounds Mentor: Frederic Koehler
Max Murin Parameters for Generalized Hecke Algebras in Type B Mentor: Seth Shelley-Abrahamson
Xianglong Ni The Bracket in the Bar Spectral Sequence for a Finite-Fold Loop Space Mentor: Hood Chatham
Juan Carlos Ortiz The Diagonal Cohomology Class of Vertical Bundles Mentor: Jackson Hance
Luke Sciarappa Model Categories in Equivariant Rational Homotopy Theory Mentor: Robert Burklund
Max Vargas and Kimberly Villalobos A Random Walk Formulation of Learning in Restricted Boltzmann Machines Mentor: Mason Biamonte
Jianqiao Xia Topology of Two-Row Type Springer Fibers Mentor: Gus Lonergan

2016 Topics

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Kavish Gandhi and Yonah Borns-Weil Bounds on Moment-Based Learning of Mixture Distributions Mentor: Amelia Perry
YiYu Zhang A Correspondence between Generic Alcoved Polytopes and Subdivisions of the Root Polytope of Lie Type $A$ Mentor: Pavel Galashin
Jonathan Tidor and Victor Wang 1-color-avoiding Paths, Special Tournaments, and Incidence Geometry Mentor: Ben Yang
Tahsin Saffat Linearizable Laurent Phenomenon Sequences Mentor: Pavel Galashin
Lingfu Zhang Refinements of 2-dimensional Strichartz Estimate by the Maximum Wave Packet Mentor: Hong Wang
Joseph Zurier Symplectic Representation Theory and the Weyl Algebra in Positive Characteristic Mentor: Augustus Lonergan
James Rowan $S$-unit equations and curves of genus $2$ with good reduction away from $3$ Mentor: Borys Kadets
Hyun Jong Kim Local Conjugacy in $\textrm{GL}_2(\mathbb{Z}/p^2\mathbb{Z})$ Mentor: Atticus Christensen
Colin Aitken Generators for Maximal Finite Subgroups of the Morava Stabilizer Group Mentor: Lyuboslav Panchev
Arkadiy Frasinich An Investigation on an Extension of Mullineux Involution Mentor: Augustus Lonergan

2015 Topics

Asra Ali Straight-line orthogonal drawings of ternary trees Mentor: Sylvain Carpentier
Robert Burklund A classification of formal group laws over torsion-free rings Mentor: Lyuboslav Panchev
Adan Medrano Martin del Campo Tropical embeddings of metric graphs Mentor: Sylvain Carpentier
Jingwen Chen In search of a Mahler-Type inequality for the external conformal radius Mentor: Nicholas Strehlke
Yuchen Fu A family of finite-dimensional representations of generalized double affine Hecke algebras of higher rank Mentor: Seth Shelley-Abrahamson
Ofer Grossman An infinite family of non-abelian monogenic number fields Mentor: Dongkwan Kim
Zachary Izzo Asymptotic properties of random polytopes Mentor: Nicholas Strehlke
Yutao Liu Geometry of minimal surfaces with layered boundary conditions Mentor: Paul Gallagher
Mark Sellke and Sammy Luo The Saxl conjecture for 4th powers via the semigroup property Mentor: Dongkwan Kim
Anderson Wang Invariants of machines in wiring diagrams Mentor: Lyuboslav Panchev
Tianyou Zhou An integral formula for triple linking in hyperbolic space Mentor: Paul Gallagher

2014 Topics

Dhroova Aiylam and Carlos Cortez Combinatorial interpretations of the trace moment sequences of certain compact Lie subgroups of USp(4) Mentor: David Corwin
Aaron Brookner On the Cohen-Macaulayness of certain hyperplane arrangements Mentor: David Corwin
Yibo Gao and Yuzhou Gu Fast Algorithms for Solving SDPs on Graphs Mentor: Adrian Vladu
Cole Graham Quantitative Bounds for Hurwitz Stable Polynomials under Multiplier Transformations Mentor: Xuwen Zhu
Felipe Hernandez Some physical space heuristics for Strichartz estimates Mentor: Chenjie Fan
Saarik Kalia Generalizations of the Szemerédi-Trotter Theorem Mentor: Ben Yang
Peter Kleinhenz Stationary Solutions of the Nonlinear Schrödinger Equation in Hyperbolic Space Mentor: Chenjie Fan
Mrudul Thatte Hausdorff dimension of cycles in d-maps on the circle Mentor: Xuwen Zhu
Suhas Vijaykumar Higher Bruhat Orders of the Weyl group B_n Mentor: Seth Shelley-Abramson
Georgios Vlachos Approximate distance oracles for sparse graphs Mentor: Adrian Vladu

2013 Topics

Hyun Sub Hwang Computational power of quantum vs. classical oracles Mentor: Adam Bouland
Supanat Kamtue Domino-tiling problem Mentor: Ben Yang
Mitchell Lee The complexity class PDQP Mentor: Adam Bouland
Zipei Nie and Anthony Wang Points on lines in F3_q Mentor: Ben Yang
Sung Gi Park and Qinru Shi New bounds on extremal numbers in acyclic ordered graphs Mentor: Rik Sengupta
Yuqi Song and Andi Wang Convergence of eigenvalues to the support of the limiting measure in a beta matrix model Mentor: Chenjie Fan
Yanlin Zhao A particle system with interlacing pattern Mentor: Xin Sun
Fan Zheng Gauss sphere problem with polynomials Mentor: Chenjie Fan

2012 Topics

Amol Aggarwal Correlation Functions of the Schur Process Through Macdonald Difference Operators Mentor: Guozhen Wang
Weixin Chen Discrete-Time Anisotropic KPZ Growth of Random Surface in 2+1 Dimensions Mentor: Xuwen Zhu
Lynn Chua Psi-Epistemic Theories: The Role of Symmetry Published in Physical Review A 88:3 (2013). Mentor: Adam Bouland
Jiaoyang Huang Spectrum Asymptotics of Airy's Operator under Perturbation Mentor: Xuwen Zhu
Yajit Jain Homological Algebra over the Representation Green Functor Mentor: John Ullman
Jelena Markovic Least Absolute Deviations Method for Sparse Signal Recovery Mentor: Ruixun Zhang
Akin Morrison A Link Theoretic Perspective on the Isotopy Type of Real Algebraic Curves Mentor: Philip Tynan
Mark Velednitsky Graph Crossing Number and Isomorphism Mentor: Adam Bouland
Praveen Venkataramana On a Z4-Symmetric Operator over a Lemniscatic Elliptic Curve Mentor: Philip Tynan
Max Wimberley Rook Placements on Young Diagrams: Towards a q-Analogue of the Harer-Zagier Formula Mentor: Alejandro Morales
Tianqi Wu Impedance of Electrochemical Cells Mentor: Yi Zeng
Jessie Zhang Periodicity in the Periodic Lambda Algebra Mentor: Guozhen Wang

2011 Topics

Sergei Bernstein Lagrangian Spheres in Hm and the Effect of Dehn Twists Mentor: Ailsa Keating
Ben Bond Modeling Abelian Networks with Sandpiles Mentor: Benjamin Iriarte
Eben Freeman A Doubling Property for the Gradient of a Harmonic Function Mentor: Lu Wang
Yunzhi Gao On the Quotient Space of Functions Modulo the Action of Divergence-free Vector Field Mentor: John Ullman
Whan Ghang Involutive Power Series and Perfect Squares of Formal Power Series Mentor: John Ullman
Brian Hamrick Computational Verification of a Conjecture in Algebraic Geometry Mentor: Kartik Venkatram
Travis Hance A New Eulerian Permutation Statistic and Generalizations Mentor: Nan Li
Yangzhou Hu On the Number of Fixed-Height Semiorders and Poset Linear Extension Maximization Mentor: Nan Li
Gabriel Karpman Application of the Hodge Decomposition to the Harmonic Map Heat Flow Mentor: Lu Wang
Minseon Shin A Generalization of an Action of the Braid Group on Upper-Triangular Matrices Mentor: Ailsa Keating
Jeffrey Wu Towards Bootstrap-less Homomorphic Encryption Mentor: Kartik Venkatram

2010 Topics

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Aldo Pacchiano Camacho Fast Optical Character Recognition Via Cryptanalysis and Geometry Mentor: Kartik Venkatram
Harrison Chen Representation of Rational Cherednik Algebras in Positive Characteristic Mentor: Martina Balagović
Andrei Frimu On the Maximal Number of Rational Points on a Curve of Genus 4 Over F11 and F13 Mentor: Bhairav Singh
Raghu Mahajan Sweepouts and Level-set Flow Mentor: Lu Wang
Christopher Policastro Category $\mathcal{O}$ for the Rational Cherednik Algebra of G12 Mentor: Martina Balagović
Jonathan Schneider Face Numbers and Ehrhart Polynomials Mentor: Hoda Bhidkori
XiaoLin Shi Combinatorial Properties and Optimization of a Rooted Graph Polynomia Mentor: Amanda Redlich
Umut Varolgunes The Dimension, the Degree, and the Initial Complex of the Secant Ideal of the Second Hypersimple Mentor: Hoda Bhidkori
Sally Wolfe Cycle Structure and Pattern Avoidance of abc-permutations Mentor: Amanda Redlich
Qiaochu Yuan Lattice Paths and the Quadratic Coefficient of Kazhdan-Lusztig Polynomials Mentor: Bhairav Singh

2009 Topics

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Asilata Bapat The Lower Central Series Quotients of a Free Associative Superalgebra Mentor: David Jordan
Emily Berger Hurwitz Equivalence in the Dihedral Group Mentor: James Pascaleff
Gabriel Bujokas On the Smallness of Laumon's Resolution of Drinfeld's Compactification Mentor: Qian Lin
Shaunak Kishore On the Critical Group of Line Graphs and Planar Graphs Mentor: Hoda Bidkhori
Qingchun Ren An Exotic Map on Extended Dynkin Diagrams Mentor: Qian Lin
Colin Sandon Curves in Tropical Geometry Mentor: James Pascaleff
Philip Tynan Explicit Examples of Strebel Differentials Mentor: David Jackson-Hanen
Brayden Ware Understanding Shrinking Curves on a Sphere Mentor: Hoskuldur Halldorsson
Alexandr Zamorzaev On (Co)Homology of 2-Groups Mentor: Jennifer French

2008 Topics

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Aleksandr Ankhipov On The Pairwise Sums Problem Mentor: Zuoquin Wang
Thomas Belulovich Three Problems in Morse Theory Mentor: Nikhil Savale
Wes Brown Antimagic Labelings and the Antimagic Strength of Graphs Mentor: Hoda Bidkhori
Peter Caday Investigation into the Original and Dual McKay Correspondences Mentor: Fucheng Tan
Rishi Gupta Computing the Zeta Function of Elliptic and Hyperelliptic Curves Mentor: Ruochuan Liu
Sungyoon Kim On Dual Stable Grothendieck Polynomials Mentor: Hoda Bidkhori
Yuncheng Lin Szemerédi-Type Problems in Finite Fields Mentor: Julia Wolf
Cordelia Link On Sets Whose Difference Set Contains No Squares Mentor: Julia Wolf
Yinghui Wang Some Study On The Generalized Euler-Maclaurin Formula Mentor: Zuoquin Wang
Bohua Zhan Representing Graphs by Linear Subspaces Mentor: Ruochuan Liu

2007 Topics

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Erika Bakse Sumsets and Graph Theory in Additive Combinatorics Mentor: Catherine Lennon
Alessandro Chiesa Generalizing Regev's Cryptosystem Mentor: Amit Jayant Deshpande
Variants of the Chromatic Number of the Plane Joseph Cooper Mentor: Luis Rademacher
Hansheng Diao Freiman-Type Theory For Small Doubling Constant Mentor: Catherine Lennon
Rebecca Freund A representation of the type BN dAHA Mentor: Xiaoguang Ma
Shinnyih Huang Discussion on Sandglass Conjecture and Generalization Mentor: Hoda Bidkhori
John Kim On the Basis of $[A_n, A_n]$ / $[[A_n, A_n], A_n]$ Mentor: Xiaoguang Ma
Khoa Lu Nguyen Some Noncompact Convexity Theorems for Hermitian Matrices Mentor: Zuoqin Wang
Anand Rajagopalan Lower bounds for linear locally decodable codes Mentor: Amit Deshpande
Xuancheng Shao Minimum Partition into Product Sets Mentor: Luis Rademacher
Charmaine Sia Zero-sum problems in finite groups Mentor: Hoda Bidkhori

2006 Topics

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Irida Altman Some Irreducible Representations of the Braid Group
Anand Deopurkar Characteristic Classes and Chern-Weil Theory
Galyna Dobrovolska Comparing Products of sln Characters
Hyun Soo Kim Networks, Surfaces, and Representability
Raju Krishnamoorthy 2-Bottom Schur Functions
Andriana Lopez Factoring Polynomials
KangHao Lu Three Dimensional Rook Theory
Jason Priestley Two Simple Computations Proving the Futaki Invariant
Dale Winter Computing De Rham Instersection Cohomology Groups for Pseudomanifolds