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

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 H_m 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 B_N 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 sl_n 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