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Past SPUR Projects

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

PDF of Abstracts

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