Past RSI Projects

2025 Participants and Topics

Anay Aggarwal	Weak Error Analysis and Small-Noise Optimization of Stochastic Linear Multistep Methods (SLMMs) for Itô and Lévy SDEs	Mentor: Joonsoo Lee
Shruti Arun	On $q$-Analogs of the Markov Equation	Mentor: Mohit Hulse
Rachel Chen	Explicit Irreducible Decomposition of the Spin Representation of the Temperley-Lieb Algebra	Mentor: Kenta Suzuki
Samanyu Ganesh	Characterizing Variations in the Ruelle Zeta Function Under Conformal Perturbations to the Metrics of Negatively Curved Riemannian 2-Manifolds	Mentor: Alain Kangabire
Sophia Jin	Coloring-Based Knot Invariants in Projective Space	Mentor: Kenta Suzuki
Jaeho Lee	Quadratic Large Sieves for “Algebraically Impossible” Sets	Mentor: Samuel Packman
Shuxuan (Judy) Li	Hilbert Series of Quasi-invariant Polynomials of $D_n$ in Characteristic $p$	Mentor: Frank Wang
Aaron Lin	Labeled Chip-Firing on $k$-ary and 3-regular Trees	Mentor: Ryota Inagaki
Susie Lu	On the Maximum Spread of Directed Graphs	Mentor: Prof. John Urschel and Genaro Laymuns
Dimana Pramatarova	Investigating the Periodicity of Weighted Catalan Numbers and Generalizing Them to Higher Dimensions	Mentor: Ryota Inagaki
Allen Qian	Parameter Estimation in Dynamic Bayesian Networks	Mentor: Joonsoo Lee

2024 Participants and Topics

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Isaac Chen	On the Crossing Profile of Rectilinear Drawings of Complete Graphs	Mentor: Oriol Solé Pi
Nikola Gyulev	On Torus Orbits of Symplectic Leaves from Upper Cluster Algebras with Poisson Structure	Mentor: Hamilton Ji Wan
Sophia Liao	Orbits of the Braid Group Action on Rank m Fp-Local Systems Over the n-Punctured Riemann Sphere	Mentor: Yonghwan Kim
Austin Luo	Chip-Firing on Directed and Binary Trees	Mentor: Ryota Inagaki
Tatiana Medved	Dynamical Torsion for Surfaces of Constant Negative Curvature	Mentor: Alain Kangabire
Christopher Qiu	Slice Genus Bounds for Knots using Grid Diagrams	Mentor: Yonghwan Kim
Akilan Sankaran	From Walking to Tunneling: A Generalized Pilot-Wave System	Mentor: Diego Israel Chavez
Eric Wang	An Isoperimetric Problem for the First Neumann Eigenvalue on the Sphere	Mentor: Shrey Aryan
Davido Zhang	Lipschitz Optimal Transport Maps	Mentor: Shrey Aryan
Ashley Zhu	Curve Shortening Flow on n-Loop Curves	Mentor: Michael Law

2023 Participants and Topics

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Srinivas Arun	Geography, Kotzig's Nim, and Variants	Mentor: Joshua Messing
Alan Bu	Concatenations of Two Incidence Matrices, Spanning Trees in Planar Graphs: Two Related Problems	Mentor: Yuchong Pan
David Dong	Comparisons of Methods in Near-to-Far-Field Transformations for Waveguides	Mentor: Rordrigo Arrieta
Deyan Hadzhi-Manich	On Longest Geometrically Increasing Sequences	Mentor: Yuchong Pan
Michelle Kang	Bounding the Diameter of Flip Graphs of Split Chessboards	Mentor: Tristan Yang
Yifan Kang	CNOT-Optimal Circuit Synthesis	Mentor: Henry Ma
Aaron Kim	The Classification and the Hilbert Polynomials of the Coloring of Quandles with size 6	Mentor: Tristan Yang
Victoria Paraoulaki de Miranda	Counting the Maximum Number of 3-rich Curves in Configurations of $n$ Points in ${{\mathbb{P}^2}_\mathbb{F}}_q$	Mentor: Luis Guzman
Joseph Vulakh	Positive Traces on Deformations of Kleinian Singularities of Type D	Mentor: Daniil Kliuev
Hongzhou (Hazel) Wu	Classifying bipolynomial Hopf algebras over graded local rings	Mentor: David Jongwon Lee
Shu-Ching Yang	Existence of Trapped Vibration Modes in One-Dimensional Crystal Lattices	Mentor: Rodrigo Arrieta Candia
Hanming Ye	The Stable Picard Groups of the Exterior Algebras $E(n)$	Mentor: David Jongwoon Lee

2022 Participants and Topics

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Madeleine de Belloy	Computing the Mosaic Number of Reduced Projections of Knots and Links	Mentor: Mary Stelow
Ruben Mason Carpenter	On Chaotic Pilot Wave Dynamics	Mentor: Nicholas Zhixian Liu
Parth Chavan	Counting Ideals in Numerical Semigroups	Mentor: Jeffery Yu
Sarth Chavan	On Discriminants of Minimal Polynomials of the Ramanujan $t_n$ class Invariants (published in the Bulletin of the Australian Mathematical Society pp. 1-12 (2022))	Mentor: Alan Peng
Matthew Chen	Mod $p$ Homology of Unordered Configuration Spaces of Surfaces	Mentor: Adela Zhang
Iliyas Noman	Spectral Conditions for Spherical Two-Distance Sets	Mentor: Yuan Yao
Apoorva Panidapu	Sparse Symmetrizers of Diagonalizable Real-$\lambda$ Matrices	Mentor: Mo Chen
Rich Wang	Level Spacing for Resonances of Open Quantum Maps	Mentor: Zhenhao Li
Xingyan (Summer) Zhou	Products of Values of Polynomials in Finite Fields	Mentor: Rachana Madhukara and Alan Peng
Sally Zhu	On the Smoothness and Regularity of the Chess Billiard Flow and Internal Waves	Mentor: Zhenhao Li

2021 Participants and Topics

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Reagan Choi	Stochastic Processes in Quantum Error Correction	Mentor: Andrey Boris Khesin
Kevin Cong	On the Sizes of Furstenberg Sets in Finite Fields	Mentor: Alexander Ortiz
Allen Lin	On the Properties of Polyas Circular Symmetrization	Mentor: Sarah Tammen
On Ki Luo	Investigation on the Johnson-Leader-Russell Question for Square Posets	Mentor: Pakawut Jiradilok
Eli Meyers	Homological Equivalence and Forman Equivalence of Discrete Morse Functions on Graphs	Mentor: Mary Stelow
Comfort Ohajunwa	On Phase Transitions in the Approximation Ratio for MAX 2-SAT	Mentor: Mitchell Harris
Isabella Quan	On Snowflakes and Pizza: Graph Theoretic Properties of 2D Steiner Solutions	Mentor: Mary Stelow
Angel Raychev	A Generalization of Descent Polynomials	Mentor: Pakawut Jiradilok
Tair Satubaldin	Examples for the Robust Qualitative Uncertainty Principle	Mentor: Alexander Ortiz
Daniel Xia	An Inequality for the Antiferromagnetic Potts Model	Mentor: David Jongwon Lee
Lucy Xiao	The Adaptive Capacity for Two Mixed States	Mentor: Andrey Boris Khesin

2020 Participants and Topics

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Lucy Cai	Optimal Heating on Parallelogram Tori	Mentor: Catherine Cawley Wolfram
Yunseo Choi	On Two-sided Matching in Infinite Markets	Mentor: Prof. Scott Duke Kominers
Elliott Fairchild	Pointwise Temporal Decay of Solutions of the Klein-Gordon Equation in Schwarzschild Spacetime	Mentor: Ethan Sussman
Gregory Li	Clique Structure of Orthomodular Posets	Mentor: Ethan Sussman
Andrei Mandelshtam	Sums of Binomial Coefficients Evaluated at $\alpha \in \bar{\mathbb{Q}}$, and applications	Mentor: Daniil Kalinov
Nikola Staykov	On the Sizes of Unions of Circles over Finite Fields	Mentor: Elia Portnoy
Rahul Thomas	Width of Graph Mappings	Mentor: Elia Portnoy
Gerald Xu	Geometric Quaternionic Quantum Mechanics	Mentor: Ethan Sussman
Alexis Yi	Bounding The Size of The Modular Pants Graph	Mentor: Catherine Wolfram

2019 Participants and Topics

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Dimitar Chakarov	On a Generalization of Artin's Conjecture for Primitive Roots in Gaussian Integers	Mentor: Yichi Zhang
Lauren Chen	Two Problems on Cantor Set Arithmetic	Mentor: Yuqiu Fu
Eddie Hu	$R_+(S)$ for Algebraic Numbers	Mentor: Daniil Kalinov
Benjamin Kang	A Variation of the Erdös-Turán Conjecture and the Minimality of Multiplicative Bases	Mentor: Yichi Zhang
Rupert Li	$\mathbb{F}_q$-rational Points of Hypersurfaces in Weighted Projective Spaces over Finite Fields	Mentor: Chun Hong Lo
Jason Liu	On Q-binomial Polynomials and Quantum Integer-Valued Polynomials	Mentor: Robert Burklund
Austen Mazenko	Determination of Markov Model Dynamics from Equilibrium Data Snapshots	Mentor: Dominic Skinner
Assylbek Olzhabayev	Diagonal Form of the Varchenko Matrices for Oriented Matroids	Mentor: Adela YiYu Zhang
AnaMaria Perez	On Generalizations of the Double Cap Conjecture	Mentor: Rose Zhang
Alexander Zhu	Modeling Local Order in Bacterial Collective Motions	Mentor: Boya Song

2018 Participants and Topics

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Jiwon Choi	Geometric Complexity of Planar Drawings	Mentor: Alexey Balitskiy
Sean Elliott	Modeling Networks of Evolving Populations	Mentor: Dominic Skinner
Karen Ge	Generating the Coefficient Field of Newforms with Inner Twists	Mentor: Robert Burklund
Kayson Hansen	The Modular Representation Theory of Cyclic Groups of Prime Power Order	Mentor: Hood Chatham
Kaiying Hou	Strang Splitting for the Variable-coefficient Burgers Equation	Mentor: Ruoxuan Yang
Aknazar Kazhymurat	Topological uniqueness results for Lefschetz fibrations over the disc	Mentor: Bar Kartal
Chavdar Lalov	Cyclic Koszul algebras and oriented graphs	Mentor: Guangyi Yue
Kevin Liu	Number Fields Generated by Torsion Points on Elliptic Curves	Mentor: Chun Hong Lo
Roshan Warman	Generalization of Bridge Length to other Cartan-Killing Types	Mentor: Yibo Gao
Katie Wu	Microscopic Simulation of Growing Bacterial Swarms	Mentor: Dominic Skinner
Saba Zerefa	A Computational Approach To Intrinsic Linkedness in Complete Graphs	Mentor: Vishal Patil

2017 Participants and Topics

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Jordan Lee	Stability of Finite Difference Schemes on the Diffusion Equation with Discontinuous Coefficients	Mentor: Sungwoo Jeong
Anqi Li	On Density of Integers and the Sumset	Mentor: Hong Wang
Tanya Otsetarova	Boundaries on the Number of Points in Acute Sets	Mentor: Zhulin Li
Alan Peng	The Lusztig-Vogan Bijection in the Case of the Trivial Representation	Mentor: Guangyi Yue
Sílvia Casacuberta Puig	On the Divisibility of Binomial Coefficients	Mentor: Oscar Mickelin
Michelle Shen	Modeling Population Dynamics in Changing Environments	Mentor: YounHun Kim
Grace M. Tian	Linear Upper Bound on the Ribbonlength of Torus Knots and Twist Knots	Mentor: Vishal Patil
David Wu	Nonuniform Distributions of Patterns of Sequences of Primes in Prime Moduli	Mentor: Robert Burklund
Karthik Yegnesh	Braid Groups on Triangulated Surfaces and Singular Homology	Mentor: Augustus Lonergan

2016 Participants and Topics

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Pawel Burzyński	Estimating Sums of Independent Random Variables	Mentor: Chiheon Kim
Benjamin Yuhang Chen	Distinct Distances Between Sets of Points on a Line and a Hyperplane in $\mathbb{R}^d$	Mentor: Thao Do
Jenning Chen	Finding $\alpha$-Hölder Continuous Curves through Points in the Unit Square	Mentor: Thao Do
Angela Deng	Growth of Module Dimensions in Auslander-Reiten Quivers of $\tilde D_n$-type and $\tilde E_{6,7,8}$-type Quivers	Mentor: Guangyi Yue
Caleb He	On the Spectral Invariance of Ellipses in Convex, Planar Domains	Mentor: Ethan Yale Jaffe
Dona-Maria Ivanova	On the Distortion of Embedding Perfect Binary Trees into Low-dimensional Euclidean Spaces	Mentor: Zhenkun Li
Asha Ramanujam	Properties Of Triangles When They Undergo The Curve-Shortening Flow	Mentor: Ao Sun
Nolan Reilly	Collective Instabilities of Linearly Coupled Parametric Oscillators	Mentor: Mason Biamonte
Sonia Reilly	Bounding the Deviation of the Valuation Property of Quermassintegrals for Non-convex Sets	Mentor: Vishesh Jain
Dhruv Rohatgi	When Two-Holed Torus Graphs are Hamiltonian	Mentor: Chiheon Kim

2015 Participants and Topics

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Amy Chou	NP-Hard Triangle Packing Problems	Mentor: James Hirst
Brandon Rafal Epstein	Maximizing the Number of Lattice Points on a Strictly Convex Curve	Mentor: Hong Wang
Kristian Georgiev	On the size of unions of lines in $\mathbb{F}^n$ satisfying the Wolff axiom	Mentor: Hong Wang
Brian Gu	Bounds on Maximal Tournament Codes	Mentor: Brandon Tran
Dylan Hendrickson	Generalizing the Inversion Enumerator to G-Parking Functions	Mentor: Pavel Galashin
Meena Jagadeesan	An Analytic Approach to the Modeling of Microbial Locomotion in Porous Media	Mentor: Andrew Rzeznik
Emily Jia	Extremal Number of Trees in Hypercubes	Mentor: Chiheon Kim
Abijith Krishnan	A Secretary Problem with a Sliding Window for Recalling Applicants	Mentor: Shan-Yuan Ho
Wilbur Li	Distributions of the $k$-major index in random words and permutations	Mentor: Cesar Cuenca
Sarvasva Raghuvanshi	New Results on Ramsey Multiplicity and Graph Commonality	Mentor: James Hirst
Pol Gómez Riquelme	A combinatorial interpretation of the ℎ- and $\gamma$-vectors of the cyclohedron	Mentor: Pavel Galashin
Uma Roy	The $\beta(\infty)$ Crystal for a Family of Generalized Quantum Groups	Mentor: Seth Shelley-Abrahamson
Jared Tramontano	The Status Update Problem: Optimal Strategies for Pseudo-Deterministic Systems	Mentors: Dr. Shan-Yuan Ho and Siddharth Venkatesh

2014 Participants and Topics

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Kavish Gandhi	Saturation Number of Trees in the Hypercube	Mentor: Chiheon Kim
Peter Gaydarov	Vector Parking Functions and Tree Inversions	Mentor: Samuel Hopkins
Noah Golowich	Acyclic Colorings and Subgraphs of Directed Graphs (published in The Electronic Journal of Combinatorics 22:3 (2015); a new version published in Discrete Mathematics 339:6 (2016))	Mentor: David Rolnick
Lev Kendrick	The Lower Central Series of the Quotient of a Free Algebra	Mentor: Gus Lonergan
Shashwat Kishore	Signatures of Multiplicity Spaces in Tensor Products of $sl_2$ and $U_q(sl_2)$ Representations, and Applications	Mentor: Gus Lonergan
Yelena Mandelshtam	Arrangements and Amounts of Equal Minors in Totally Positive Matrices	Mentor: Miriam Farber
David Stoner	On the Minimal Reset Words of Synchronizing Automata	Mentor: Chiheon Kim
Peter Tian	Sequences of formation width 4 and alternation length 5	Mentor: Jesse Geneson
Kelvin Wang	Homomesy in Minuscule Posets	Mentor: David Rush
Ingrid Zhang	Homomesy of Alignments in Perfect Matchings	Mentor: Sam Hopkins
Jesse Zhang	Laplacians Associated with Regular Bipartite Graphs and Application to Finite Projective Planes	Mentor: David Rush

2013 Participants and Topics

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Leigh Marie Braswell	Angles of the Cookie Monster Problem	Mentor: Benjamin Iriarte
Evan Chen	Diagrammatic Computation of Morphisms between Bott-Samelson bimodules via Libedinsky's Light Leaves	Mentor: Francisco Unda
Rumen Dangovski	On the Lower Central Series of PI-Algebras	Mentor: Nathan Harman
Annie Hu	On the Number of Linear Extensions of Graphs	Mentor: Benjamin Iriarte
Rohil Prasad	On Binary Formations and Sequence Extremal Functions	Mentor: Jesse Geneson
Raj Raina	Minimum Degrees of Minimal Ramsey Graphs	Mentor: Rik Sengupta
Sarah Shader	Weighted Catalan Numbers and Their Divisibility Properties	Mentor: Gaku Liu
Jessica Shi	The Speeds of Families of Intersection Graphs	Mentor: Francisco Unda
Albert Soh	Crossing Numbers on the Disk with Multiple Holes	Mentor: Gaku Liu
Bertrand Stone	Characterization of the Line Complexity of Cellular Automata Generated by Polynomial Transition Rules	Mentor: Chiheon Kim
Nickolay Stoyanov	On Lower Central Series of the r,q-polynomial algebra	Mentor: Nathan Harman

2012 Participants and Topics

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Matthew Babbitt	On Visibility Graphs - Upper Bounds and Classification of Special Types	Mentor: Jesse Geneson
Surya Bhupatiraju	On the Complexity of the Marginal Satisfiability Problem	Mentor: Alex Arkhipov
Joshua Brakensiek	Bounds on the Size of Sound Monotone Switching Networks Accepting Permutation Sets of Directed Trees	Mentor: Aaron Potechin
Katherine Cordwell	Lower Central Series Quotients of Finitely Generated Algebras over the Integers	Mentor: Teng Fei and Pavel Etingof
Kevin Garbe	Patterns in the Coefficients of Powers of Polynomials over a Finite Field	Mentor: Dorin Boger
Simanta Gautam	A Novel Approach to the Spherical Codes Problem	Mentor: Dmitry Vaintrob
Gil Goldshlager	Characterizing Outerplanar and x-Monotone Thrackles	Mentor: Aaron Potechin
Jacob McNamara	A Bound on the Norm of Shortest Vectors in Lattices Arising from CM Number Fields	Mentor: Dmitry Vaintrob
Charles Pasternak	Random Error Models in Quantum Error Correction	Mentor: Matthew Coudron
Lilly Shen	On the Column Extremal Functions of Forbidden Patterns in 0-1 Matrices	Mentor: Jesse Geneson
Maurice Shih	On the Splitting of MO(2) over the Steenrod Algebra	Mentor: John Ullman
Kathleen Zhou	On Successive Quotients of Lower Central Series Ideals for Finitely Generated Algebras	Mentor: Teng Fei and Pavel Etingof

2011 Participants and Topics

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Stanislav Atanasov	Rational Fixed Points of Polynomial Involutions	Mentor: Kestutis Cesnavicius
Megan Belzner	Emptying Sets: The Cookie Monster Problem	Mentor: Wuttisak Trongsiriwat
Rebecca Chen	A Computational Analysis of Triangle Subdivision	Mentor: Wenzhe Wei
Sitan Chen	On the Rank Number of Grid Graphs	Mentor: Jesse Geneson
Sidharth Dhawan	Complexity of Interlocking Polyominoes	Mentor: Zachary Abel
Eric Mannes	Bounds on Monotone Switching Networks for the Matching Problem	Mentor: Aaron Potechin
Todor Markov	On Extremal Degrees of Minimal Ramsey Graphs	Mentor: Wuttisak Trongsiriwat
Jessica Oehrlein	Book Thickness of Graphs and their Subdivisions	Mentor: Aaron Potechin
Matthew Rauen	On Strongly Multiplicative Graphs	Mentor: Jesse Geneson
Abraham Shin	Analysis of Random Surfaces Representing the Motion of Strings	Mentor: Wenzhe Wei
Adam H. Su	Rank-Generating Functions for the Distributive Lattice of Order Ideals for Comb Posets	Mentor: Benjamin Iriarte
Zacharias Tsampasidis	Non-divisibility of Binomial coefficients with a Given Set of Primes	Mentor: Kestutis Cesnavicius

2010 Participants and Topics

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Rohit Agrawal	Avoiding Paradoxes in Positional Voting Systems	Mentor: Gregory Minton
Wenyu Cao	Expander Graphs, Eigenvalues, and Four-Cycles	Mentor: Rosalie Belanger-Rioux
Aubrey Faust	Orbits of Lower Triangular Matrices under Braid Group Transformations	Mentor: Ailsa Keating
Christopher Guthrie	Tropical Oriented Matroids and Subdivisions of Products of Simplices	Mentor: Kartik Venkatram
Kevin Hu	Enumerating Multiplicity-Free Labeled Floor Diagrams for Rational Curves	Mentor: John Lesieutre
Randy Jia	Simple Connectedness of Some Flip Complexes	Mentor: John Lesieutre
Matthew Kilgore	A New Look at the Unknotting Question	Mentor: Ailsa Keating
Brian Kim	Polynomials and 2-adic Analogues of the Collatz Problem	Mentor: John Ullman
Benjamin Kraft	Entries of Random Matrices	Mentor: Gregory Minton
Styliani Pantela	On Prime Factors of Fibonacci Numbers	Mentor: Wang Lu
Rafael Rafailov	The Hausdorff Dimension of Cycles Generated by Degree d Maps	Mentor: Fang Wang
David Ye	Generalization of a Coin-Weighing Problem	Mentor: John Ullman
Leon Zhang	On Alternative Error Indicators for an Adaptive Newton's Method	Mentor: Rosalie Belanger-Rioux

2009 Participants and Topics

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Anirudha Balasubramanian	On the Lower Central Series Quotients of a Graded Associative Algebra	Mentor: Martina Balagović
Martin Camacho	Lattice Representations and Linear Extensions of Series-Parallel and (m + n) - free Posets.	Mentor: Yan Zhang
Jonathan Hung	The Kummer congruence for Hurwitz numbers	Mentor: Jennifer French
Jacob Hurwitz	Decycling Density of Tessellations	Mentor: Nan Li
Tian-Yi (Damien) Jiang	On the Period Lengths of the Parallel Chip-Firing Game	Mentor: Yan Zhang
George Kerchev	On the Filtration of the Free Algebra by Ideals Generated by its Lower Central Series.	Mentor: Bhairav Singh
Akhil Mathew	A Classication of Finite-Dimensional Simple Objects in the Generic Deligne Category of the Degenerate Affine Hecke Algebra.	Mentor: Dustin Clausen
Dimitrios Pagonakis	An Improved Lower Bound on Moser's Worm Problem	Mentor: Tirasan Khandhawit
Arjun Puranik	Finite-dimensional Irreducible Representations of Rational Cherednik Algebras Associated to the Coxeter Group H3.	Mentor: Martina Balagovic
Lauren Stephens	Bounds on the Relative Sizes of Sumsets	Mentor: Bhairav Singh
Dennis Tseng	Generalized Nonaveraging Integer Sequences	Mentor: Nan Li
Lynnelle Lin Ye	Chomp on Graphs and Subsets	Mentor: Tirasan Khandhawit

2008 Participants and Topics

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Noah Arbesfeld	On the lower central series for the free algebra with two generators	Mentor: David Jordan
Kristin Cordwell	On G-Dierence: A Property of Permutations and Words	Mentor: Joel Lewis
Miles Edwards	2-Sylow subgroups of ideal class groups of imaginary quadratic elds	Mentor: Liang Xiao
Katrina Evtimovay	Representations of Rational Cherednik Algebras of Rank 1 and 2	Mentor: Emanuel Stoica
Hyun-Sub Hwang	Permutations with a Special Property and their Extension to Abelian Groups	Mentor: Joel Lewis
Eric Larson	Fusion categories of dimension qp²	Mentor: David Jordan
Paul Lee	Modelling Salt Eect on DNA Conformations	Mentor: Xia (Carol) Hua
Patricia Li	On the number of permutations with a given number of cycles and left-to-right maxima	Mentor: Matjaz Konvalinka
Zane Li	On the intersection of quadric and cubic surfaces	Mentor: Ryan Reich
Xiao Tian Liew	Predominant intersection vertices in spanning trees	Mentor: Maxim Maydanskiy
Young Wook Lyoo	On The Linear Extensions and Interval Extensions of Poset	Mentor: Yulan Qing
Benjamin Mirabelli	Finding non-degenerate critical points of the superpotential associated to a smooth Fano plytope.	Mentor: Maxim Maydanskiy
Dimitrios Papadimitriou	Factorization in terms of Cyclotomic Polynomials and Algorithms for their Coecients.	Mentor: Tathagata Sengupta
Eliyahu Putterman	Determination of the Rate of Convergence of the Equi-Energy Sampler	Mentor: Xia (Carol) Hua
Maxim Rabinovich	On the Scaling Limit of a Generalized Divisible Sandpile Model	Mentor: Emanuel Stoica
David Harry Richman	Counting diagonal matrices over finite fields	Mentor: Tonghoon Suk
Adam Sealfron	Hypergraph Property Testers: The Role of Adaptivity	Mentor: Victor Chen
Jean Shiao	A study on nite subgroups of multiplicative non-zero Quaternions and SO(3) groups	Mentor: Tonghoon Suk
Sang-Hun Song	Imaginary quadratic elds with class groups exponent a power of 2	Mentor: Liang Xiao
Galin Statev	Fermat-Euler Dynamics	Mentor: Tathagata Sengupta
Daniel Vitek	Hamiltonicity of Conguration Spaces	Mentor: Yulan Qing
Brent Woodhouse	Characters of Induced Representations in Coxeter Groups	Mentor: Matjaz Konvalinka
Peter Zhang	The integrability of ƒ e^x²dx in elds of characteristic p	Mentor: Ryan Reich

2007 Participants and Topics

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Utsav Bhat	Mathematical Model of the Single Transferable Vote Election
Alex Churchill	Self-Reflective Comma-Free Codes
Alex Chen	On the Reducible Quintic Complete Base Polynomials
Benjamin Dozier	Descriptive Complexity of Random Bit Strings
Philip Hu	On the Kakeya Conjecture in Three Dimensions
Paul Kominers	On Various Chip-Firing Games
Laney Kuenzel	Modeling Choices in the Travelers Dilemma
Winston Luo	Cake-Cutting with Locally Negative Preference Functions
Ping Fung Ng	On the Problem of Finding the 27 Tropical Lines On A Tropical Cubic Surface
Yasin Razlik	Counting Nodal Curves in CP2 Via Floor Diagrams
David Rolnick	Subspace Intersection: Multi- dimensional Representation of Graphs
Caroline Suen	On Search Techniques for Root-Unitary Polynomials
Anne Ye	Finding Rootless Matrices Using Jordan Normal Form
Qiaochu Yuan	Elliptic Curves as Space Quartics
Susan Zhang	Decomposition of Algebraic Models of Quantum Information Transference