Past RSI Projects

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

PDF of Abstracts

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

PDF of Abstracts

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

PDF of Abstracts

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

PDF of Abstracts

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

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

PDF of Abstracts

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

Past RSI Projects

2012 Participants and Topics

2011 Participants and Topics

2010 Participants and Topics

2009 Participants and Topics

2008 Participants and Topics

2007 Participants and Topics