# Past RSI Projects

## 2018 Participants and Topics

PDF of Abstracts

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

PDF of Abstracts

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

PDF of Abstracts

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

PDF of Abstracts

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

PDF of Abstracts

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

PDF of Abstracts

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

PDF of Abstracts

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

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

## 2010 Participants and Topics

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

## 2009 Participants and Topics

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

## 2008 Participants and Topics

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

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

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

Peter Zhang - The integrability of ƒ ex2dx in elds of characteristic p
Mentor: Ryan Reich

## 2007 Participants and Topics

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