# Past RSI Projects

## 2021 Participants and Topics

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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

**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 qp^{2}

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^{x2}dx in elds of characteristic p

Mentor: Ryan Reich

## 2007 Participants and Topics

**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