# Past RSI Projects

## 2024 Participants and Topics

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

## 2022 Participants and Topics

## 2021 Participants and Topics

## 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

## 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

## 2015 Participants and Topics

## 2014 Participants and Topics

## 2013 Participants and Topics

## 2012 Participants and Topics

## 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 |