Past RSI Projects

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 ex2dx 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