## Honors Papers and Future Plans

### 2023:

Honors Thesis Student | Future Plans |

Livia Betti: VC-dimension of Spherical Hypothesis Classes over . (Advisor: Iosevich) | |

David Crncevic: Algebraic properties of Artin-Mazur zeta function in positive characteristic. (Advisor: Rivera-Letelier) | Mathematics Ph.D. program at École Normale Supérieure, Paris, France. |

Rachel Dennis: Polymorphisms and Neural Networks for Image Classification. (Advisors: Iosevich, Aten) | |

Avery Girsky: Cusp Width in Modular Curves. (Advisor: Hopper) | Analytics Masters program at Georgia Tech. |

Yuqiao Huang: Correspondence between Lie groups and Lie algebras. (Advisor: Pakianathan) | Mathematics Ph.D. program at Rutgers University. |

Matthew Kaminskas: An Alternative Construction of the L | |

Henry Lin: A Primer to Integral Equations of the Second Kind. (Advisor: Geba) | Computer Science Masters program at Columbia University. |

Yurong Liu: Reconstruction on Markov Tree. (Advisors: Stefankovic, Mkrtchyan) | Computer Science Ph.D. program at New York University. |

Jack Mandell: Applications of linear and semidefinite programming to approximation algorithms. (Advisor: Stefankovic) | Applied Mathematics Ph.D. program at RPI. |

Justin Murante: Multiplicative Correlations Between Multiplicative Functions. (Advisor: Gonek) | Optics Ph.D. program at University of Arizona. |

Anna Myakushina: Exploring Sampling Techniques in Large Graphs and Networks. (Advisor: Iosevich) | Statistics and Operations Research Ph.D. program at UNC Chapel Hill. |

Yixu Qiu: A survey of some special subgroups of the symmetric group on pq letters where p,q are primes. (Advisor: T. Tucker) | |

Yun Long Xu: Learning in Biologically Plausible Neural Networks. (Advisor: Iosevich) | Computational Neuroscience Ph.D. program at University of Chicago. |

Yukun Yang: Stochastic Gradient Descent | Statistics Masters program at University of Michigan, Ann Arbor. |

### 2022:

Honors Thesis | Future Plans |

Alex Bowman: Kneading Invariants of Fibonacci Quotient Rotations. (Advisors: Jorge Olivares and Juan Rivera-Letelier) | |

Xuchen Fang: On Last Passage Time in Periodic Environments. (Advisor: Krishnan) | Mathematics Ph.D. program (Statistics specialization) at IUPUI. |

Filippo Iulianelli: Estimates on constants related to Minkowski dimension. (Advisor: Iosevich) | |

Mandar Juvekar: Notions of Tensor Rank.(Advisors: Kaave Hosseini and Iosevich) | Computer Science Ph.D. program at Boston University. |

Phuc Lam: On the rate of escape or approach to the origin of a random string. (Advisor: Mueller)(Talk Video Link) | Applied Mathematics Ph.D program at Brown University. |

Tianxiang Liu: The L-functions of elliptic curves and modular forms. (Advisor: Thakur)(Talk Video Link) | |

Jose Manuel Torres Lopez: Geodesics on the Lorentz Lie group equpped with a non-invariant metric.(Advisor: Sarada Rajeev) (Talk Video link) | Physics Ph.D. program at University of Texas at Austin. |

Michele Martino: Fractal dimension, configuration problems, and their connection to machine learning.(Advisors: Emmett Wyman and Iosevich) | |

Jacob Miller: Quandle invariants of knots and links. (Advisor: Pakianathan)(Talk Video Link) | Mathematics Ph.D program at University of Iowa. |

Arian Nadjimzadah: Existence of dot product trees in thin subsets of Euclidean space. (Advisor: Iosevich)(Talk Video Link) | Mathematics Ph.D program at U.C.L.A. |

Thomas O'Neill: Mathematical applications of Reinforcement Learning. (Advisor: Iosevich) | Taking a gap year with the plan to apply to Ph.D. programs the following year. |

Lloyd Page: Leaky Abelian Sandpile Model with multiple starting points. (Advisor: Mkrtchyan)(Talk Video Link) | Economics Ph.D. program at UNC-Chapel Hill. |

Conor Taliancich: Discrete energy analysis on fractal sets. (Advisor: Iosevich) | |

Cierra Tinson: The reaction-diffusion theory of Morphogenesis. (Advisor: Iosevich) | Physics Ph.D. program at Michigan State University. |

Nathan Whybra: The Centipede Game: Nash Equlibria versus Machine Learning. (Advisor: Iosevich) |

### 2021:

Honors Thesis | Future Plans |

Jeremy Atkins: Conformal field theory.(Advisor: Rajeev) | |

Noah Bertram: Computing partial Zeta functions.(Advisor: Haessig) | Computer Science Ph.D. program at Cornell University. |

Cole Durham: A Survey of Differential Topology: Intersection Numbers, Morse Theory, and Morse Homology.(Advisor: Pakianathan) | Mathematics Ph.D. program at University of Connecticut. |

Linus Ge: Existence of isosceles triangles in subsets of Euclidean space of high Hausdorff dimension.(Advisor: Iosevich) | |

Samuel King: Young Tableaux and Their Connection to Sampling Contingency Tables.(Advisors: Stefankovic, Mkrtchyan) | Computer Science Ph.D. program at Georgetown University. |

Benjamin Kuehnert: Algorithms for Galois Theory.(Advisor: A. Tucker) | Software Engineer at Google. |

Zhengkai Li: Properties of Bases in Banach Spaces.(Advisor: Geba) | Mathematics Ph.D. program at University of Washington. |

Xiaobo Luo: Probabilistic and Experimental Methods in Sum-Product Theory.(Advisor: Iosevich) | Data Science M.S. program at Harvard University. |

Trung Nguyen: Integral Bases.(Advisor: Jochnowitz) | Mathematics Ph.D. program at Pennsylvania State University. |

Tyler Perlman: The Hardy Inequality and variants.(Advisor: Geba) | Mathematics M.S. program at N.Y.U. |

Donovan Snyder: Quantum Probability in a Two State Random Walk.(Advisor: Rajeev) | Mathematics Ph.D. program at University of Rochester. |

Yiyang Su: Computer Experiments with Higher-Dimensional Probability.(Advisor: Iosevich) | Computer Science Ph.D. program at Michigan State University. |

Giang Truong: Uniqueness of a three dimensional stochastic differential equation.(Advisor: Mueller) | Financial Mathematics Ph.D. program at Princeton University. |

Chuanyi Wang: Dynamics of Rotation-like Logistic Maps.(Advisor: Rivera-Letelier) | |

Yue Wang: Relativistic Brownian Motion.(Advisor: Rajeev) | Physics Ph.D. program at U.C. Berkeley. |

Kyhl Weber: Qualitative properties for solutions to a differential equation associated with the Skyrme model.(Advisor: Geba) | Pursuing research and industry positions with the aim of later going to grad school. |

Tongyu Yang: The Ihara Zeta function.(Advisor: Haessig) | Computer Science M.S. program at Yale University. |

Matthew Zevenbergen: | Mathematics Ph.D. program at Boston College. |

### 2020:

Honors Thesis | Future Plans |

Dustin Kasser: Series Rearrangements Using Density Functions. | Mathematics Ph.D. Program at University of Georgia. |

Xin Lu: On NP-intermediate, Isomorphism problems, and Polynomial Hierarchy. | MS Computer Science program at Stanford University. |

Gregory Michajlsyzyn: On the discriminant of the Hecke ring and its index in the corresponding ring of integers. | Mathematics Ph.D. program at University of Connecticut. |

John Ennis: Curvature of Riemannian Manifolds. | |

Byron Osterweil: Geometric problems in vector spaces over finite fields, and a generalization of a sum estimate. | Mathematics Ph.D. Program at University of California, Irvine. |

Orion Haunstrup: New Findings on the Collatz Conjecture Reveal a Hidden Global Stability - a possible road to a proof. | |

Chengyuan Wang: Models of epidemic spread. |

### 2019:

Honors Thesis | Future Plans |

Joshua Beck: An application of differential geometry to freeform optics manufacturing. | Optimax Systems Inc. |

Kevin Hunt: The eigenvalue distribution of random matrices with distortion. | PhD Economics, U. Wisconsin-Madison |

Shenxiong Li: On the Spectrum and Essential Minimum of Heights in the Projective Plane. | |

Zachary Polansky: Equilateral triangles in vector spaces over finite fields. | Google Inc. |

Guowei Shan: On zeros of the p-adic zeta function and generic Newton polygons of Hecke polynomials. | |

Manuel Stoeckl: Approaches for the hinge and distinct distance problems. |

### 2018:

Honors Thesis | Future Plans |

Dionel Jaime: Method of Stationary Phase and Applications. | |

Shir Maimon: Elliptic Curve Cryptography. | |

Logan Meredith: On the Cauchy-Kowalevski theorem for analytic nonlinear partial differential equations. | |

Kenneth Plante: Free Actions on products of spheres. | |

Gabrielle Scullard: Factorization Properties of Integer-Valued Polynomials. | PhD Mathematics, Penn State |

David Soukup: Embeddings of Weighted Graphs in Erdos-type Settings. | |

Zhonghui Sun: Projection Theorems in Vector Spaces over Finite Fields. | |

Mark Sweeney: Model Theory. | PhD Mathematics, Brown |

Alfredo Vargas: Minimal Surfaces in R^3. | |

Jean Weill: Yang-Mills Theory on a Cylinder. |

**2017:**

Honors Thesis | Future Plans |

Charlotte Aten: The Topology of Magmas. | PhD Mathematics, UR |

Noah Chrein: Enriched Coproducts and the Twisted Adjunction. | |

Benjamin Dees: Analogs of the Erdos integer distance principle in vector spaces over finite fields. | PhD Mathematics, Johns Hopkins |

Adam Lott: Roth's Theorem on Arithmetic Progressions. | |

Lee Murphy: The Jordan-Brouwer Separation Theorem. | |

Daniel Rubery: On a finite field analog of the bilinear spherical averaging operator. | |

Emily Windes: The Frobenius Theorem and Foliations. | PhD Mathematics, UR |

**2016:**

Honors Thesis | Future Plans |

Luke Cybulski: Sugawara's construction of the Virasoro algebra for c=1,h=0. | |

Bai Lin: Sums of permutations. | PhD Mathematics, UR |

Haoran Liu: Infinite Galois theory. | |

Brian McDonald: Hinges in Z_p^d and applications to pinned distance sets. | PhD Mathematics, UR |

Lisa Rosenfeld: The box problem in two and higher dimensions. | FDIC |

Adam Scrivener: On incomplete distance sets in Z_p x Z_p. | |

Yinuo Zhang: Shifted K-theoretic Pourier-Reutenauer algebra. | PhD Economics, Princeton |

**2015:**

Honors Thesis | Future Plans |

Douglas Miller | Jump Trading (Chicago) |

David Sekora: Discrete valuation rings and Dedekind domains. | |

Luke Vaicunas | PhD Mathematics, MSU |

Elizabeth Winkelman: The CW-complex of translation surfaces of genus 2 with one singularity. | PhD Mathematics, U. of Utah |

**2014:**

Honors Thesis | Future Plans |

Lawrence Barrett | |

James Haley | MS Mathematics, U. of Waterloo |

Peihong Jiang: Controlling generic formal fibers of polynomial rings. | |

Jia Shuo Liu | |

Alexander McDonald | PhD Mathematics, UR |

Sean Spriggens | PhD Mathematics, Syracuse |

Ari Stoler: Conjugacy classes and irreducible representations of metacyclic groups. |

**2013:**

Honors Thesis | Future Plans |

Yuefeng Liang | MS Statistics, U. of Chicago |

Emmett Wyman: Two geometric combinatorial problems in vector spaces over finite fields. | PhD Mathematics, Johns Hopkins |

Yujia Zhai: Areas of triangles and Beck's theorem in places over finite fields. | PhD Mathematics, Cornell |

**2012:**

Honors Thesis | Future Plans |

Matej Penciak | PhD Mathematics, Illinois Urbana-Champaign |

Peter Richter | |

Xiaoqing Tang: Simple proof of the Guth-Katz joints theorem. |