Honors Papers and Future Plans
2024:
| Honors Thesis Student | Future Plans |
Elana Elman: Kolmogorov complexity and distance sets: two notions of set complexity. (Advisor: Iosevich)[Video of Talk] | Software Engineer for ASML. |
Matthew Fraser: Intersection Theory and the Poincaré-Hopf Theorem. (Advisor: Pakianathan)[Video of Talk] | Plans to work in the actuarial industry. |
Xu Huang: A Model for the Multi-Virus Contact Process. (Advisor: Mueller)[Video of Talk] | Statistics and Operation Research Ph.D. program at University of North Carolina, Chapel Hill. |
Fuyi Kuang: Van der Corput's method for exponential sums and the Divisor Problem. (Advisor: Gonek) | U.C. Berkeley Law school program. |
Sangwu Lee: On Spectral properties of the Sierpinski gasket. (Advisor: Pakianathan)[Video of Talk] | Founding Software Engineer of NYC firm "Quizard". |
Peter MacNeil: On the predictability of time series: a fractal perspective. (Advisor: Iosevich)[Video of Talk] | Technical Solutions Engineer at Epic in Madison, Wisconsin. |
Svetlana Pack: Bounding the Kolmogorov complexity of pseudorandom graphs. (Advisor: Iosevich)[Video of Talk] | Mathematics Ph.D. program at Penn State. |
Eli Seamans: Uncertainty Principles and Signal Recovery with Incomplete Data. (Advisor: Iosevich) [Video of talk] | Mathematics Ph.D. program at Syracuse University. |
Nathan Skerrett: The Erdos Distance Problem on Compact Riemannian Manifolds Without Boundary. (Coadvisors: Iosevich and Kleene)[Video of Talk] | Mathematics Ph.D. program at University of Rochester. |
Xuan Wang: Dividing the Indivisible: A Comprehensive Analysis of the Banach-Tarski Paradox. (Advisor: Iosevich)[Video of Talk] | Quantitative Management program, Fuqua School of Business, Duke University. |
Yinghan Yu: A Discussion on the Optimization of Multi-Echelon Cross-Docking Supply Chain Structures. (Advisor: Herman)[Video of Talk] | Simon School of Business (University of Rochester) Ph.D. program. |
2023:
| Honors Thesis Student | Future Plans |
Livia Betti: VC-dimension of Spherical Hypothesis Classes over | Computer Science Ph.D. program at U.Colorado, Boulder. |
David Crncevic: Algebraic properties of Artin-Mazur zeta function in positive characteristic. (Advisor: Rivera-Letelier) | Mathematics Ph.D. 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 at Georgia Tech. |
Yuqiao Huang: Correspondence between Lie groups and Lie algebras. (Advisor: Pakianathan) | Mathematics Ph.D. at Rutgers U. |
Matthew Kaminskas: An Alternative Construction of the L1 Space. (Advisor: Geba) | |
Henry Lin: A Primer to Integral Equations of the Second Kind. (Advisor: Geba) | Comp. Science Masters at Columbia U. |
Yurong Liu: Reconstruction on Markov Tree. (Advisors: Stefankovic, Mkrtchyan) | Comp. Science Ph.D. at NYU. |
Jack Mandell: Applications of linear and semidefinite programming to approximation algorithms. (Advisor: Stefankovic) | Applied Mathematics Ph.D. at RPI. |
Justin Murante: Multiplicative Correlations Between Multiplicative Functions. (Advisor: Gonek) | Optics Ph.D. at University of Arizona. |
Anna Myakushina: Exploring Sampling Techniques in Large Graphs and Networks. (Advisor: Iosevich) | Operations Research Ph.D. 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. at U. Chicago. |
Yukun Yang: Stochastic Gradient Descent | Statistics Masters at U. Michigan. |
.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. (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. at Boston U. |
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 at Brown U. |
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. at UT Austin. |
Michele Martino: Fractal dimension, configuration problems, and their connection to machine learning.(Advisors: Emmett Wyman and Iosevich) | Applied Math Ph.D. at University of Washington. |
Jacob Miller: Quandle invariants of knots and links. (Advisor: Pakianathan)(Talk Video Link) | Mathematics Ph.D at U. of Iowa. |
Arian Nadjimzadah: Existence of dot product trees in thin subsets of Euclidean space. (Advisor: Iosevich)(Talk Video Link) | Mathematics Ph.D at UCLA. |
Thomas O'Neill: Mathematical applications of Reinforcement Learning. (Advisor: Iosevich) | Gap year; plan to apply to Ph.D. programs. |
Lloyd Page: Leaky Abelian Sandpile Model with multiple starting points. (Advisor: Mkrtchyan)(Talk Video Link) | Economics Ph.D. 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. at MSU. |
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) | Comp. Sci. Ph.D. at Cornell U. |
Cole Durham: A Survey of Differential Topology: Intersection Numbers, Morse Theory, and Morse Homology.(Advisor: Pakianathan) | Mathematics Ph.D. at UConn. |
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) | Comp. Sci. Ph.D. at Georgetown U. |
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. at U. of Wash. |
Xiaobo Luo: Probabilistic and Experimental Methods in Sum-Product Theory.(Advisor: Iosevich) | Data Science M.S. at Harvard U. |
Trung Nguyen: Integral Bases.(Advisor: Jochnowitz) | Mathematics Ph.D. at Penn. State U. |
Tyler Perlman: The Hardy Inequality and variants.(Advisor: Geba) | Mathematics M.S. at N.Y.U. |
Donovan Snyder: Quantum Probability in a Two State Random Walk.(Advisor: Rajeev) | Mathematics Ph.D. at U. of Rochester. |
Yiyang Su: Computer Experiments with Higher-Dimensional Probability.(Advisor: Iosevich) | Comp. Science Ph.D. at MSU. |
Giang Truong: Uniqueness of a three dimensional stochastic differential equation.(Advisor: Mueller) | Financial Mathematics Ph.D. at Princeton University. |
Chuanyi Wang: Dynamics of Rotation-like Logistic Maps.(Advisor: Rivera-Letelier) | |
Yue Wang: Relativistic Brownian Motion.(Advisor: Rajeev) | Physics Ph.D. at U.C. Berkeley. |
Kyhl Weber: Qualitative properties for solutions to a differential equation associated with the Skyrme model.(Advisor: Geba) | Pursuing industry positions; possibly transtioning to grad school. |
Tongyu Yang: The Ihara Zeta function.(Advisor: Haessig) | Computer Science M.S. program at Yale University. |
Matthew Zevenbergen: Crushtaceans and Complements of Fully Augmented and Nested Links.(Advisor: Cohen) | Mathematics Ph.D. program at Boston College. |
2020:
| Honors Thesis | Future Plans |
| Dustin Kasser: Series Rearrangements Using Density Functions. | Mathematics Ph.D. at U. of Georgia. |
| Xin Lu: On NP-intermediate, Isomorphism problems, and Polynomial Hierarchy. | MS Comp. Science at Stanford U. |
| Gregory Michajlsyzyn: On the discriminant of the Hecke ring and its index in the corresponding ring of integers. | Mathematics Ph.D. at UConn. |
| 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. at UC 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 | Most Recent Update |
| 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 | Most Recent Update |
| 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. | |
| Ophelia (Mark) Adams: Model Theory. | Obtained Ph.D. in Mathematics, Brown University. Now Visiting A. Prof. at University of Rochester (2024). |
| Alfredo Vargas: Minimal Surfaces in R^3. | |
| Jean Weill: Yang-Mills Theory on a Cylinder. |
2017:
| Honors Thesis | Most Recent Update |
| Charlotte Aten: The Topology of Magmas. | Obtained Ph.D. in Mathematics, U. of Rochester. Now postdoc at University of Denver (2024). |
| Noah Chrein: Enriched Coproducts and the Twisted Adjunction. | |
| Benjamin Dees: Analogs of the Erdos integer distance principle in vector spaces over finite fields. | Obtained Ph.D. Mathematics, Johns Hopkins U. Now Tamarkin postdoc at Brown U (2024). |
| 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 | Most Recent Update |
| 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 | Most Recent Update |
| Douglas Miller | R&D Software Engineer at Jump Trading, Chicago branch (2024). |
| David Sekora: Discrete valuation rings and Dedekind domains. | Obtained Ph.D. in Computer Science (2022). |
| Luke Vaicunas | Analytical consultant at the Parker Avery group (2024). |
| Elizabeth Winkelman: The CW-complex of translation surfaces of genus 2 with one singularity. | Obtained MS in Math. Senior member of engineering staff at Lockheed Martin (2024). |
2014:
| Honors Thesis | Most Recent Update |
| Lawrence Barrett | Obtained MS Math. Working at Vida Health (2024). |
| James Haley | Obtained MS Math. Working at SHYFT Analytics (2017). |
| Peihong Jiang: Controlling generic formal fibers of polynomial rings. | Obtained Ph.D. in mathematics, Brown University (2021). |
| Jia Shuo Liu | |
| Alexander McDonald | Obtained Ph.D. in mathematics. Ross Assistant Prof. at Ohio State University (2024). |
| Sean Spriggens | |
| Ari Stoler: Conjugacy classes and irreducible representations of metacyclic groups. | Software developer at Edia (2024). |
2013:
| Honors Thesis | Most Recent Update |
| Yuefeng Liang | Obtained Ph.D. in Statistics. Working for LinkedIn Corp (2024). |
| Emmett Wyman: Two geometric combinatorial problems in vector spaces over finite fields. | Obtained Ph.D. in Mathematics. Assistant Prof at Binghamton University (2024). |
| Yujia Zhai: Areas of triangles and Beck's theorem in places over finite fields. | Math Postdoctoral Associate, Université de Nantes (2019). |