Honors Papers and Future Plans

2024: 

 

Honors Thesis StudentTopicAdvisorRest of Committee

Matthew Fraser

Degree Theory and the Poincaré-Hopf Theorem.Pakianathan

Iosevich

Greenleaf

Xu Huang

A Model for the Multi-Virus Contact Process.Mueller

Mkrtchyan

Rivera-Letelier

Fuyi Kuang

Van der Corput's method and the Gauss Circle Problem.Gonek

Pakianathan

Thakur

Sangwu Lee

On Spectral properties of the Sierpinski gasket.Pakianathan

Iosevich

Mkrtchyan

Peter MacNeil

On the predictability of time series: a fractal perspective.Iosevich

Mrktchyan

Kuzgun

Svetlana Pack

Kolmogorov complexity of pseudorandom graphs.IosevichPakianathan

Eli Seamans

IosevichPakianathan

Nathan Skerrett

The Erdos Distance Problem on Compact Riemannian Manifolds Without Boundary.

Iosevich

Kleene

Pakianathan

Yinghan Yu

A Discussion on the Optimization of Multi-Echelon Cross-Docking Supply Chain Structures.Herman

Mueller

Pakianathan

 

2023: 

 

Honors Thesis StudentFuture Plans

Livia Betti: VC-dimension of Spherical Hypothesis Classes over \mathbb{F}_q^d. (Advisor: Iosevich)

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)

Statistics/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
Convergence: Exploring Variants and their Convergence Rates. (Advisor: Iosevich)

Statistics Masters at U. Michigan.

 

 

2022: 

Honors ThesisFuture 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)

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 ThesisFuture 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 research/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 ThesisFuture 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 ThesisFuture 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 ThesisFuture 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 ThesisFuture 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 ThesisFuture 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 ThesisFuture Plans
Douglas MillerJump Trading (Chicago)
David Sekora: Discrete valuation rings and Dedekind domains.
Luke VaicunasPhD Mathematics, MSU
Elizabeth Winkelman: The CW-complex of translation surfaces of genus 2 with one singularity.PhD Mathematics, U. of Utah

2014:

Honors ThesisFuture Plans
Lawrence Barrett
James HaleyMS Mathematics, U. of Waterloo
Peihong Jiang: Controlling generic formal fibers of polynomial rings.
Jia Shuo Liu
Alexander McDonaldPhD Mathematics, UR
Sean SpriggensPhD Mathematics, Syracuse
Ari Stoler: Conjugacy classes and irreducible representations of metacyclic groups.

2013:

Honors ThesisFuture Plans
Yuefeng LiangMS 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 ThesisFuture Plans
Matej PenciakPhD Mathematics, Illinois Urbana-Champaign
Peter Richter
Xiaoqing Tang: Simple proof of the Guth-Katz joints theorem.