Honors Papers and Future Plans

2024: 

 

2024 Honors Thesis
Honors Thesis StudentTalk Date/Time/locRest of Committee

Elana Elman: Kolmogorov complexity and distance sets: two notions of set complexity. (Advisor: Iosevich)

Friday, April 26, 3:30-4:20PM in Hylan 203. 

Jochnowitz

Geba

Matthew Fraser: Intersection Theory and the Poincaré-Hopf Theorem. (Advisor: Pakianathan)

Thursday, May 2, 2-2:50PM in Hylan 105. 

Iosevich

Greenleaf

Xu Huang: A Model for the Multi-Virus Contact Process. (Advisor: Mueller)

Friday, May 3, 11AM-11:50AM in Hylan 105. 

Mkrtchyan

Rivera-Letelier

Fuyi Kuang: Van der Corput's method for exponential sums and the Divisor Problem. (Advisor: Gonek)

Tuesday, April 30, 2-2:50PM in Computer Science Building 209. 

Pakianathan

Thakur

Sangwu Lee: On Spectral properties of the Sierpinski gasket. (Advisor: Pakianathan)

Thursday, May 2, 11AM-11:50AM in Hylan 105.

Iosevich

Mkrtchyan

Peter MacNeil: On the predictability of time series: a fractal perspective. (Advisor: Iosevich)

Thursday, May 9, 12:30-1:20PM in Hylan 105.

Mrktchyan

Kuzgun

Svetlana Pack: Bounding the Kolmogorov complexity of pseudorandom graphs.(Advisor: Iosevich)

Friday, May 10, 11-11:50AM in Hylan 105. 

Pakianathan

Rivera-Letelier

Eli Seamans: Uncertainty Principles and Signal Recovery with Incomplete Data.(Advisor: Iosevich)

Tuesday, April 23, 9:30-10:20AM in Hylan 303. 

Geba

Pakianathan

Nathan Skerrett: The Erdos Distance Problem on Compact Riemannian Manifolds Without Boundary. (Coadvisors: Iosevich and Kleene)

Friday, May 3, 12:30-1:20PM in Hylan 105. 

Pakianathan

Xuan Wang: Dividing the Indivisible: A Comprehensive Analysis of the Banach-Tarski Paradox. (Advisor: Iosevich)

 

Jochnowitz

Yinghan Yu: A Discussion on the Optimization of Multi-Echelon Cross-Docking Supply Chain Structures. (Advisor: Herman)

Thursday, May 2, 9:30-10:20AM in Hylan 105. 

Mueller

Pakianathan

 

2023: 

 

2023 Honors Thesis
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: 

2022 Honors Thesis
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:

2021 Honors Thesis
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:

2020 Honors Thesis
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:

2019 Honors Thesis
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:

2018 Honors Thesis
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:

2017 Honors Thesis
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:

2016 Honors Thesis
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:

2015 Honors Thesis
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:

2014 Honors Thesis
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:

2013 Honors Thesis
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:

2012 Honors Thesis
Honors ThesisFuture Plans
Matej PenciakPhD Mathematics, Illinois Urbana-Champaign
Peter Richter
Xiaoqing Tang: Simple proof of the Guth-Katz joints theorem.