# Former PhD Students

**2024**

**Guanning Zhang**

Dissertation Title: Mathematical Topics in Block Copolymer

Advisor: Xiaofeng Ren

**Keshav Srinivasan**

Dissertation Title: Effective Ultrapowers of Computable Structures

Advisor: Valentina Harizanov

**2023**

**Dario Verta**

Dissertation Title: Computability theory: countable magmas and their properties

Advisor: Valentina Harizanov

**2022**

**Gabriel Montoya Vega**

Dissertation Title: A Historical Exploration of Knot Theory, Khovanov Homology, and Framing Changes of Links and Skein Modules

Advisor: Jozef Przytycki

**Kevin Long**

Dissertation Title: Some Problems on Matroid Invariants and Integer Polymatroids

Advisor: Joseph E. Bonin

**Hyungjung Choi**

Dissertation Title: Numerical Methods for Block Copolymer Systems with Long Range Interaction

Advisor: Yanxiang Zhao

**Jingjing Xu**

Dissertation Title: Analysis and Scientific Computing on Some Nonlocal PDEs

Advisor: Yanxiang Zhao

**Dionne Ibarra**

Dissertation Title: Framed links in 3-manifolds, its applications, and algebraic approaches to knot theory

Advisor: Jozef Przytycki

**Jiayuan Wang**

Dissertation Title: Factorization Combinatorics in Complex Reflection Groups

Advisor: Joel B Lewis

**2021**

**Rhea Palak Bakshi**

Dissertation Title: Skein Modules, Skein Algebras, and Their Ramifications

Advisor: Jozef Przytycki

**Hyeeun Jang**

Dissertation Title: "Directional expansiveness"

Advisor: E Arthur Robinson

**Pavel Avdeyev**

Dissertation Title: Mathematical Models of Ancestral Genome Reconstruction

Advisor: Jozef Przytycki

**Xinyu Zhang**

Dissertation Title: Approximation Methods of Caputo Derivatives and Their Applications to Non-local Porous Medium Equations.

Advisor: Maria Gualdani

## 2020

**Jason Suagee**

Dissertation Title: "Existence and Construction of Schnyder Orientations over a Large Class of Higher Genus Surface Triangulations."

Advisor: Lowell Abrams

**Iva Bilanovic**

Dissertation Title: “Detecting Properties of Algebraic and Relational Structures”

Advisor: Valentina Harizanov

**Konstantinos Smpokos**

Dissertation Title: “A Geometric Variational Problem on a Periodic Domain”

Advisor: Xiaofeng Ren

## 2019

**Debdeep Bhattacharya**

Dissertation Title: “Harmonic Analysis Techniques in Nonlinear Dispersive Equations and Signal Processing”

Advisor: Frank Baginski

**Sujoy Mukherjee**

Dissertation Title: “On Skein Modules and Homology Theories Related to Knots Theory”

Advisor: Jozef H. Przytycki

## 2018

**Kai Yang**

Dissertation Title: Formation of Singularities in Nondispersive Partial Differential Equations

Advisor: Svetlana Roudenko and Yanxiang Zhao

**Xiao Wang**

Dissertation Title: Knot Theory and Algebraic Structures Motivated by and Applied to Knots

Advisor: Jozef Przytycki

**Chong Wang**

Dissertation Title: Analysis and Modeling of Self-organizing Systems with Long Range Interaction,

Advisor: Xiaofeng Ren and Yanxiang Zhao

**Jiajun Lu**

Dissertation Title: Pattern Formation in Binary Systems with Long-range Interaction

Advisor: Frank Baginski

**Chubo Deng**

Dissertation Title: Stability in a Trend-depending price formation model

Advisor: Maria Gualdani

**Trang Ha**

Dissertation Title: “On Algorithmic Properties of Computable Magmas”

Advisor: Valentina Harizanov

**Harpreet Bedi**

Dissertation Title: “Cohomology of Line Bundles with Rational Degree”

Advisor: Yongwu Rong and Jozef H. Przytycki

## 2017

**Sergey Aganezov**

Dissertation Title: “Phylogenomics Meets Genome Assembly: From Evolutionary Analysis to Scaffolding”

Advisor: Max Alekeyev

**Hakim Walker**

Dissertation Title: Computable Isomorphisms of Directed Graphs and Trees

Advisor: Valentina S. Harizanov

**Seung Yeop Yang**

Dissertation Title: Khovanov Homology, Distributive Structure Homology and Applications to Knot Theory

Advisor: Jozef H. Przytycki

## 2016

**Yeyao Hu**

Dissertation Title: Disc Assemblies and Spik Assemblies in inhibitory system

Advisor: Xiaofeng Ren

**Lara El Sherif**

Dissertation Title: Matchings of Intersection Graphs and the Maximum Genus Problem

Advisor: Lowell Abrams

## 2015 and Earlier

**Leah Marshall (2015)**

Dissertation: Computability-Theoretic Properties of Partial Injections, Trees, and Nested Equivalences

Advisor: Valentina S. Harizanov

**Jing Wang (2015)**

Dissertation: Homology of Small Categories and Its Applications

Advisor: Jozef H. Przytycki

**Thomas Jason Savitsky (2015)**

Dissertation: Some Problems on Matroids and Integer Polymatroids

Advisor: Joseph E. Bonin

**Carl Crawford Hammarsten (2015)**

Dissertation: "Decorated Heegaard diagrams and combinatorial Heegaard Floer homology"

Advisor: Alexander Shumakovitch

**David Shoup (2015)**

Dissertation: Half Disc Stationary Sets on the Boundary of a Binary Inhibitory System

Advisor: Xiaofeng Ren

**Steven Schluchter (2014)**

Dissertation: Ordinary Voltage Graphs In Pseusosurfaces And Derived Cellular Homology With Applications To Graph Embeddability.

Advisor: Lowell Abrams

**Erblin Mehmetaj (2014)**

Dissertation: On the r-Continued Fraction Expansions of Real Numbers

Advisor: E. Arthur Robinson, Jr.

**Kai Maeda (2013)**

Dissertation: Self-Distributive Magmas and Their Richter’s Degrees

Advisor: Valentina S. Harizanov

**Joseph L Herning (2013)**

PhD George Washington University 2013

Dissertation: Spectrum and Factors of Substitution Dynamical Systems

Advisor: E. Arthur Robinson, Jr.

**Lu Xie (2013)**

Dissertation: Analysis of the Long Range Interaction in the Ternary System

Advisor: Xiaofeng Ren

**Ken Shoda (2012)**

Dissertation: Large Families of Matroids with the Same Tutte Polynomial

Advisor: Joseph E. Bonin

**Tyler White (2012)**

Dissertation: Topologically Mixing Tilings of R^2 Generated by a Generalized Substitution

Advisor: E. Arthur Robinson, Jr.

**Forest Fisher**

PhD George Washington University 2010

Dissertation: CoZinbiel Hopf Algebras in Combinatorics

Advisor: William R. Schmitt

**Hillary Einziger**

PhD George Washington University 2010

Dissertation: Incidence Hopf Algebras: Antipodes, Forest Formulas, and Noncrossing Partitions

Advisor: William R. Schmitt

**Michael J. Coleman**

PhD George Washington University 2010

Dissertation: Surface Accuracy Analysis and Mathematical Modeling of Deployable Large Aperture Elastic Antenna Reflectors

Advisor: Frank E. Baginski

**Jieun Lee**

PhD George Washington University 2010

Dissertation: Modeling the Equilibrium Configuration of a Piecewise Orthotropic Pneumatic Envelope and the Phase Separation Problem in a Membrane

Advisors: Frank E. Baginski and Xiaofeng Ren

**Radmila Sazdanović**

PhD George Washington University 2009

Dissertation: Categorification of Knot and Graph Polynomials and the Polynomial Ring

Advisor: Jozef H. Przytycki

**Jennifer Chubb**

PhD George Washington University 2009

Dissertation: Ordered Structures and Computability

Advisor: Valentina S. Harizanov

**Kerry Luse**

PhD George Washington University 2008

Dissertation: Invariants of Knots, Graphs, and Feynman Diagrams

Advisor: Yongwu Rong

**Sarah Pingrey**

PhD George Washington University 2008

Dissertation: Strong Degree Spectra of Relations

Advisor: Valentina S. Harizanov

**Tanya Andress**

PhD George Washington University 2007

Dissertation: The spectrum and the first Cech cohomology group of a one dimensional tiling dynamical system

Advisor: E. Arthur Robinson

**Geoffrey McKenna**

PhD George Washington University 2007

Dissertation: Graphs, Algebra, and Probability

Advisor: Daniel H. Ullman

**Fanny Jasso-Hernandez**

PhD George Washington University 2007

Dissertation: A Homological Algebraic Approach to the Tutte Polynomial

Advisor: Yongwu Rong

**Michael Barg**

PhD George Washington University 2007

Dissertation: Direct Methods in the Calculus of Variations with Applications to Tendon-Reinforced Piecewise-Isotropic Membranes

Advisor: Frank E. Baginski

**Maciej Niebrzydowski**

PhD George Washington University 2007

Dissertation: Some Applications of Quandles and their Homology to the Geometry of Knots

Advisor: Jozef H. Przytycki

**Eric Ufferman**

PhD George Washington University 2006

Dissertation: Structures and Partial Computable Automorphisms

Advisor: Valentina S. Harizanov

**Malgorzata Dabkowska**

PhD George Washington University 2006

Dissertation: Turing Degree Spectra of Groups and Their Spaces of Orders

Advisor: Valentina S. Harizanov

**Michael Veve**

PhD George Washington University 2006

Dissertation: Skien Modules, Orderable Magmas, and Billiards

Advisor: Jozef H. Przytycki

**Laure Helme-Guizon**

PhD George Washington University 2005

Dissertation: A Categorification of the Chromatic Polynomial

Advisor: Yongwu Rong

**Amir Togha**

PhD George Washington University 2004

Dissertation: On Automorphisms of Structures in Logic and Orderability of Groups in Topology

Advisors: Valentina S. Harizanov and Ali Enayat

**Mieczyslaw Dabkowski**

PhD George Washington University 2003

Dissertation: Cubic Skein Modules and Burnside Groups

Advisor: Jozef H. Przytycki

**Rumen Dimitrov**

PhD George Washington University 2002

Dissertation: Computably Enumerable Vector Spaces, Dependence Relations, and Turing Degrees

Advisor: Valentina S. Harizanov

**Krzysztof Wargan**

PhD George Washington University 2002

Dissertation: S-adic Dynamical Systems and Bratteli Diagrams

Advisor: E. Arthur Robinson, Jr.

**David Hough**

PhD George Washington University 2001

Dissertation: The Genus of Partitions and C-trees

Advisors: Daniel H. Ullman and Frank Schmidt

**Rachelle Ankney**

PhD George Washington University 2001

Dissertation: The geometries PG(n-1,q)\PG(k-1,q)

Advisor: Joseph E. Bonin

**Amir Pirnazar**

PhD George Washington University 2000

Dissertation: Girth, genus and fractional coloring of graphs

Advisor: Daniel H. Ullman

**Hongxun Qin**

PhD George Washington University 2000

Dissertation: Tutte polynomials and matroid constructions

Advisor: Joseph E. Bonin

**Maxim V. Sokolov**

PhD George Washington University 2000

Dissertation: Quantum invariants, skein modules, and periodicity of 3-manifolds

Advisor: Jozef H. Przytycki

**Tatsuya Tsukamoto**

PhD George Washington University 2000

Dissertation: The fourth skein module of 3-dimensional manifolds

Advisor: Jozef H. Przytycki

**William Collier**

PhD George Washington University 2000

Dissertation: Applications of variational principles to modeling a partially inflated scientific research balloon

Advisor: Frank E. Baginski

**Clifford Hansen**

PhD George Washington University 2000

Dissertation: Dynamics of muldimensional substitutions

Advisor: E. Arthur Robinson Jr.

**Thomas Fitzkee**

PhD George Washington University 1998

Dissertation: Weakly mixing tiling flows arising from interval exchange transformations

Advisor: E.Arthur Robinson Jr.

**Jules Kouatchou**

PhD George Washington University 1997

Dissertation: High-order multigrid techniques for partial differential equations

Advisor: Murli M. Gupta

**Michael Edward McDaniel**

PhD George Washington University 1997

Dissertation: Subspaces of Vassiliev invariants using cablings

Advisor: Yongwu Rong

**Jun Zhang**

PhD George Washington University 1997

Dissertation: Multigrid acceleration techniques and applications to the numerical solution of partial differential equations

Advisor: Murli M. Gupta

**Sita Ramamurti**

PhD George Washington University 1995

Dissertation: Dynamics near the essential singularity for zero-free entire vector fields of finite order

Advisor: Kevin Hockett

**William P. Miller**

PhD George Washington University 1995

Dissertation: Approaches to matroid reconstruction problems

Advisor: Joseph E. Bonin

**Timothy McNicholl**

PhD George Washington University 1995

Dissertation: The inclusion problem for generalized frequency classes

Advisor: Valentina S. Harizanov

**Hassan Sedaghat**

PhD George Washington University 1990

Dissertation: New constructions in semigroup compactification theory

Advisor: Hugo D. Junghenn

**Karma Dajani**

PhD George Washington University 1989

Dissertation: Simultaneous recurrence of weighted cocycles.

Advisor: E.Arthur Robinson, Jr.

**Amir Afrasiab Maleki**

PhD George Washington University 1985

Dissertation: Semigroups of quasicompact operators: Convergence and mean ergodic property

Advisor: Choy-Tak Taam

**Thomas Lewrie Mifflin**

PhD George Washington University 1984

Dissertation: Almost periodic selections

Advisor: Hugo D. Junghenn

**Ramaiah Devadoss Pandian**

PhD George Washington University 1983

Dissertation: Relatively almost periodic and distal semigroup compactifications and related fixed point theorems

Advisor: Hugo D. Junghenn

**Tyler Henry Haynes (Jr)**

PhD George Washington University 1983

Dissertation: Invariant means on semi-topological transformation semigroups

Advisor: Hugo D. Junghenn

**Ali Saleh Arwini**

PhD George Washington University 1982

Dissertation: Order compactness and complete regularity in topological preordered spaces

Advisor: Marvin D. Green

**Amir Hamzeh Barzegar**

PhD George Washington University 1981

Dissertation: Syntopological characterization of algebraic structures and Bohr syntopological group compactification

Advisor: Marvin D. Green

**John Richard Tucker**

PhD George Washington University 1980

Dissertation: Mixing, Ergodicity, and Amenability for Weekly Almost Periodic Semigroups

Advisor: Choy-Tak Taam

**Steven Zalmon Kahn**

PhD George Washington University 1980

Dissertation: Chromatic equivalence and chromatic uniqueness

Advisor: Ruth Aaronson Bari

**Bao Ting Chen Lerner**

PhD George Washington University 1979

Dissertation: C*-Algebra Compactifications of semidirect products of semitopological semigroups

Advisor: Hugo D. Junghenn

**Arthur Valliere, III**

PhD George Washington University 1979

Dissertation: On Matrices A such that AT is a Polynomial in A

Advisor: Irving J. Katz

**Walter Lane Stanley**

PhD George Washington University 1977

Dissertation: On the structure of the torsion subgroup of the group of units of a group ring

Advisor: Myrna Pike Lee

**Henry Kwong Tan**

PhD George Washington University 1977

Dissertation: Ergodic theorems and semigroups of *Homomorphisms on C* and W*-Algebras

Advisor: Choy-Tak Taam

**Robert Edward O'Brien**

PhD George Washington University 1977

Dissertation: Controllability and Stabilization of contraction semigroups on Hilbert spaces

Advisor: Choy-Tak Taam

**Daniel Rucker Batigne**

PhD George Washington University 1977

Dissertation: Integral Generalized Inverses of Integral Matrices

Advisor: Irving J. Katz

**John Frank Schmeelk**

PhD George Washington University 1976

Dissertation: Test surfunctions and generalized surfunctions

Advisor: Thomas Liverman

**Lawrence Allen Lee**

PhD George Washington University 1975

Dissertation: On chromatically equivalent graphs

Advisor: Ruth Aaronson Bari

**David Schedler**

PhD George Washington University 1971

Dissertation: On topologies determined by clustering sequences: a generalization of sequential space

Advisors: Hewitt Kenyon

**Kim Ki-Hang Butler**

PhD George Washington University 1970

Dissertation: On (0,1)-Matrix Semigroups

Advisors: Jin B. Kim

**Hugo Dietrich Junghenn**

PhD George Washington University 1970

Dissertation: Almost Periodic Compactifications and Applications to One-Parameter Semigroups

Advisor: Choy-Tak Taam

**John Jones, Jr.**

PhD George Washington University 1970

Dissertation: Properties of strong solutions of first and second order differential equations and inequalities in Hilbert space

Advisor: Thomas Liverman

**Ruth Doris Koidan**

Ph.D. George Washington University 1969

Dissertation: Convergence bases and subbases in general topology

Advisor: Hewitt Kenyon

**John Kent Minichiello**

Ph.D. George Washington University 1967

Dissertation: Negationless Intuitionistic mathematics

Advisor: David Nelson

**Mahmoud Khairat Ahmed Khairat**

Ph.D. George Washington University 1965

Dissertation: Some results for random elements taking values in a linear space

Advisor: Solomon Kullback

**Hubert Whitman Lilliefors**

Ph.D. George Washington University 1964

Dissertation: An Information Theoretic Application of Linear Discriminant Functionals to Stochastic Processes

Advisor: Solomon Kullback

**Janos Edvard Hanson**

Ph.D. George Washington University 1960

Dissertation: On linear sequence spaces which permit ommision and adjunction and have finite dimension modulo convergence

Advisor: Florence Marie Mears

**Joseph Blum**

Ph.D. George Washington University 1958

Dissertation: Banach Spaces Functionals and Matrix Summability Methods

Advisor: Florence Marie Mears

**Valdemars Punga**

Ph.D. George Washington University 1954

Dissertation: Affine connection in space of line elements

Advisor: James Henry Taylor

**Robert Harrison Shaw**

Ph.D. George Washington University 1952

Dissertation: On the proof of a theorem of Frobenius without the use of group characters

Advisor: Francis Edgar Johnston

**Solomon Kullback**

Ph.D. George Washington University 1934

Dissertation: An application of characteristic functions to the distribution problem of statistics

Advisor: Frank Weida

**Abraham Sinkov**

Ph.D. George Washington University 1933

Dissertation: Families of groups generated by two operators of the same orders

Advisor: Francis Edgar Johnston