# Student Profiles

## hh

I am currently a Ph.D. candidate in mathematics at UIC, and my current research concerns the elementary theory of toral relatively hyperbolic groups, which arise as the fundamental groups of hyperbolic manifolds with torus cusp cross-sections. As a math grad student at UIC, I’ve had a lot of great opportunities for teaching, research, and travel. I have taught my own independent workshop sections of Calculus 2 as part of the Emerging Scholars Program, and I have helped incoming freshmen place into 100-level courses by teaching the Summer Enrichment Math Workshop. I have traveled around the United States and to Britain, Germany, and Israel to attend conferences and work with other mathematicians. I helped to organize the 2018 Graduate Student Topology and Geometry Conference at UIC. Finally, being a graduate student in a city like Chicago is great. I live in the Logan Square neighborhood, which has a lot to do and is only a train ride away from UIC.

I am a fifth year student in Applied Mathematics, my research is on theoretical and numerical aspects of the Water Wave Equation. With my advisor Prof. David Nicholls, we are trying to prove the well-posedness of the equation with viscosity and with forcing. Prior to UIC, I was a student at the University of Paris XI (Orsay) where I got a Master in Partial Differential Equations and Scientific Computing and I also got an Engineering degree in Computer Science from INP-ENSEEIHT in Toulouse (South of France).

My research area is algebraic combinatorics and matrix theory. My advisor Is Shmuel Friedland. A general question I am interested in is; assume that G has a double cycle cover. Then the double cycle cover defines a singular surface Σ. One can define the dual of G which gives a desingularized surface de Σ. I work on the contraction of de Σ induced by contraction of some edges of de Σ. This corresponds to a deletion of some edges in G. I have also worked on problems concerning matchings in groups and field extensions. I recently proved that there are infinitely many prime p such that Zp has acyclic matching property. After taking a matrix theory course with Shmuel I became interested in this field and we wrote a book entitled

Linear Algebra and Matrix Theory. I am also interested in psychology, politics, and my favorite sport is table tennis.

I began my math PhD journey in pure mathematics and later pivoted to mathematical computer science after gaining exposure to computer science topics in internships and taking interesting MCS graduate courses. One of the benefits of our department is that you can explore courses from pure math, applied math, mathematical computer science (MCS), and statistics, with the freedom to choose any of these routes as your PhD focus. I have a variety of research interests in MCS, including network science, data science, machine learning, and deep learning. Most recently, my research has been focused on learning theory, developing probably approximately correct (PAC) algorithms to train classifiers with noisy labeled data obtained in crowdsourcing and collaborative settings.