Share This

Meet our students

Department of Mathematics
0

Meet our students

Meet Pavel Javornik

Meet one of our undergraduates and summer research interns, Pavel Javornik! 

--
This summer I will be continuing my work under the mentorship of Dr. Patrick Hooper. Our current project is to describe the dynamical properties of geodesic flows on non-compact surfaces composed entirely of boundary unions of various polyhedrons. Certain characteristics of these infinite surfaces, such as the symmetries of the canonical forms of their quotient spaces, determine the behavior of geodesic flows given properties of said flow (such as their initial trajectories). The goal this summer is to adapt various methods used in studying infinite surfaces constructed from compact translation surfaces to better understand surfaces that might admit transformations of geodesic flows in the form of rotations. Much of the study of Veech surfaces is applicable to certain rational billiards problems on infinite surfaces like the Ehrenfest-Wind Tree Model, but these transformations often admit reflections off of boundaries in the form of perfectly elastic collisions. The translation surfaces and (consequently) Veech groups of these infinite surfaces have symmetrical properties unlike those of surfaces constructed of polyhedrons. Understanding how these boundaries might affect geodesic flow on flattened structures is key to understanding their dynamical properties. 

What drives my work is my love for mathematics. Studying the underlying structures of objects such as manifolds fascinates me. With low-dimensional topology there is a geometric intuition when trying to characterize these kinds of surfaces. Describing the homology classes of non-compact, infinite (possibly infinite genus) surfaces in the form of their compact covering/translation spaces is a somewhat novel undertaking. There's an extraordinary number of possibilities in this realm of mathematics and they all begin with asking simple questions that begin to unravel the mysteries of the objects we study. 

 

 

Meet Minwoo Bae!

Meet one of our graduate students and summer research interns, Minwoo Bae! 
--

This Summer I am going to continue the work on developing algorithms to solve computational problems in the field of Mathematical Neuroscience under the supervision of Professor Amarasingham. His laboratory is currently engaged in the development and application of tools for inferring neuronal connectivity maps from extracellular spike data obtained from electrophysiological brain recordings in in vivo conditions. This is in collaboration with G. Buzsaki’s experimental lab at NYU. There are many mathematical challenges, ranging from the development of biophysical models to the development of nonparametric spike train analysis tools. Regarding the latter, some of the major obstacles are computational. A theory is in place for performing connectivity inference, drawing from previous tools developed in the laboratory, but at current data scales the computational costs are prohibitive. My summer research aims for developing algorithms to accelerate these computations. There are two principal approaches I will pursue. The first will involve accelerating the computation of distributions  of sums of random variables, in the style of the fast Fourier transform (FFT), and related tools. The challenge is accommodating nontrivial dependency structures (expressed as graphs; so-called “graphical models”) among these random variables. I will research approaches to handling these elaborations. A second approach is to use asymptotic approximations. I will research the literature to see what bounds are available, adapting them as necessary, to justify and combine asymptotic approximations. I will apply the ideas developed in these investigations to in vivo neurophysiology data, in the context of the laboratory’s other work. 

Since 2011, I had been working as a software developer in Manhattan. Since I designed and developed several web applications for a HIV research team, I naturally gained interest in how a disease is transmitted though a network. In 2014, I had the honor of being selected as Young Talent in the Field of Software by the South Korean government, which provided me with a fund for advanced study of mathematics and computer science. I used the fund for some graduate-level coursework in computer science to study random processes on a network. During this part-time student experience, I realized that without the advanced mathematical foundation, it would be very difficult to proceed much further in this kind of studies. This led to my decision to fully return to school to pursue studying Mathematics since 2015. Now in 2017, I am very excited by the fact that it is possible to tackle many technical challenges ranging from biology to artificial intelligence by using Mathematical concepts and techniques. This why I am passionate about Mathematics.

 

Meet Julia Saccamano!

Meet one of our undergraduate students and summer research interns, Julia Sacamano! 
--

Over the summer I will be studying Game Theory under the direction of Professor Akin. I will be using my experience with probability theory and linear algebra to understand the nature of games. The theory, first introduced by mathematician John von Neumann and economist Oskar Morgenstern in the 1940s, is the branch of mathematics which addresses situations in which there is conflict, competition, and potential strategies between rational thinking human ‘players’. We can see its uses in economics, politics, philosophy, and psychology. I will be focusing the majority of my studies on both two-person zero-sum games and two-person nonzero-sum games. Through these studies I will be taking a look at topics such as utility theory, payoff matrices, and Nash equilibrium in hopes of better understanding how to discern ‘solutions’ to games or predict potential outcomes of these situations. I will be reading Game Theory and Strategy by Philip Straffin, The Evolution of Cooperation by Robert Axelrod, and Game Theory: A Nontechnical Introduction by CCNY Emeritus Professor Morton D. Davis.

I will be using this knowledge to further examine the classic paradox of the Prisoner’s Dilemma which was originally proposed by Merrill Flood and Melvin Dresher as well as the iterated (repeated play) version. I am an Applied Mathematics major and will begin my Junior year in the fall. I hope to relate my studies in game theory to classes I've taken at CCNY, such as Probability Theory, Linear Algebra, Philosophy, and Economics, as well as things in everyday life. I love challenges, puzzles, and problems that come with studying math and am forever chasing the feeling of satisfaction when I find a solution and truly understand a topic. I love the universal and dynamic aspects of math and how it is the same in every country around the world, how it is used in every facet of life, and how its presence might not be noticed a first glance.