**Thursdays, 4:30-5:30pm, Hunter East 920 or GC Room 6496 (currently hosted remotely; please email vrmartinez-at-hunter-dot-cuny-dot-edu for password)**

He was a fine applied mathematician.

In the spirit of John's open-mindedness and willingness to foster and maintain a diverse community of mathematics, HCAM hosts speakers across a wide range of disciplines, from both academia and industry. HCAM also showcases the work of rising graduates of the Applied Math MA program at Hunter and regularly hosts Applied Math MA alumni to share their post-graduate experiences with current students. If you are interested in giving a talk at this seminar, please contact me at vrmartinez-at-hunter-dot-cuny-dot-edu. Please note that this seminar is partially shared with the Nonlinear Analysis and PDEs seminar at the Graduate Center, so that some talks are hosted there instead.

**Fall 2020 Schedule**

**October 1, 2020, Zoom**

Yu-Min Chung (University of North Carolina-Greensboro)

*What is the shape of your data? An Introduction to Topological Data Analysis and its Application to Data Sciences*

Topological Data Analysis is a relatively young field in algebraic topology. Tools from computational topology, in particular persistent homology, have proven successful in many scientific disciplines. Persistence diagrams, a typical way to study persistent homology, contain fruitful information about the underlying objects. Extracting features from persistence diagrams is one of the major research areas in this field. In this talk, we will give a brief introduction to persistent homology, and we will demonstrate methods we propose to summarize persistence diagrams. Applications to various datasets from cell biology, medical imaging, physiology, and climatology, will be presented to illustrate the methods. This talk is designed for a general audience in mathematics. No prior knowledge in algebraic topology is required.

**October 8, 2020, Zoom**

Luan Hoang (Texas Tech University)

*Long-time asymptotic expansions for viscous incompressible fluid flows*

We study the long-time dynamics of viscous incompressible fluids for both Eulerian and Lagrangian descriptions. For the Eulerian description, a solution of the Navier-Stokes equations with a potential or time-decaying body force admits a Foias-Saut asymptotic expansion as time tends to infinity. This expansion provides very precise asymptotic approximations of the solution in terms of polynomial and exponential functions. For the Lagrangian description, we prove that the trajectories of the fluid particles also have similar asymptotic expansions. This is established by studying the system of nonlinear ordinary differential equations relating the Lagrangian trajectories to the solutions of the Navier-Stokes equations.

**October 15, 2020, Zoom**
(Recording)

Tural Sadigov (Hamilton College)

*Support Vector Machines: Overview and Applications*

In this talk, we review the main idea behind statistical (machine) learning and focus on binary classification. We define the problem of classification and introduce the maximal margin classifier, support vector classifier, and, eventually, support vector machines. We formulate optimization problems for the maximization of the margin and apply the algorithms to simulated and real datasets.

**October 22, 2020, Zoom**

Deniz Bilman (University of Cincinnati)

What do Riemann-Hilbert problems tell us about nonlinear waves?*
*

Riemann-Hilbert problems provide a powerful analytical tool to study various problems in pure and applied mathematics. In particular, they provide analogues of integral representations for solutions of integrable nonlinear wave equations (e.g. the Korteweg-de Vries equation), from which we can extract detailed information about the wave field with the aid of nonlinear asymptotic analysis methods. This framework leads also to a powerful method for numerical solution of the Cauchy problem. In this talk, I will describe the role of Riemann-Hilbert problems in studying solutions of nonlinear wave equations and discuss recent results obtained using this approach. One example will be on formation of rogue waves, which are large disturbances of the sea surface that appear out of nowhere and disappear just as suddenly.

**October 29, 2020, Zoom**

Angeline Aguinaldo (University of Maryland-College Park)

*
Category Theory for Software Modeling and Design
*

This talk will discuss category theory and its potential applications to software modeling. Category theory provides a convenient algebraic system for encoding processes and their composition. This may be useful in precisely and intuitively characterizing the modularity and interoperability of software programs and systems. This talk will discuss an application of category theory to robot manipulator programming.

**November 5, 2020, Zoom**

Pawan Patel (Millenium Management)

**November 12, 2020, Zoom**

Victor Ginting (University of Wyoming-Laramie)

**November 19, 2020, Zoom**

Jeungeun Park (University of Cincinnati)

*Collective behavior in bacterial chemotaxis
*

**December 3, 2020, Zoom**

Jared Berman (Spark Foundry, Applied Math MA Alum 2019, Adviser: Vincent Martinez)

**Past Seminars**