**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** (Recording)

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)

*
Covariance Estimators, Portfolio Theory, and RMT
*

Estimation of true covariance matrices in real world predictive modelling is one of the key challenges to accurate modelling. It's importance arises in a range of real world applications: from election modelling, to numerous applications in Machine Learning prediction, and even Portfolio Theory for stock trading. In this talk we'll review the basics of covariance matrices and their importance in portfolio theory. We'll discuss some common methods for covariance estimation and where Random Matrix Theory can help.

**November 12, 2020, Zoom**

Victor Ginting (University of Wyoming-Laramie)

*A Petrov-Galerkin FEM for solving second-order IVP and its a
posteriori error estimation*

We present a Petrov-Galerkin FEM for solving second-order IVPs from which a class of time integration schemes can be derived. Several standard techniques can also be recovered from this variational setting. The key in the derivation is the choice of finite element spaces and the numerical integration techniques utilized to calculate the functional in the variational equation. We discuss an adjoint-based a posteriori error estimate of the approximation. Several numerical examples are given to illustrate the performance of the resulting schemes and the corresponding error estimate.

**November 19, 2020, Zoom**
(Recording)

Jeungeun Park (University of Cincinnati)

*Collective behavior in bacterial chemotaxis
*

The preferred movement of a bacterium along the gradient of chemical substances is called chemotaxis. Bacterial chemotaxis has been widely studied from both the microscopic and macroscopic points of view; in particular, it is important to connect these different levels of description to understand better a realistic model of bacterial chemotaxis. In this talk, we analyze the collective motion of a population of Escherichia coli bacteria in response to multiple external stimuli by incorporating the signaling machinery of individual cells. Motivated by some experiments from the literature, we consider two chemical stimuli and show that the collective motion of bacteria depends on the ratio of their corresponding chemoreceptors. Furthermore, we examine our theory with Monte-Carlo agent-based simulations, which qualitatively captures the experimental observation from the literature. This is joint work with Zahra Aminzare.

**December 3, 2020, Zoom**
(Recording)
(Audio Transcript)

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

*Efficient Model Building with Python
*

When building a machine learning model for predictions, a part of the canonical workflow is to try out many combinations of data pre-processing transformations on different models and hyperparameter sets for which, with the objective of shortlisting the best combinations. Luckily we don't have to reinvent the wheel to accomplish this. Scikit-learn provides utilities to automate the trying-out process. Moreover, the interfaces follow a clean API very closely, making the code logic very easy to follow, and therefore making the code very practical. I've found that this greatly enhances the model building process by reducing the amount of time spent on tedium.

**December 10, 2020, Zoom**

Kenneth Brown (Hunter College, Applied Math MA Thesis, Adviser: Vincent Martinez)

*
Higher-order synchronization for a data assimilation algorithm with nodal value observables
*

The analytical study of a nudging algorithm in the infinite-dimensional setting of PDEs was initially carried out by Azouani, Olson, and Titi for the two-dimensional (2D) incompressible Navier-Stokes equations (NSE). In their seminal work, convergence of the approximating solution to the true solution was shown to take place at least in the topology of the Sobolev space H1 . However, their analysis did not treat uniform convergence or higher-order Sobolev spaces. This talk will discuss convergence in stronger Sobolev topologies, including the uniform topology, of this nudging based algorithm for data assimilation in the context of the 2D NSE when observations of the flow are given as nodal values of the velocity field.

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**Past Seminars**