Hunter College Applied Mathematics (HCAM) Seminar

Thursdays, 4:15-5:15pm, Hunter East 920 or GC Room 6496

HCAM was initiated by the late John Arthur Loustau, a former professor of the Mathematics and Statistics Department here at Hunter, with his then post-doc Emmanuel Asante-Asamani in 2018. John had an eclectic mix of mathematical interests, each of which he pursued with gusto and depth. In a career spanning nearly 50 years, he began his journey in Commutative Algebra, transitioned afterwards to Computer Science, then Numerical Analysis, and eventually into Mathematical Biology. John recounted once a vacation he took with his family to Reno long ago. His father, a hardware merchant who also did plumbing and electric work, had taken him to the School of Mining Engineering at University of Nevada and told John that he had once dreamt of enrolling there when he was younger. Nevertheless, as John fondly recalled, 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.

Spring 2020 Schedule

February 13, 2020, GC Room 6496

Mimi Dai (University of Illinois-Chicago)

Wild solutions for MHD models

We will discuss some wild behaviors exhibited by weak solutions of the magnetohydrodynamics with Hall effect and one of its limit cases. It includes lack of uniqueness of weak solutions in the Leray-Hopf class and construction of finite energy weak solutions that do not conserve magnetic helicity and magnetic energy.


February 20, 2020, HE 930

Cecilia Mondaini (Drexel University)

Rates of convergence to statistical equilibrium: a general approach and applications

This talk focuses on the study of convergence/mixing rates for stochastic dynamical systems towards statistical equilibrium. Our approach uses the weak Harris theorem combined with a generalized coupling technique to obtain such rates for infinite-dimensional stochastic systems in a suitable Wasserstein distance. In particular, we show two scenarios where this approach is applied in the context of stochastic fluid flows. First, to show that Markov kernels constructed from a suitable numerical discretization of the 2D stochastic Navier-Stokes equations converge towards the invariant measure of the continuous system. This depends crucially on a spectral gap result for the discrete Markov kernel that is independent of the level of discretization. Second, to approximate the posterior measure obtained via a Bayesian approach to inverse PDE problems, particularly when applied to advection-diffusion type PDEs. In this latter case, the Markov transition kernel is constructed with an exact preconditioned Hamiltonian Monte Carlo algorithm in infinite dimensions. A rigorous proof of mixing rates for such algorithm was an open problem until quite recently. Our approach provides an alternative and flexible methodology to establish mixing rates for other Markov Chain Monte Carlo algorithms. This is a joint work with Nathan Glatt-Holtz (Tulane U).


March 19, 2020, Zoom

Na Cai (Hunter Applied Math MA student, Adviser: Emmanuel Asante-Asamani)

An Exponential Time Differencing-Real Distinct Poles Scheme for Solving Reaction Diffusion Equations

We focus on solving a non-homogeneous ordinary differential equation with initial conditions. First, we find a one-step solution using the Exponential Time Differencing (ETD) Scheme. Then we use the Real Distinct Poles (RDP) Scheme to deal with the exponential part of the solution. This results in the ETD-RDP Scheme, which provides low computational cost for solving ODEs without sacrificing efficiency.


April 23, 2020, Zoom

Michael Barile (Yardi Systems, Applied Math MA Alum 2019, Adviser: John Loustau and Emmanuel Asante-Asamani)

RealTech for Investment Management

The presenter will discuss working at Yardi Systems, a leading property management software company, in the Investment Management department. He will present an overview of the core functionality of the IM module, and describe the basic features that clients typically use to automate accounting activity, track transactions and measure investment performance. Additionally, he will discuss where skills developed in studying math have been useful in the workplace, as well as related areas that math students intending to work in the Fin/RealTech industries should spend some time developing before graduation.


April 30, 2020, Zoom

Padi Fuster Aguilera (Tulane University)

A PDE model for chemotaxis with logistic growth

Chemotaxis is the movement of an organism in response to a chemical stimulus and is a fundamental mechanism of motion for many organisms in nature. In this talk we will explain how chemotaxis can be modeled as a partial differential equation (PDE), as well as announce some recent results for a Keller-Segel-type chemotaxis model that accounts for logistic growth. This is joint work with Vincent Martinez and Kun Zhao.


May 7, 2020, Zoom

Michael Y. Levy (St. John's University)

Dependence Structure of Hyperball Distribution

The purpose of this seminar is to describe the dependence structure of a multivariate joint distribution obtained from a Cartesian product of finitely many hyperballs of a given dimension. The method I use to obtain the dependence structure is to apply Sklar’s theorem. The results include the explicit calculation univariate marginal cumulative distribution functions of certain random variables and its copula, which links the random variables. The copula of the hyperball distribution is interpreted within the context of the unique independence copula. The univariate marginal cumulative distribution functions of the hyperball distribution is a transcendental equation interpreted within the context of classical and quantum mechanics. The univariate marginal distribution functions of the hyperball distribution relates to Kepler’s equation. I interpret my results by comparing the trajectories that I observe in the philosophy of political thought with the trajectories that I observe in celestial mechanics and quantum mechanics. I assert that because of the inherent indeterminism and uncertainty in political systems, the dynamics will behave more similarly to quantum systems and statistical systems than celestial systems. While this seminar offers a complicated description of independent random variables distributed on a hyperball; I anticipate that making these results patent in this manner will allow for the application of Sklars theorem on more complicated product manifolds.


May 14, 2020, Zoom

Say Park (Hunter Applied Math MA student, Adviser: Emmanuel Asante-Asamani)

The role of cell geometry in steady-state bleb size and shape

Dictyostelium discoideum is a soil-living amoeba which can move by making pressure driven protrusions of its plasma membrane, referred to as blebs. This eukaryotic microbe is a model organism for biomedical research as its fundamental cellular processes and molecular genetic pathways are similar to cells linked to human disease and cancer cells. We study specifically its motility in response to a chemoattractant (chemotaxis), as the process is an essential early event in metastasis of cancer cells. Chemotaxing cells are typically polarized, adopting a plethora of non-symmetric morphologies. Yet, not much is known about the influence of local cell geometry on the steady-state size and shape of blebs. Existing mathematical models of bleb expansion use prototypical spherical geometries to represent the cell boundary, thus easing the burden of numerical computations. As a result, the simulated bleb expansion process is insensitive to membrane curvature. In this work, we develop a curvature dependent mathematical model to predict terminal bleb size via a variational approach. We demonstrate for the first time the use of B-splines in discretizing the resulting functional, thereby simplifying its application to realistic cell geometries. Our model reproduces known effects of membrane tension, linker tension and hydrostatic pressure on terminal bleb size. The model along with data obtained from D.discoideum cells show that blebs are dependent on local cell geometry and preferentially terminate in negative curvature regions.


May 21, 2020, Zoom

Paul Popa (Hunter Applied Math MA student, Adviser: Vincent Martinez)

Conditioned Ensemble Kalman Filters for Data Assimilation with Noisy Observations

The Lorenz equations of 1963, originally derived as a simplified model of atmosphere dynamics, are a classical example of a chaotic dynamical system. Assuming that the true state of our system is given by the Lorenz equations, we seek to improve forecasts on its future state, given noisy, partial observations at the current time by leveraging apriori knowledge about the true state. In particular, we modify the Ensemble Kalman Filter (EnKF) conditioned to this apriori knowledge in three different ways. Numerical studies are carried out to test whether or not these modifications increase the accuracy of forecasts relative to the standard EnKF algorithm. The results of the studies are presented.


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