**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 2021 Schedule**

**September 30 Zoom**
(Recording)

Sushovan Mahji (UC Berkeley, School of Information)

*
A Taste of Topological Data Analysis (TDA): Reconstruction of Shapes
*

Topological data analysis (TDA) is a growing field of study that helps address data analysis questions. TDA is deemed a better alternative to traditional statistical approaches when the data inherit a topological and geometric structure. Most of the modern technologies at our service rely on geometric shapes in some way or the other, be it the Google Maps showing you the fastest route to your destination or the 3D printer on your desk creating an exact replica of a relic---shapes are being repeatedly sampled, reconstructed, and compared by intelligent machines. In this talk, we will catch a glimpse of how some of the famous topological concepts---like persistent homology, Vietoris-Rips and Cech complexes, Nerve Lemma, etc---lend themselves well to the reconstruction of shapes from a noisy sample.

**October 7 Zoom**
(Recording)

Yassin Chandran (CUNY Graduate Center, Department of Mathematics)

*
Automorphisms of the k-curve graph
*

Our main objective is to study symmetry groups of surfaces which are called mapping class groups. To any surface, we can construct a graph whose vertices correspond to certain equivalence classes of simple closed curves and whose edges are drawn whenever the associated curves can be *realized disjointly*. These graphs are known as curve graphs. Nikolai Ivanov showed that the automorphism group of the curve graph is exactly the mapping class group of the surface, which led him to propose the following meta-conjecture: Any *sufficiently rich* graph associated to a surface must have the same symmetry group as the surface. In this talk, we'll discuss a large class of graphs, known as *k*-curve graphs, associated to the surface, for which Ivanov's meta-conjecture holds true. This is joint work with S. Agrawal, T. Aougab, M. Loving, J. R. Oakley, R. Shapiro, and Y. Xiao.

**October 14 Zoom**
(Recording)

Stephen W. Morris (University of Toronto, Department of Physics)

*
Consider the Icicle
*

Icicles are harmless and picturesque winter phenomena, familiar to anyone who lives in a cold climate. The shape of an icicle emerges from a subtle feedback between ice formation, which is controlled by the release of latent heat, and the flow of water over the evolving shape. The water flow, in turn, determines how the heat flows. The air around the icicle is also flowing, and all forms of heat transfer are active in the air. Ideal icicles are predicted to have a universal "platonic" shape, independent of growing conditions. In addition, many natural icicles exhibit a ripply shape, which is the result of a morphological instability. The wavelength of the ripples is also remarkably independent of the growing conditions. Similar shape and ripple phenomena are also observed on stalactites, although certain details of their formation differ. We built a laboratory icicle growing machine to explore icicle physics. We learned what it takes to make a platonic icicle and the surprising origin of the ripples.

**October 21 Zoom**
(Recording)

Vincent Martinez (CUNY Hunter, Department of Mathematics and Statistics)

*
Parameter estimation for nonlinear dynamical systems
*

An inherent problem in the modeling of natural phenomena is in obtaining accurate estimation of the parameters in the system. For instance, when studying fluid motion, the Navier-Stokes equations provides a model for a viscous, incompressible fluid flow in the form of a partial differential equation for the velocity of the fluid. The material parameter in this system is the fluid's kinematic viscosity. Typically, the value of this parameter is determined empirically by experiments or statistically by data, and its exact value depends on the particular fluid itself. This poses the following fundamental mathematical question: Is it possible to recover the true value of the viscosity by having only partial information about the motion of the velocity itself? In other words, under what scenarios is it mathematically possible for one to recover this unknown viscosity? In this talk, we discuss a dynamic algorithm that allows one to learn the true values of parameters in certain nonlinear dynamical systems as partial observations are made on the system.

**October 28 Zoom**
(Recording)

Nga Yu Lo (Macaulay Honors College at Hunter, Mathematics and Computer Science Major)

*
Evaluating Object Recognition Behavioral Consistency on Out-of-Distribution Stimuli
*

State-of-the-art artificial neural networks (ANN) trained on ImageNet are known for their top performance on object recognition tasks. They are the best model of the primate ventral stream with moderate success at explaining neural activities as well as visual behavior. To an ANN trained on object recognition, an out-of-distribution (o.o.d.) stimulus is an image with features that differs drastically from the train dataset and usually reduces a model's object recognition performance. Geirhos et al (2020) shows that models are little above chance at predicting human behavior on o.o.d. stimuli. With a dataset consisting of 16 categories and 3 o.o.d. domains, they measure agreement between model and human responses at a visual classification task, using a word association to extract behavioral choices from Imagenet trained models. We find, however, that using an image-level discriminability metric (Rajalingham, Issa et al, 2018) and training a logistic regression model, ANNs have a higher behavior consistency than reported in Geirhos et al. With different ANN models varying in human behavior consistency, these results imply the need to integrate multiple behavioral benchmarks in a unified manner to enable comparisons of models of the human ventral stream. This is joint work with Tiago Marques and James DiCarlo at M.I.T.

**November 4 Zoom**
(Recording)

Yuan Pei (Western Washington University, Department of Mathematics)

*
Velocity-vorticity-Voigt model for PDEs in fluid dynamics
*

In this talk, we propose the so-called velocity-vorticity-Voigt (VVV) model for the Navier-Stokes system as well as the the Boussinesq equations, both in three dimension. We briefly introduce the two fundamental models in fluid dynamics, and the Voigt regularization. Then, we outline the back- ground and motivation of the model. In our work, we add a Voigt regularization term only to the momentum equation in velocity-vorticity formu- lation without regularizing the vorticity. We prove global well-posedness and regularity of this model along with an energy identity. We also show convergence of the model's velocity and vorticity to their counterparts in the 3D Navier-Stokes equations as the Voigt modeling parameter tends to zero. Similar discussion will be given for the Boussinesq system with thermal fluctuation. Part of the work is jointly with Adam Larios at University of Nebraska-Lincoln and Leo Rebholz at Clemson University.

**November 11 Zoom**
(Recording)

Sathyanarayanan Chandramouli (Florida State University, Department of Mathematics)

*
Theoretical characterization of viscous conduit breathers
*

The spatio-temporal evolution of the circular interface between two miscible fluids of high viscosity contrast (a viscous conduit) has proven to be an ideal platform for studying nonlinear dispersive hydrodynamic (DH) excitations. The two-fluid dynamics in the bulk is essentially described by a Stokes flow, while the conduit interface is effectively non-dissipative, thanks to extremely slow rates of mass diffusion. We investigate the existence and characterization of envelope solitary waves (breather solutions) of the conduit equation, a long wavelength, fully nonlinear PDE model of conduit interfacial dynamics. Bright and dark breathers represent a class of fundamental multi-scale, propagating DH excitations. Bright breathers have been obtained numerically and investigated across the entire range of nonlinearity. We propose a three-parameter characterization of these solutions, with a counterintuitive, continuous deformation into the dark breathers across the zero-dispersion line. The talk will highlight the novelties of the numerical scheme used to compute conduit breathers, the identification of universal frameworks to study such solutions, and future applications in internal oceanic waves.

**November 18, 25 (Seminar Break)**

**December 2, Zoom**
(Recording)

Evelyn Lunasin (United States Naval Academy, Department of Mathematics)

*
Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows
*

Optimal stirring for transient mixing is a particularly timely problem and the ability to investigate optimized flows computationally yields both intuitive insights into effective stirring strategies and allows testing of the a priori analysis. The thrust of studies in this direction will be toward determining sharp estimates on the rate of mixing (in terms of the *H*^{-1} mix-norm) and understanding qualitative and quantitative properties of flows that realize those absolute limits.
We consider passive scalar mixing by a prescribed divergence-free velocity vector field in a periodic box and address the following question: Starting from a given initial inhomogeneous distribution of passive tracers, and given a certain energy budget, power budget, or finite palenstrophy budget, what incompressible flow field best mixes the scalarquantity?
We present explicit example demonstrating finite-time perfect mixing when there is finite energy constraint on the stirring flow. On the other hand, we show that finite-time perfect mixing is ruled out in the case of finite palenstrophy. Finally, we show how theorems of transportation distances and rearrangement costs be linked into sharp results for the *H*^{-1} mix-norm with power-constrained flows.
This is joint with Zhi Lin, Alexei Novikov, Anna Mazzucato, and Charlie R. Doering

**December 9, Zoom**
(Recording)

Yu-Min Chung (Research Scientist, Eli Lilly and Company)

*
My transition from academia to industry
*

''Math can do anything'' is a famous quote from one of IBM ads. It is inspiring but I didn't quite understand it when I was a graduate student. I have spent most of my life in academia from a college student to a tenure-track professor studying and researching mathematics, in particular, the applied mathematics. During the time in academia, it is fascinating to witness how mathematics can be applied in other scientific fields. To further explore more possibilities, recently, I have switched my role from a math professor to a research scientist in a pharmaceutical company. In this forum, I wish to share my personal experiences in both academia and industry such as their differences/similarities, interview processes, expectations, and the math that we use. Any questions you may have are particularly welcome.

**December 16 Zoom**
(Recording)

Tom Fleming (Quantitative Analyst, Finance Sector)

*
Ill-posed problems and too many tools: A case study in applied mathematics
*

An applied mathematician often works as a subject matter expert within a broader business organization. As a result, their work can resemble that of a technical consultant; non-technical people realize they have a problem that would benefit from quantitative modeling or analysis, but aren't sure how to frame or even fully describe the problem. It is up to the applied mathematician to not only find or develop techniques to solve the problem, but to figure out what exactly needs to be solved. We will walk through an example from the speaker's experience in finance that demonstrates the difficulty in discovering what the problem actually is, as well as the challenges in choosing among possible techniques for solving it.

**Past Seminars**