Group Meeting
Past Events

Thursday, December 7, 202312:30PM, Warren Weaver Hall 1302
A twopoint boundary value problem from ODEs with algebraic restrictions
Vicente Gomez, Courant InstituteSynopsis:
Describing incompressible fluids necessitates incorporating pressure, however, it is introduced in the equations with a lower differential order compared to velocity. This discrepancy complicates numerical schemes, often requiring additional boundary conditions or different discretization approaches for pressure and velocity.
In this talk we introduce a new formulation for the periodic channel, presenting an unexpectedly simple yet effective solution to resolve the mismatch between pressure and velocity in incompressible fluids. By employing this seemingly unconventional approach, we craft a wellconditioned system that successfully eliminates the traditional mismatch problem. Notably, this method's versatility extends beyond incompressible fluids, applicable to various differentialalgebraic equations, such as inelastic fibers and curlfree fluids

Thursday, November 30, 202312:30PM, Warren Weaver Hall 1302
On flows and diffusions: from manybody FokkerPlanck to stochastic interpolants
Nicholas Boffi, Courant InstituteSynopsis:

Thursday, November 16, 202312:30PM, Warren Weaver Hall 1302
Tensor trains and A spectral approach for learning spatiotemporal neural differential equations
Natalia Hajlasz and Mingtao Xia, Courant InstituteSynopsis:

Thursday, November 9, 202312:30PM, Warren Weaver Hall 1302
Intro to Algorithmic Differentiation and Research Talk
Charles Margossian and Ella King, Flatiron Institute and NYU PhysicsSynopsis:
Charles will give an introduction of algorithmic differentiation, followed by a research talk from Ella.

Thursday, November 2, 202312:30PM, Warren Weaver Hall 1302
Career opportunities and research at PNNL
Tony Chiang, PNNLSynopsis:
In this talk, I will give an overview of PNNL and working at the national laboratory. I will go over our strategic mission at a high level and focus on the work being done in AI/ML through the Mathematics in Artificial Reasoning in Sciences (MARS) laboratory initiative. I will showcase some of the research that my team has done under the initiative.

Thursday, October 26, 202312:30PM, Warren Weaver Hall 1302
New faculty introductions
Yanjun Han, Alan Kaptanoglu, HauTieng Wu, Courant InstituteSynopsis:
New Courant faculty working on applied and computational mathematics will introduce themselves and their research to the group.

Thursday, October 19, 202312:30PM, Warren Weaver Hall 1302
Faculty talk and graphic design tools for figuremaking
Leif Ristroph, Georg Stadler, Mariya Savinov, New York UniversitySynopsis:
Prof. Leif Ristroph will introduce his research group and current direction. After, there will be a series of short 510 minute demos of useful graphic design tools for figuremaking, including a Tikz demo from Prof. Georg Stadler and an Adobe Illustrator demo from Mariya Savinov

Thursday, October 12, 202312:30PM, Warren Weaver Hall 1302
Applications of and outlook for code generating large language models in chemistry
Glen Hocky, New York University (Chemistry Dept)Synopsis:

Thursday, October 5, 202312:30PM, Warren Weaver Hall 1302
Julia Tutorial & Short Faculty Talks
Praharsh Suryadevara, Edwin Gerber, Shafer Smith, Courant InstituteSynopsis:
Praharsh will give a Julia tutorial with demos to demonstrate its use and benefits. Then, Ed and Shafer will give short 1520 min talks introducing their research groups and current direction.

Thursday, September 28, 202312:30PM, Warren Weaver Hall 1302
Minifestival of 4th years
Mariya Savinov, Olivia Pomerenk, Ryan Du, Paul Beckman, Courant InstituteSynopsis:
This is a minifestival of short, 1015 minute presentations by current 4th years working in applied and computational mathematics at Courant.
Mariya will discuss their work with Prof. Alex Mogilner on the modeling and simulation of various cell skeleton structures and their dynamics. They will outline two of their published works: the first on sizedependent periodic contractile dynamics of cell extracts in water droplets, and the second on how friction can robustly control in vitro actomyosin contraction. Finally, Mariya will introduce ongoing research in which they utilize the immersed boundary method to investigate the dynamics of stress fibers.
Olivia will talk about her work with Leif Ristroph on the existence and stability of equilibria of freefalling thin flat plates. She will first prove the existence of a unique equilibrium gliding mode for any choice of physical properties of the plate, and then explore the stability of such equilibria using linear stability analysis. She will conclude by proposing a new flight mode in addition to those characterized in previous literature, and show some preliminary experimental demonstrations of its existence.
Ryan will show simulations of a balanced model of the ocean. At the scale of O(110 km), the ocean flow exhibits statistical asymmetries because of the abundance of fronts at that scale. The balanced model is a reducedorder model from the full fluids equation that can capture these statistical asymmetries and the growth of fronts.
Paul will discuss ongoing work with Mike O’Neil on numerical methods for elliptic PDEs with random boundary data. In the case where the boundary data is a Gaussian process, we will construct boundary integral equation representations of the covariance of the solution, and apply these methods to build statistical models of experimental data in acoustic and electromagnetic scattering problems.

Thursday, September 21, 202312:30PM, Warren Weaver Hall 1302
Short Courant Faculty Talks
Esteban Tabak, Charles Peskin, Leif Ristroph, Courant InstituteSynopsis:
A subset of MSG faculty will each introduce their research group and current direction. These short talks are aimed to be broadly accessible to those interested in applied and computational mathematics, showcasing current research being done at Courant.

Thursday, September 14, 202312:30PM, Warren Weaver Hall 1302
EcoEvolutionary Dynamics of Populations in Fluctuating Environments
Mauro Mobilia, Professor of Applied Mathematics, University of LeedsSynopsis:
Environmental variability greatly influences how the size and composition of a population evolve. In microbial communities, variations of the composition and size of the population, i.e. their ecoevolutionary dynamics, are key to understand the mechanisms of antimicrobial resistance, and may lead to population bottlenecks, where new colonies consisting of few individuals are prone to fluctuations. How the composition and size of these communities evolve is often interdependent, and demographic fluctuations are generally coupled to environmental variability, often resulting in feedback loops and cooperative behavior.
In this seminar, I will focus on a class of simple and insightful models of populations of fluctuating size whose growth is limited by a binary carrying capacity that endlessly switches between values corresponding to abundant and scarce resources. In these models, the population consists of two strains, one growing faster than the other, that compete under various scenarios. In the basic model, the competition is only for the same resources, and one classically expects that the faster strain always prevails (exclusion principle). Using analytical tools and computational means, I will show how the population size distribution and the strains fixation/extinction probability are dramatically influenced by the coupling of demographic fluctuations and environmental variability. In addition to the basic model with random binary switching, the cases of periodic switching and different forms of environmental noise (of discrete and continuous range) will be mentioned. I will then discuss how these ideas and techniques are being generalized to study the ecoevolutionary dynamics of cooperative antimicrobial resistance, as well as the role of twofold environmental variability (toxin concentration and nutrients abundance) on the longlived coexistence of the strains.
References:
Phys. Rev. Lett.119, 158301 (2017); J. Roy. Soc. Interface 15, 20180343 (2018); Phys. Rev. Lett. 25, 048105 (2020); J. Theor. Biol. 491, 110135 (2020); J. Roy. Soc. Interface 18, 20210613 (2021); Phys. Rev. Research 5, L022004 (2023); bioRxiv 2023.07.06.547929; arXiv:2307.06314