Colloquium Series

Fall 2021

All talks are 3:45-4:45 p.m. online at this Google Meet link

• Nov

  18
• Some Applications of Symplectic Geometry

  Clayton Shonkwiler

  Colorado State University

  Location: CH 110 (IN PERSON)

  Time: 03:45 PM

  View Abstract

  Symplectic geometry originally developed as a conceptual framework in which the Hamiltonian formalism for classical mechanics applies. It is also closely related to complex algebraic geometry and has been used and developed in many areas of modern geometry and topology which are seemingly quite far from its roots. In this talk I will introduce some of the fundamental concepts in symplectic geometry, including connections to Archimedes' Theorem, Hamiltonian mechanics, conserved quantities, and the Schur–Horn Theorem, and then highlight some recent applications to polymer physics and signal processing. The latter includes some joint work with Jason Cantarella and Tom Needham.

• Nov

  17
• Supply Chain Game Theory Network Models for Disaster Relief

  Anna Nagurney

  University of Massachusetts, Amherst

  Location: Virtual Talk

  Time: 03:45 PM

  View Abstract

  Game theory is an essential analytical tool for numerous security applications. In this presentation, we demonstrate, through a series of novel network models, how game theory can also assist in disaster preparedness and response of organizations. We describe models that integrate financial and logistical elements and that consist of multiple organizations, freight service providers, and points of demand. The models capture the behavior of decision-makers and yield solutions that help victims while reducing materiel convergence. Case studies on real-life disasters demonstrate the efficacy of the framework and provide managerial insights. In addition, some of our results on blood supply chains and cybersecurity will also be highlighted.

• Nov

  10
• Let’s train more Sherlock Holmes's of and for Data Science: Data Minding before Date Mining

  Xiao-Li Meng

  Harvard University

  Location: Virtual Talk

  Time: 03:45 PM

  View Abstract

  Much of the research and teaching in data science has been on theories and methods for extracting information from data, whether via model fitting in statistical inference or pattern recognitions in machine learning, almost all of which treat data as input. The broader data science ecosystem, however, needs to deal with the entire data life cycle, including the phases that output data. This talk argues that it would benefit (data) science and society if we foster more research and teaching on treating data as products in and of themselves, and accordingly subject them to data minding, a stringent quality inspection process that scrutinizes data conceptualization, data collection, data pre- processing, data curation, and data provenance. Data minding is a demanding process to do well but it is both scientifically necessary and intellectually rewarding, because it essentially entails being the Sherlock Holmes of data science. A collection of articles in a special issue on data science for societies published by Journal of Royal Statistical Society (UK) provides multiple demonstrations of the need for data minding. The talk ends by revealing striking consequences of failing to scrutinize data quality in the context of estimating COVID-19 vaccination uptake, a case of the big data paradox: the bigger the data, the surer we fool ourselves.

• Nov

  03
• RONS: Reduced-order nonlinear solutions for PDEs with conserved quantities

  Mohammad Farazmand

  North Carolina State University

  Location: Virtual Talk

  Time: 03:45 PM

  View Abstract

  Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced solutions depend nonlinearly on time-dependent variables have thus far been derived in an ad hoc manner. I introduce Reduced-order Nonlinear Solutions (RONS): a unified framework for deriving reduced-order models that depend nonlinearly on a set of time-dependent variables. The set of all possible reduced-order solutions are viewed as a manifold immersed in the function space of the PDE. The variables are evolved such that the instantaneous discrepancy between reduced dynamics and the full PDE dynamics is minimized. This results in a set of explicit ordinary differential equations on the tangent bundle of the manifold. In the special case of linear parameter dependence, our reduced equations coincide with the standard Galerkin projection. Furthermore, any number of conserved quantities of the PDE can readily be enforced in our framework. Since RONS does not assume an underlying variational formulation for the PDE, it is applicable to a broad class of problems. I demonstrate its applications on a few examples including the nonlinear Schrodinger equation and Euler's equation for ideal fluids.

• Oct

  27
• Statistical reduced-order models and machine learning-based closure strategies for turbulent dynamical systems

  Di Qi

  Purdue University

  Location: Virtual Talk

  Time: 03:45 PM

  View Abstract

  The capability of using imperfect statistical reduced-order models to capture crucial statistics in complex turbulent systems is investigated. Much simpler and more tractable block-diagonal models are proposed to approximate the complex and high-dimensional turbulent dynamical equations using both parameterization and machine learning strategies. A systematic framework of correcting model errors with empirical information theory is introduced, and optimal model parameters under this unbiased information measure can be achieved in a training phase before the prediction. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the reduced-order model in various dynamical regimes of the flow field with distinct statistical structures. In addition, new machine learning strategies are proposed to learn the expensive unresolved processes directly from data.

• Oct

  13
• Frameworks in motion: theory, design, and fabrication

  Jessica Sidman

  Mount Holyoke College

  Location: Virtual Talk

  Time: 03:45 PM

  View Abstract

  What do your umbrella, a folding gate, and a scissor lift have in common? They are all made of rigid parts attached at joints designed to yield a structure that can move with one degree of freedom and then locked in a rigid state to perform a useful function. In 1981, famed architect Santiago Calatrava wrote a PhD thesis, "Concerning the Foldability of Space Frames," consisting of a systematic exploration of the geometry and design of foldable frameworks. I'll use his thesis as a jumping off point to explore the fundamentals of rigidity theory and share some ongoing work on the design of a tent framework in collaboration with architect Naomi Darling and Mount Holyoke students Sohini Bhatia, Stephanie Einstein, Nana Aba Turkson, and Zainab Umar.