Scientific

Exposure of bacteria to cidal stresses typically select for the emergence of stress-tolerant cells refractory to killing. Stress tolerance has historically been attributed to the regulation of discrete molecular mechanisms, including though not limited to regulating pro-drug activation or pumps abrogating antibiotic accumulation. However, fractions of mycobacterial mutants lacking these molecular mechanisms still maintain the capacity to broadly tolerate stresses. We have sought to understand the nature of stress tolerance through a largely overlooked axis of mycobacterial-environmental interactions, namely microbial biomechanics. We developed Long-Term Time-Lapse Atomic Force Microscopy (LTTL-AFM) to dynamically characterize nanoscale surface mechanical properties that are otherwise unobservable using other established advanced imaging modalities. LTTL-AFM has allowed us to revisit and redefine fundamental biophysical principles underlying critical bacterial cell processes targeted by a variety of cidal stresses and for which no molecular mechanisms have previously been described. I aim to highlighting the disruptive power of LTTL-AFM to revisit dogmas of fundamental cell processes like cell growth, division, and death. Our studies aim to uncover new molecular paradigms for how mycobacteria physically adapt to stress and provide expanded avenues for the development of novel treatments of microbial infections.

An important problem in machine learning and computational statistics is to sample from an intractable target distribution, e.g. to sample or compute functionals (expectations, normalizing constants) of the target distribution. This sampling problem can be cast as the optimization of a dissimilarity functional, seen as a loss, over the space of probability measures. In particular, one can leverage the geometry of Optimal transport and consider Wasserstein gradient flows for the loss functional, that find continuous path of probability distributions decreasing this loss. Different algorithms to approximate the target distribution result from the choice of the loss, a time and space discretization; and results in practice to the simulation of interacting particle systems. Motivated in particular by two machine learning applications, namely bayesian inference and optimization of shallow neural networks, we will present recent convergence results obtained for algorithms derived from Wasserstein gradient flows.

Mathematics can help Art Historians and Art Conservators in studying and understanding art works, their manufacture process and their state of conservation. The presentation will review several instances of such collaborations, explaining the role of mathematics in each instance, and illustrating the approach with extensive documentation of the art works.

Speaker Biography

Ingrid Daubechies is a Belgian Physicist and Mathematician, one of the leaders in the area of wavelets, a part of applied harmonic analysis. Wavelets are widely used in data compression and image encoding. Indeed, a wavelet pioneered by Daubechies is the basis of the standard for digital cinema. Ingrid Daubechies has held positions at the Free University in Brussels, Princeton University, and is currently James B. Duke Professor at Duke University. She is a Member of the National Academy of Sciences and of the National Academy of Engineering and a Fellow of the American Association for the Advancement of Science. Ingrid Daubechies has received many awards including the Leroy P. Steele Prize for Seminal Contribution to Research of the American Mathematical Society.

This talk focuses on the central role played by optimal transport theory in the study of incomplete econometric models. Incomplete econometric models are designed to analyze microeconomic data within the constraints of microeconomic theoretic principles, such as maximization, equilibrium and stability. These models are called incomplete because they do not predict a single distribution for the variables observed in the data. Incompleteness arises because of multiple equilibria in game theoretic solutions, unobserved heterogeneity in choice sets, interval predictions in auctions, and unknown sample selection mechanisms. The problem of confronting the model parameters (possibly infinite dimensional) and the data can be formulated as an optimal transport problem, where the transport cost is some measure of departure from the microeconomic theoretic principles. We will discuss a selection of inference methodologies on the model parameter based on different choices of transport cost, and applications to industrial organization, consumer demand theory and network formation.

I will discuss several geometric constraints of the finite-time blowup of smooth solutions of the Navier-Stokes equation in the regularity criteria related to the eigenvalue structure of the strain matrix and to the vorticity direction. These regularity criteria suggest that strain self-amplification via axial compression/planar stretching drives any possible blowup. I will also discuss model equations where this form of blowup does indeed occur.

Speaker Biography:

Evan Miller received his PhD in mathematics from the University of Toronto under the supervision of Prof. Robert McCann in 2019. He was then a postdoc at McMaster University, working with Prof. Eric Sawyer. He was also a visiting postdoc at the Fields Institute in Toronto and the Mathematical Sciences Research Institute in Berkeley for thematic programs in mathematical fluid mechanics. At MSRI, he worked with Prof. Jean-Yves Chemin. Evan is now a PIMS postdoctoral fellow at the University of British Columbia working with Prof. Tai-Peng Tsai and Prof. Stephen Gustafson.