Integrated Calendar

Human exposure to atmospheric aerosols is increasingly recognized as the leading global environmental determinant of health and longevity. However, ground-based monitoring remains sparse in many regions of the world. Deep learning offers immense potential to advance understanding of air quality by leveraging large satellite remote sensing datasets. However, the spatial heterogeneity and autocorrelation of ground-based measurements pose challenges to the training and testing of algorithms for true out of sample prediction. Thus, algorithms benefit from additional process-based constraints from a chemical transport model and targeted ground-based measurements of aerosol chemical composition.  This talk will highlight recent advances in applying deep learning by building on satellite remote sensing, global modeling, and ground-based measurements to improve understanding of air quality and planetary health from global toward urban scales

In this talk, we will demonstrate how the celebrated connection between Ricci curvature, optimal transport, and geometric inequalities such as the Brunn-Minkowski inequality, extends to the setting of general Lagrangians on weighted manifolds. As examples, we will consider classical (mechanical and electromagnetic) Lagrangians on Riemannian manifolds. In particular, we will state a generalization of the horocyclic Brunn-Minkowski inequality to complex hyperbolic space of arbitrary dimension, and a new Brunn-Minkowski inequality for contact magnetic geodesics on odd-dimensional spheres.

Identifying microbial genomic factors that underlie important phenotypes is a key goal of microbiological and microbiome research. Current approaches for this goal, however, cannot tap into the wealth of genomic information in a systematic manner, particularly in microbes that are not well-characterized. I will present a new conceptual and methodological approach for analyzing microbial communities using multi-sample sequence graphs. Our results demonstrate that this approach captures sequence and variant information more accurately than traditional approaches, provides graphs that are more suitable for comparative analyses, and is computationally tractable. I will end by demonstrating an application for predicting gut colonization trajectories of Vancomycin-resistant Enterococcus. Overall, our results underscore the value of graph-based frameworks for comparative metagenomic analyses.

ReLU networks are a standard example of neural networks. We will discuss the expressivity of neural networks, focusing on their depth. The plan is to start with a general introduction and a survey of basic results, including the duality between ReLU networks and a model for constructing polytopes. We will then discuss polytopes and discuss how their properties can help us understand the depth of neural networks. 

Based on joint works with Bakaev, Brunck, Hertrich and Stade.

For diffusive systems (i.e., systems which satisfy Fourier's law or Fick's law) maintained in a non-equiilibrium steady state by contact with two heat baths or two reservoirs, the macroscopic fluctuation theory developed over the last 25 years has become a major tool to calculate the fluctuations  and the large deviation function of the heat or of the particle currents. After a review of the main achievements of the theory, I will try to list some open issues. In particular,  although the theory predicts the same large deviationfunction of the current in all dimensions, numerical calculations exhibit some small discrepancy in space dimension d > 2.This talk will try to explain the origin of these discrepancies.work in collaboration with Thierry Bodineau