Georgia Institute of Technology College of Sciences

In this talk I first wish to review my work with Balakrishnan and Muller, giving an algorithm for finding integral points on curves under certain (strong) assumptions. The main ingredients are the theory of p-adic height pairings and the theory of p-adic metrized line bundles. I will then explain a new proof of the main result using a p-adic version of Zhang's adelic metrics, and a third proof which only uses the metric at one prime p. At the same time I will attempt to explain why I think this last proof is interesting, being an indication that there may be new p-adic methods for finding integral points.

When we get to the point of including the huge and relevant experience of finite element fluid modeling collected in over 25 years of experience in the treatment of cardiovascular diseases, the risk of getting “lost in translation” is real. The most important issues are the reliability that we need to guarantee to provide a trustworthy decision support to clinicians; the efficiency we need to guarantee to fit into the demand coming from a large volume of patients in Computer Aided Clinical Trials as well as short timelines required by special circumstances (emergency) in Surgical Planning. In this talk, we will report on some recent activities taken at Emory to make this transition possible. Reliability requirements call for an appropriate integration of measurements and numerical models, as well as for uncertainty quantification. In particular, image and data processing are critical to feeding mathematical models. However, there are several challenges still open, e.g. in simulating blood flow in patient-specific arteries after stent deployment; or in assessing the correct boundary data set to be prescribed in complex vascular districts. The gap between theory, in this case, is apparent and good simulation and assimilation practices in finite elements for clinical hemodynamics need to be drawn. The talk will cover these topics. For computational efficiency, we will cover some numerical techniques currently in use for coronary blood flow, like the Hierarchical Model Reduction or efficient methods for coping with turbulence in aortic flows. As Clinical Trials are currently one of the most important sources of information for medical research and practice, we envision that the suitable achievement of reliability and efficiency requirements will make Computer Aided Clinical Trials (specifically with a strong Finite-Elements-in-Fluids component) an important source of information with a significant impact on the quality of healthcare. This is a joint work with the scholars and students of the Emory Center for Mathematics and Computing in Medicine (E(CM)2), the Emory Biomech Core Lab (Don Giddens and Habib Samady), the Beta-Lab at the University of Pavia (F. Auricchio ). This work is supported by the US National Science Foundation, Projects DMS 1419060, 1412963 1620406, Fondazione Cariplo, Abbott Vascular Inc., and the XSEDE Consortium.

Clash with "The IDEaS Seminar Series": the talk of Ravi Kannan at 3pm on "Topic Modeling: Proof to Practice" might of interest (Location: TSRB Auditorium) -- Topic Modeling is used in a variety of contexts. This talk will outline from first principles the problem, and the well-known Latent Dirichlet Al-location (LDA) model before moving to the main focus of the talk: Recent algorithms to solve the model-learning problem with provable worst-case error and time guarantees. We present a new algorithm which enjoys both provable guarantees as well performance to scale on corpora with billions of words on a single box. Besides corpus size, a second challenge is the growth in the number of topics. We address this with a new model in which topics lie on low-dimensional faces of the topic simplex rather than just vertices.