Erik Christensen, University of Copenhagen
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A question on the domain of definition for a spectral triple has caused an interest in the Schur product of operator valued matrices. It then turned out that this is a completely bounded bilinear operator, which is a special case of the Hadamard product in a crossed product of a C*-algebra by a discrete group. This observation lead to an extension of the concept named rapid decay from group algebras to crossed products.

Stephen Taylor, New Jersey Institute of Technology
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In contrast with classic centralized risk sharing, a novel peer-to-peer risk sharing framework is proposed. The presented framework aims to devise a risk allocation mechanism that is structurally decentralized, Pareto optimal, and mathematically fair. An explicit form for the pool allocation ratio matrix is derived, and convex programming techniques are applied to determine the optimal pooling mechanism in a constrained variance reduction setting. A tiered hierarchical generalization is also constructed to improve computational efficiency. As an illustration, these techniques are applied to a flood risk pooling example. It is shown that peer-to-peer risk sharing techniques provide an economically viable alternative to traditional flood policies.

Yu-Min Chung, University of North Carolina at Greensboro
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Topological data analysis (TDA) is a rising field at the intersection of Mathematics, Statistics, and Machine Learning. Techniques from this field have proven successful in analyzing a variety of scientific problems and datasets. The main driving force in TDA is the development of persistent homology, which studies the intrinsic shape of data. Persistent homology is a mathematical construction from the field of algebraic topology, and in practice, persistence diagrams (summaries of the persistent homology) yield topological information. However, the space of persistence diagrams is notoriously difficult to work with (for instance, the mean of persistence diagrams may not be unique). Transforming persistence diagrams into vectors or functions while preserving their critical information is one of the major research areas in TDA. In this talk, we will give a brief introduction to persistent homology, and we will demonstrate methods we propose to summarize persistence diagrams. Applications to various datasets from cell biology, medical imaging, physiology, and climatology, will be presented to illustrate the methods. This talk is designed for a general audience in mathematics. No prior knowledge in algebraic topology is required.

Ian Runnels, University of Virginia
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Ben Hayes, University of Virginia
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I’ll discuss joint work with Lewis Bowen and Frank Lin. In it, we generalize the classical Multiplicative Ergodic Theorem (MET) of Oseledets to cocycles taking values in a semi-finite von Neumann algebra. In contrast with previous work, the limiting operator we get is typically not the exponential of a compact operator and often has diffuse spectrum.

Stefan Czimek, Brown University
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Penghang Yin, University at Albany
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Michael Mihalik, Vanderbilt University
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Carina Curto, Pennsylvania State University
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(Contact person: Ioana Suvaina)

Sam Mellick, ENS de Lyon
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Alexandru Ionescu, Princeton University
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Anna Marie Bohmann, Vanderbilt University
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David Womble, Oak Ridge National Laboratory
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Sayan Das, UC Riverside
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Ling Long, Louisiana State University
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Emily Stark, Wesleyan University
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Liviu Păunescu, Institute of Mathematics of the Romanian Academy
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Igor Kukavica, University of Southern California
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Rachel, Norton, Fitchburg State University
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Wei-Lun Tsai, University of Virginia
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Bernhard Heim, RWTH Aachen University
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Georgios Moschidis, University of California Berkeley
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Alex Margolis, Vanderbilt University
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Soon-Yi Kang, Kangwon National University
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Michael Landry, Washington University in St. Louis
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Cain Edie-Michell, Vanderbilt University
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Mahya Ghandehari, University of Delaware
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Caroline Turnage-Butterbaugh, Carleton College
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