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Title: Mathematical modeling of polymerization processes in physiology Abstract: Polymerization, or aggregation, is essential for many physiological systems. For example, the emergence of a fibrin polymer mesh during the formation of a blood clot is required for a stable clot and long-term, sustained intracellular transport in neurons rely on persistent yet dynamic polymers that comprise the […] |
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"A Tale of Two Cities" is a novel told in three books/parts. Here we describe three projects related both to published work and ongoing pieces: PROJECT 1: In the world of combinatorics, parking functions are combinatorial objects arising from the situation of parking cars under a parking strategy. In this part of the talk, we […] |
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Title: Packing lines, minimizing energy, and applications to communications Speaker: Josiah Park, Department of Mathematics, Texas A&M University Abstract: Structured geometric point sets play important roles in coding theory, mathematical biology, computational chemistry, wireless communications, compressed sensing, and 'big data' applications due to their often desirable statistical properties for measurement and transmission. Best packings of […] |
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The members of the “Invisible College” and the early Royal Society championed an experimental approach to the study of nature as the proper path to the advancement of knowledge and the preservation of civic peace. Mathematics, while admired, was also viewed with suspicion, as potentially dogmatic and coercive. John Wallis, the leading mathematician in the […]
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Title: Randomized Sums of Graph Spectra Abstract: The adjacency matrix of an Erdős-Rényi-Gilbert graph is a random symmetric matrix whose entries are Bernoulli random variables. These entries, modulo the constraints imposed by symmetry, are independent. We aim to understand the asymptotic behavior of randomized sums of the spectra and singular spectra of these matrices. In […] |
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Given a degree d polynomial f(x) in Q, consider the subset S_f of Q consisting of rational numbers t for which the translated polynomial f(x) - t factors completely in Q. For example, if f is linear or quadratic then S_f is always infinite, but if degree of f is at least 3, then interesting […] |
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Title: Shape Optimization: Old and New Speaker: Edouard Oudet, LJK, Université Grenoble Alpes Abstract: We first introduce what is shape Optimization and the most classical problems of the field like the isoperimetric problem, the study of minimal surfaces, the characterization of irrigation networks, etc. In a second step we focus on a more recent question related […] |
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We introduce a family of norms on the space of self-adjoint trace class symmetric tensor power of linear operators acting on an infinite-dimensional Hilbert space. Our technique is to extend to infinite dimension an original and nice idea of a very recent result by K. Aguilar, Á. Chávez, S. R. Garcia and J. Volčič, in […] |
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Title: Data-driven large eddy simulation of atmospheric turbulence Abstract: Over the last few years, machine learning has been critical in science and engineering and emerged as a data-driven turbulence model. However, machine learning depends on training data from previous experiments on turbulent flows. Typically, training data capture only a fraction of the active scales of […] |
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The Mahler measure of a polynomial is the modulus of its leading term multiplied by the moduli of all roots outside the unit circle. The Mahler measure of an algebraic number b, M(b) is the Mahler measure of its minimal polynomial. By a result of Kronecker, an algebraic number b satisfies M(b)=1 if and only […] |
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Title: Decision Problems in Low-Dimensional Topology Speaker: Kate Petersen, Department of Mathematics and Statistics, CSU, University of Minnesota Duluth Abstract: Due to Perelman’s proof of the Geometrization conjecture every closed 3-manifold can be decomposed into geometric pieces. These pieces exhibit one of Thurston’s eight model geometries. This gives rise to the natural question: Given a 3-manifold how (quickly) […] |
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The Human Betterment Foundation was a pro-eugenics think-tank operating in the 1930s and early 1940s out of Pasadena, California. Its aim was to influence public and medical opinion in favor of sterilization of "socially undesirable elements": disabled, poor, and racialized people. Many board members had ties to Caltech, most notably Caltech's then-president Robert Millikan. Upon […]
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Title: Scattering Resonances Through Subwavelength Holes and Their Applications in Imaging and Sensing Abstract: The so-called extraordinary optical transmission (EOT) through metallic nanoholes has triggered extensive research in modern plasmonics and their applications in bio-sensing, imaging, etc. This talk aims to provide quantitative mathematical theories to understand a variety of resonances that induce the EOT […] |
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Title: Using Mutual Information of Hypergraph Compressions for Clustering Abstract: Hypergraphs are often used to represent higher order observed relationships between subjects of study. In particular, the vertices of a hypergraph could represent the basic elements of study, and edges represent observed relationships between the vertices. Implicitly, the assumption is that observed edges are more […] |
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Young diagrams are all possible arrangements of n boxes into rows and columns, with the number of boxes in each subsequent row weakly decreasing. For a partition λ of n, a standard Young tableau S of shape λ is built from the Young diagram of shape λ by filling it with the numbers 1 to […] |
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Let x_1,...,x_n be an overdetermined spanning set for the Euclidean space R^k, where n > k. Let L be the integer span of these vectors. Then L is an additive subgroup of R^n. When is it discrete in R^n? Naturally, this depends on the choice of the spanning set, but in which way? We will […] |
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