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Title: Pareto optimization of resonances and optimal control methods Abstract: First successes in fabrication of high-Q optical cavities two decades ago led to active applied physics and numerical studies of optimization problems involving resonances. The questions is how to design an open resonator that has an eigenvalue as close as possible to the real line […] |
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This talk is based on joint work with Jens Marklof, and with Roland Roeder. The three distance theorem states that, if x is any real number and N is any positive integer, the points x, 2x, … , Nx modulo 1 partition the unit interval into component intervals having at most 3 distinct lengths. We […]
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(Joint with Ichihara, Jong, and Saito). We show that two-bridge knots admit no purely cosmetic surgeries, ie no pair of distinct Dehn surgeries on such a knot produce 3-manifolds that are homeomorphic as oriented manifolds. Our argument is based on a recent result by Hanselman and a study of signature and finite type invariants of […] |
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Title: On sparse geometry of numbers Speaker: Prof. Lenny Fukshansky, Department of Mathematics, Claremont McKenna College Abstract: Geometry of Numbers is an area of mathematics pioneered by Hermann Minkowski at the end […] |
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By Hilbert’s theorem 90, if K is a cyclic number field with Galois group generated by g, then any element of norm 1 can be written as a/g(a). This gives […]
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We talk about building knots using mosaics which were as introduced as a way of modeling quantum knots by Lomonaco and Kauffman and a newer variant, hexagonal mosaics, introduced by […] |
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The Field Committee Meeting is our chance to socialize with our colleagues and coordinate our course offerings for the coming academic year (2022-2023). Please come to discuss course offerings and […] |
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Title: Connections between Iterative Methods for Linear Systems and Consensus Dynamics on Networks Abstract: There is a well-established linear algebraic lens for studying consensus dynamics on networks, which has yielded significant theoretical results in areas like distributed computing, modeling of opinion dynamics, and ranking methods. Recently, strong connections have been made between problems of consensus […] |
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We describe a natural way to continuously extend arithmetic functions that admit a Ramanujan expansion and derive the conditions under which such an extension exists. In particular, we show that […]
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The Jones polynomial is an invariant of knots in R^3. Following a proposal of Witten, it was extended to knots in 3-manifolds by Reshetikhin-Turaev using quantum groups. Khovanov homology is […] |
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Title: The 6 Cs - Covid and the 5 Claremont Colleges Speaker: Maryann E. Hohn, Department of Mathematics and Statistics, Pomona College Abstract: The Claremont Colleges' (5Cs) environment consists of students, […] |
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Peg solitaire is a popular one person board game that has been played in many countries on various board shapes. Recently, peg solitaire has been studied extensively in two colors on […]
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Skein modules were introduced by Jozef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) […] |
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Title: Voronoi Tessellations: Optimal Quantization and Modeling Collective Behavior Speaker: Prof. Rustum Choksi, Department of Mathematics and Statistics, McGill University Abstract: Given a set of N distinct points (generators) in […] |
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