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Wednesday February 27, 2019 12:00 C101 Radosław Kycia (Krakow University of Technology and Masaryk University, Brno) Entropy, Landauer's principle and Category Theory Abstract: Usual popular-science 'definition' of entropy is: 'Entropy is some measure of disorder and disorder is what entropy measures'. In this talk I will show how to construct (and understand) the notion of entropy from first principles, that is outlined in [1]. Then I will describe the Landauer's principle that relates irreversible operations on computer memory with heat emission from the device. It explains the Maxwell's demon paradox in thermodynamics. Finally the intriguing interplay between the Landauer's principle and the notion of the Galois connection will be provided. Some hints on application to DNA computing and biological evolution will be also given. The talk based on my recent paper [2]. Literature: [1] Elliott H. Lieb, Jakob Yngvason, A Guide to Entropy and the Second Law of Thermodynamics, Notices Amer. Math. Soc. 45 (1998), 571-581 [2] Radosław A. Kycia, Landauer's Principle as a Special Case of Galois Connection, Entropy 20 (2018), no.12, 971 |
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Thursday February 28, 2019 11:00 A106 David Saunders (University of Ostrava) Lagrangians with reduced-order Euler-Lagrange equations Abstract: Any Lagrangian form of order k obtained by horizontalization of a form of order k-1 gives rise to Euler-Lagrange equations of order strictly less than 2k. But these are not the only possibilities. For example, with two independent variables, the horizontalization of a first-order 2-form gives a Lagrangian quadratic in the second-order variables; but there are also cubic second-order Lagrangians with third-order Euler-Lagrange equations. In this talk I shall show first that any Lagrangian of order k with Euler-Lagrange equations of order less than 2k must be a polynomial in the k-th order variables of order not greater than the number of different symmetric multi-indices of length k. I shall then describe a geometrical construction, based on Peter Olver's idea of differential hyperforms, which gives rise to Lagrangians with reduced-order Euler-Lagrange equations. A version of this talk was given at Ostrava in June 2017. The work has been published in SIGMA 14 (2018), 089, 13 pages. |
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Wednesday March 6, 2019 12:00 C101 Pasha Zusmanovich (University of Ostrava) TBA |
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Wednesday March 20, 2019 12:00 C101 Igor Khavkine (Institute of Mathematics of the Czech Academy of Sciences, Prague) IDEAL characterization of cosmological and black hole spacetimes Abstract: On a (pseudo-)Riemannian manifold \((M,g)\), an IDEAL characterization of a reference geometry \((M_0,g_0)\) consists of a list of tensors \(\{T_i[g]\}\) locally and covariantly constructed from the metric \(g\), such that \(T_i[g] = 0\) iff \((M,g)\) is locally isometric to \((M_0,g_0)\). Unfortunately, to date only a few IDEAL characterizations are known for interesting geometries. But if known, they have interesting applications to analysis and geometry on the reference background \((M_0,g_0)\). I will discuss how such characterizations were recently obtained for a class of cosmological and black hole spacetimes. |
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Thursday March 21 or Friday March 22, 2019 Alexander Iwanow (Silesian University of Technology, Gliwice) Pseudocompact structures of unitary representations of finitely generated groups Literature: Continuous theory of operator expansions of finite dimensional Hilbert spaces, continuous structures of quantum circuits and decidability, arXiv:1805.03070. |
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