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DTSTART;TZID=Europe/Sofia:20230309T150000
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DTSTAMP:20260617T091514
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UID:13967-1678374000-1678377600@math.bas.bg
SUMMARY:Семинар на секция "Математически основи на информатиката"
DESCRIPTION:На 9 март 2023 г. (четвъртък) от 15:00 часа в зала 503 на ИМИ-БАН\nще се проведе заседание на семинара на секция „Математически основи на информатиката”. Доклад на тема:\n\nIntroduction to the dimer model on the plane: scaling limit and conformal invariance\n\nще изнесе\nд-р Михаил Басок\, гостуващ учен по програма ПИКОМ.\n\nАбстракт:  Dimer model is a classical model in planar statistical physics. Given a finite graph\, the model is described as a probability distribution on the set of dimer covers (=perfect matchings) of the graph. In the case when the graph is planar each dimer cover is described with the so-called height function\, which is a certain function on the faces of the graph.\n\nIn this talk we consider a particular setup when the graph is given as a subgraph of a square lattice on the plane and the distribution on the space of dimer covers is uniform. Given a simply-connected domain we consider a sequence of such graphs approximating this domain as the step of the lattice tends to zero and sample the dimer model on each of the graphs. Classical theorem of Kenyon asserts that under a certain local combinatorial conditions the sequence of the corresponding (random) height functions has a conformally invariant limit. Moreover\, this limit is proven to be the Gaussian free field with Dirichlet boundary conditions in the initial domain. \nWe will discuss heuristics behind this theorem and the approтach to proving it via discrete complex analysis developed by Kenyon. If time permits\, we will also discuss random loop ensembles arising from a pair of two independent dimer covers and its convergence to a conformally invariant limit proved in our joint work with Dmitry Chelkak.
URL:https://math.bas.bg/event/copy-%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bd%d0%b0-%d1%81%d0%b5%d0%ba%d1%86%d0%b8%d1%8f-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b8-%d0%be%d1%81%d0%bd/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
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DTSTART;TZID=Europe/Sofia:20220705T140000
DTEND;TZID=Europe/Sofia:20220705T153000
DTSTAMP:20260617T091514
CREATED:20220701T092523Z
LAST-MODIFIED:20220701T092624Z
UID:12591-1657029600-1657035000@math.bas.bg
SUMMARY:Семинар "Математически основи на информатиката"\, доклад на Александър Барг
DESCRIPTION:На 05.07.2022г. oт 14:00 в заседателната зала на ИМИ-БАН\nще се състои сбирка на семинара на секция „Математически основи на информатиката“.\nДокладчик ще бъде проф. Александър Барг от Университета на Мериленд.\nТой ще изнесе доклад на тема \nRemarks on the 1st linear programming bound for binary codes\nAbstract: The “linear programming bound” on the rate of binary codes (1977) is a fundamental result in coding theory that continues to attract attention to this day\, with new proofs appearing every now and then. I will discuss 2 proofs from about 2006-08\, appearing in arXiv:cs/0512025 (Barg-Nogin) and arXiv:math/0702425 (Navon and Samorodnitsky). Both proofs are based on Fourier analytic arguments on the Boolean cube and exhibit interesting parallels and differences (none of them actually uses linear programming). One of the applications enables us to establish upper bounds on the maximum size of binary codes of large distance\, d=n/2 – t√n. \nПоканват се всички желаещи.
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b8-%d0%be%d1%81%d0%bd%d0%be%d0%b2%d0%b8-%d0%bd%d0%b0-%d0%b8%d0%bd%d1%84%d0%be/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
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