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shared:seminars_graphs [28.11.2019 18:04]
guterman 		shared:seminars_graphs [18.06.2020 16:31] (текущий)
guterman
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====Спецсеминар "Графы на поверхностях и кривые над числовыми полями"==== ====Спецсеминар "Графы на поверхностях и кривые над числовыми полями"====
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- 
-**Семинар проходит по средам в ауд. 14-15 Главного здания, начало в 18:30.** 
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 +
 +**Семинар регулярно работает с сентября 1991г. Обычно проходит по средам в ауд. 14-15 Главного здания. В настоящее время проводится он-лайн, с использованием технологии Zoom, начало в 18:30.**
 + 
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 +Для участия в он-лайн семинаре напишите elena -dot- kreines @ gmail -dot- com.
 +
 +**01.07.2020**
 +
 +Fedor Pakovich (Ben Gurion University of Negev), Recomposing rational functions
 +
 +{{:specialcourses:abs.pdf|Abstract}}
 +
 +**24.06.2020**
 +
 +David Roberts (University of Minnesota Morris), Hypergeometric Belyi Maps
 +
 +Abstract: A classical hypergeometric function {}_n F_{n-1)(alpha,beta,t) and an auxiliary prime number determine a Belyi map.  We will give an overview of this class of Belyi maps, and why it is important to explicitly compute them.  To illustrate this theory, we present a new computation of a degree 120 hypergeometric Belyi map with monodromy group Sp_8(F_2).
 +
 +**17.06.2020**
 +
 +David Torres-Teigell (Universidad Autónoma de Madrid), Teichmüller curves: where to find them and how to cut them out
 +
 +Abstract: Teichmüller curves are totally geodesic curves inside the moduli space of Riemann surfaces. They can always be seen, via certain Prym-Torelli map, as Kobayashi geodesics inside a Hilbert modular variety parametrizing abelian varieties with real multiplication. Our main objective is to cut Teichmüller curves out as the vanishing locus of a Hilbert modular form.
 +The building blocks of these modular forms turn out to be certain theta functions and their derivatives, which can be made very precise. This calculation allows us to compute the Euler characteristics of the Teichmüller curves and the Masur-Veech volume of the affine invariant manifold where they live. In this talk we will give an overview of the subject and focus on the case of gothic Teichmüller curves.
 +
 +**10.06.2020**
 +
 +Leonardo Zapponi (Sorbonne Université), Belyi theorem in positive characteristic and its applications.
 +
 +Abstract: The first part of the talk is a review of the different aspects of Belyi theorem,  from the original characteristic 0 case, through its odd characteristic version, concluding with its recent proof in characteristic 2. The second part is an illustration of these results and their applications for elliptic curves, involving cellular decomposition of moduli spaces and realizations of modular curves as Hurwitz spaces.
 +
 +**03.06.2020**
 +
 +Alexander Mednykh (Sobolev Institute of Mathematics, Novosibirsk State  University, Novosibirsk, Russia), Volumes of two-bridge knots in spaces of constant curvature  
 +
 +Abstract: We investigate the existence of hyperbolic, spherical or Euclidean structure on cone manifolds whose underlying space is the three-dimensional sphere and singular set is a given two-bridge knot. For two-bridge knots with not more than 7 crossings we present trigonometrical identities involving the lengths of singular geodesics and cone angles of such cone manifolds. Then these identities are used to produce exact integral formulae for volume of the corresponding cone manifold modeled in the hyperbolic, spherical and Euclidean geometries.
 +
 +**27.05.2020**
 +
 +George Shabat, On the Belyi height
 +
 +Abstract: Belyi height of a complex curve is defined as the smallest possible degree of a Belyi function on it. For a fixed genus it is considered as a function on the moduli space; according to Belyi theorem, the Belyi height of a curve is finite if and only if the curve is defined over the field of algebraic numbers.
 +
 +Belyi height will be compared with the other heights and with the Kolmogorov complexity. Some examples due to the speaker and to Leonardo Zapponi will be presented. The recent result by Ariyan Javanpeykar and John Voight on the algorithmic computability of the Belyi height will be formulated and the algorithmic aspects of the passport realizability discussed.  
 +
 +**20.05.2020**
 +
 +Konstantin Golubev (ETH Zürich), High-Dimensional Expanders and Property Testing
 +
 +Abstract: Expander graphs can be defined in a number of equivalent ways, each of which however gives rise to a different notion when generalized to higher dimensions. In my talk, I will describe one of them, F2-coboundary expansion, and describe its connection to the theory of Property Testing.
 +
 +**13.05.2020**
 +
 +Vasilisa Shramchenko (Université de Sherbrooke), Poncelet theorem and Painlevé VI equation
 +
 +In 1995 Hitchin constructed explicit algebraic solutions to the Painlevé VI (1/8,-1/8,1/8,3/8) equation starting with any Poncelet trajectory, that is a closed billiard trajectory inscribed in a conic and circumscribed about another conic. In this talk I will show that Hitchin's construction is actually the Okamoto transformation between Picard's solution and the general solution of the Painlevé VI (1/8,-1/8,1/8,3/8) equation. Moreover, this Okamoto transformation can be written in terms of an Abelian differential of the third kind on the associated elliptic curve, which allows to write down solutions to the corresponding Schlesinger system in terms of this differential as well. This solution of the Schlesinger system admits a natural generalization to hyperelliptic curves.
 +
 +**06.05.2020**
 +
 +Alexander Zvonkin (LaBRI, University of Bordeaux), Construction of regular maps from their small quotients
 +
 +Every bicolored map may be represented by a triple of permutations (x,y,z) acting on the set E of edges and such that xyz=1. Here the cycles of x are black vertices, the cycles of y are white vertices, and the cycles of z are faces. To every map one can associate two groups: the monodromy group G=<x,y,z>, and the automorphism group H. A map is called regular if these two groups are isomorphic. In this case the set E of edges can be identified with the group, and this group acts on itself by multiplications. Thus, a construction of a regular map, even a large one, may be reduces to a construction of a group with desired properties, and this group may be constructed as a monodromy group of another map, often much smaller.
 +
 +As an example of special interest we will consider Hurwitz maps. In 1893, Hurwitz proved that for a map of genus g>1 the order of its automorphism group is bounded by 84(g-1). Hurwitz maps are interesting not only because they are very symmetric but also because they are very rare. Marston Conder (Aucland) classified all regular maps of genus from 2 to 101. Their number is more 19 thousand, and only seven of them are Hurwitz.
 +
 +This is a joint work with Gareth Jones (Southampton).
 +
 +**29.04.2020**
 +
 +George Shabat, Is it possible to understand Mochizuki?
 + 
 +Shinichi Mochizuki is the author of a great amount of long and very interesting texts; every month this corpus is growing.   The author claims to have developed the "Inter-universal Teichmüller theory", from which, e.g., the  ABC-conjecture follows.
 +
 +It will be shown that the ordinary procedure of comprehension of  Mochizuki's texts is close to impossible. However, some of his results are clearly formulated and related to the traditional subjects of our seminar, These ones will be formulated, and then the attempt to enter the fascinating  Mochizuki's mathematical world will be made.
 +
 +**22.04.2020**
 +
 +Hartmut Monien (University Bonn), Dessins d'enfants and modular curves  associated to the sporadic group Co3 and Janko 2.  
 +
 +Dessins d'enfants and their realization as Belyi maps of compact Riemann surfaces were originally discovered by Felix Klein. Their importance and relevance was finally understood by Alexander Grothendieck who rediscovered and named them in his "Esquisse d'un programme" in 1984. The most important aspect of dessins is the operation of the absolute Galois group on them. Accordingly, dessins d'enfants provide fascinating insights and fundamental links between different fields of mathematics like inverse Galois theory, Teichmüller spaces, hypermaps, algebraic number theory and mathematical physics. The related problem of the construction of Riemann surfaces with given automorphism group turns out to be rather challenging. 
 +
 +**15.04.2020**
 +
 +Г.Б. Шабат, Верификация длинных доказательств: мечты, планы и реальность  
 +
 +Речь в основном пойдет о незавершенном проекте Владимира Воеводского (предварительный итог которого подведен в коллективной монографии [1]), в котором предполагалось существенно расширить взаимодействие математиков c компьютерами при построении и проверке доказательств.
 +
 +После краткого обзора унивалентных оснований математики внимание будет сосредоточено на проблемах, возникающих в связи с доказательствами, традиционное понимание которых затруднено или невозможно по причине их длины и сложности. Будут приведены примеры; позиции докладчика будут критически сопоставлены с положениями известного провокационного текста Николая Вавилова [2].
 +
 +В заключение будут высказаны соображения о формализации преподаваемой математики.
 +
 +[1] Homotopy Type Theory: Univalent Foundations for Mathematics. Univalent Foundations Project, Institute for Advanced Study, 2013. (465 pages) arXiv: 1308.0729
 +
 +[2] Nikolai Vavilov. Reshaping the metaphor of proof. Philosophical Transactions of the Royal Society A. Mathematical, Physical, and Engineering Sciences, 2019. DOI: 10.1098/rsta.2018.0279
 +
 +Заседание будет совмещенным с Научно-исследовательским семинаром по математической логике кафедры Математической логики и теории алгоритмов, [[http://lpcs.math.msu.su/rus/nis.htm|ссылка на запись семинара]].
 +
 +**08.04.2020**
 +
 +Г.Б. Шабат, Деформации пар Белого
 +
 +**01.04.2020** <fc #FF0000>Начало: 16.00!</fc>
 +
 +1. Дима Звонкин, Несколько классов когомологий на Mbar_{g,n}, вычисленных с помощью классификации полупростых когомологических теорий поля.
 +
 +Я приведу несколько примеров естественных классов когомологий на пространстве модулей стабильных кривых и формул для них. Все эти формулы по виду похожи друг на друга, и это не случайно: все они получены применением одной и той же классификации полупростых когомологических теорий поля, разработанной Гивенталем и Телеманом.
 +
 +2. Разное
 +
 +**25.03.2020**
 +
 +Г.Б. Шабат, Арифметико-геометрическое среднее и семейства Фрида.
 +
 +**26.02.2020**
 +
 +1. Н.Я. Амбург, Г.Б. Шабат, О препринте Манина-Марколли;
 +
 +2. А.М. Ватузов, TBA
 +
 +**19.02.2020**
 +
 +Г.Б. Шабат, Семейство Фрида, связанное с преобразованием Гаусса-Ландена.
 +
 +**04.12.2019**
 +
 +1. Г.Б. Шабат, Рациональные функции на кубических кривых (продолжение);
 +
 +2. Н.М. Адрианов, О симметрических квадратах функций Белого  (дополнение).
 +
**27.11.2019** **27.11.2019**