Физико-математический клуб при ПОМИ и СПбГУ

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Colloquium dedicated to International Women in Mathematics Day May 11, 2021
by Egor Pifagorov - Friday, 30 April 2021, 03:36 PM
 

Colloquium dedicated to International Women in Mathematics Day

May 11, 2021

If you plan to take part in the colloquium please register to obtain a link to the Zoom meeting.

11:10 – 11:15 Introductory word by Peter Zograf (PDMI and SPbU)

11:15 – 12:00 Anton Zorich (Center for Advanced Studies, Moscow, and University of Paris)
"How Maryam Mirzakhani has counted simple closed geodesics on Riemann surfaces"

I will say several words about Maryam Mirzakhani and then will present her results on asymptotic count of simple closed geodesics on a Riemann surface. At the end of the talk I will mention a development of the results of Mirzakhani in the case when the genus of the surface is large. This development is obtained jointly with V. Delecroix, E. Goujard and P. Zograf, using recent progress due to A. Aggarwal. The talk would be informal, not always rigorous, and the proofs would be omitted. As a compensation I will do my best to make it accessible to students of the third year. The text of the presentation is in English, but (if the audience does not object) the talk will be given in Russian.

12:05 – 12:50 Elise Goujard (University of Bordeaux)
"Variations on meanders" (after a joint work with V. Delecroix, P. Zograf and A. Zorich)

A meander is a topological configuration of a line (the road) and a transverse curve (the river) in the plane, or equivalently a pair of simple closed curves on the sphere. They appear in combinatorics, theoretical physics, and computational biology. Counting meanders with a given number of intersections (bridges) is still an open problem. Similarly one can define meanders on higher genus surfaces: they correspond to topological configurations of pairs of simple closed curves on surfaces of higher genus. In this talk I will present some results, joint with V. Delecroix, P. Zograf and A. Zorich, on the counting of meanders and their variants with additional combinatorial constraints, as well as their large genus asymptotics. We will see in particular that meanders can be encoded by some other combinatorial objects, namely square-tiled surfaces, that are easier to count.

12:55 – 13:25 Peter Zograf (PDMI and SPbU)
"Asymptotics of volumes of moduli spaces" (after a joint work with M. Mirzakhani)

Moduli spaces of Riemann surfaces (complex algebraic curves) of genus g with n marked points carry a natural Kaehler metric called Weil-Petersson metric. This metric and the corresponding volumes play an important role in geometry and dynamics of moduli spaces, as well as in topological quantum gravity. In this talk I will explain how the Weil-Petersson volumes behave for growing g and n.

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Cluster Algerbas and Moduli Spaces” 1-7 August 2021, Sochi
by Egor Pifagorov - Friday, 30 April 2021, 02:54 PM
 
Summer school

Cluster Algerbas and Moduli Spaces” 1-7 August 2021, Sochi

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Differential Geometry Seminar on Generalized Complex Geometry
by Egor Pifagorov - Monday, 12 April 2021, 05:26 PM
 
Differential Geometry Seminar on
Generalized Complex Geometry

venue SPbU, Dept. of Mathematics & Computer Science
time TBD
organizer Casey Blacker (cblacker271@gmail.com)
PDMI coordinator Sylvain Lavau (lavau@math.univ.lyon1.fr)




A generalized complex structure \mathcal J on a smooth manifold M is an assignment to each fiber of the
extended tangent bundle  TM\oplus T^*M of a linear complex structure in a locally compatible manner. The
resulting formalism extends both complex and symplectic geometry, and was introduced in 2003 by
Nigel Hitchin with an eye to string theory.
The aim of this learning seminar is first to review the foundational material, and then to acquaint
ourselves with the state of the art and open questions.
Related constructions include,
• Lie algebroids
• Dirac structures
• Courant brackets
• moment maps
• generalized K ̈ahler structures
• T-duality
This seminar should appeal to students and researchers with interests in differential geometry and
mathematical physics.


Mathematical references:
• Gil Cavalcanti. Introduction to generalized complex geometry. Publica ̧c ̃oes Matem ́aticas do IMPA.
Instituto Nacional de Matem ́atica Pura e Aplicada (IMPA), Rio de Janeiro, 2007. 26o Col ́oquio
Brasileiro de Matem ́atica, https://impa.br/wp-content/uploads/2017/04/26CBM_05.pdf
• Marco Gualtieri. Generalized complex geometry. PhD thesis, University of Oxford, November
2003, https://arxiv.org/abs/math/0401221
• Nigel Hitchin. Lectures on generalized geometry. In Surveys in differential geometry. Volume
XVI. Geometry of special holonomy and related topics, volume 16 of Surv. Differ. Geom., pages
79–124. Int. Press, Somerville, MA, 2011
• Nigel Hitchin. Generalized Calabi-Yau manifolds. Q. J. Math., 54(3):281–308, 2003,
https://proxy.library.spbu.ru:2060/10.1093/qmath/hag025
Physical references:
• Paul Koerber. Lectures on generalized complex geometry for physicists. Fortschr. Phys., 59(3-
4):169–242, 2011, https://proxy.library.spbu.ru:2150/doi/abs/10.1002/prop.201000083
• Maxim Zabzine. Lectures on generalized complex geometry and supersymmetry. Arch. Math.
(Brno), 42(suppl.):119–146, 2006, https://www.emis.de/journals/AM/06-S/zabzine.pdf
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Кружок по дополнительным главам алгебры
by Egor Pifagorov - Friday, 5 March 2021, 04:40 PM
 
Продолжает работу

Кружок по дополнительным главам алгебры

Под руководством доцентов СПбГУ К. И. Пименова и И. М. Зильберборда.
Большая просьба регистрироваться на Indico сайте кружка
Большая часть тем ориентирована на первокурсников и не требует дополнительных знаний сверх стандартной программы 1-го семестра. При желании слушателей, мы можем провести занятия по доп. главам теории представлений для 2-3 курса параллельно или в альтернативное время. Как и в прошлом году, на кружке планируется обсудить несколько независимых тем, которые:
с одной стороны - дополняют общий курс алгебры;
с другой стороны – некоторые из них могут стать стартом для курсовой работы;
с третьей стороны - дают возможность посмотреть на что-то в исторической перспективе.

С нами можно связаться в группе В контакте: https://vk.com/club192456307 Предполагается, что пока занятия кружка будут по субботам, в 11:50, посредством MS Teams, в апреле, вероятно, частично перейдут в очный режим --- в ПОМИ на Фонтанке 27. Группа кружка в MSTeams, где также будут размещаться материалы и текущие объявления

Первое занятие состоится в субботу 6.03.21 https://indico.eimi.ru/event/283/



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имени Леонарда Эйлера

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