• Indico site https://indico.eimi.ru/category/50/

    Differential Geometry Seminar on
    Generalized Complex Geometry

    venueSPbU, Dept. of Mathematics & Computer Science
    timeFridays, 11am
    organizerCasey Blacker (cblacker271@gmail.com)
    PDMI coordinator Sylvain Lavau (lavau@math.univ-lyon1.fr)
    zoom409 987 5545 (9D3ZyM)

    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 an orthogonal 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 algebroids
    • moment maps
    • generalized Kähler structures
    • T-duality

    This seminar should appeal to students and researchers with interests in differential geometry and mathematical physics.

    Mathematical references:

    Physical references:

  • Indico site https://indico.eimi.ru/category/51/

    Bioinformatics Algorithms

    Alexey Gurevich (SPbU)

    Course Description

    The course will cover the algorithmic foundations of bioinformatics, ranging from generic algorithmic techniques to specific algorithms used in various areas of computational biology. In particular, topics include string algorithms used in the analysis of biological sequences; combinatorial algorithms for gene finding and motif discovery; graph algorithms used in genome assembly and comparative genomics; clustering algorithms for the gene expression analysis and reconstruction of evolutionary trees. Theoretical background will be complemented with solving practical problems (coding challenges). This course will be given in a flipped classroom format. All text and video materials will be available online and should be studied beforehand. The class time will be dedicated to resolving learning breakdowns, answering curiosity questions and discussions. All course materials are in English.

  • Lecture course "Geometry, integrability and field theories"

    Sylvain Lavau (EIMI)

    Thursdays, PDMI, 16:30, room 106. First lecture 11.03.2021
    Please register here to participate and receive updates.

    The idea of the course is to provide notions of topology and geometry to mathematical physi-

    cists, as well as present concrete applications of such notions to pure algebraists and geometers.

    The idea would be not to fall in a too abstract presentation, and to anchor it into examples taken
    from physics. I propose to start from the basics and grow in complexity to reach higher grounds
    which are much more intricate. Here is a tentative plan of what i would like to talk about. I
    think most items need more than one seance and maybe not everything could be addressed.
    1. Basics on differential forms: exterior algebra, Hodge star operator, differential forms on
    $\mathbb R^n$, de Rham cohomology and div/grad/curl, codifferential operator and Laplace-Beltrami
    operator, Poincaré Lemma, Aharanov-Bohm effect.

    2. Integration of differential forms: manifolds, tangent vectors, covectors and differen-
    tial forms on a manifold, volume form, integration of differential forms, manifolds with

    boundaries, Stokes theorem, Maxwell equations.
    3. Poisson geometry and analytical mechanics: polyvector fields, Schouten-Nuijenhuis
    bracket, Poisson manifolds, Hamiltonian mechanics, tautological one form and Legendre
    transform, Liouville theorem, constraints, coisotropic reduction, Dirac bracket.

    4. Yang-Baxter Equations: Lie groups, Lie algebras, Lie bi-algebras, the R-matrix, Yang-
    Baxter equations, Poisson Lie groups.

    If you have ideas that would be beneficial to the program please do not hesitate to share it
    with me! What lies below are more advanced topics that I would really like to reach eventually
    (in a few months):
    5. Gauge theories: Vector bundles, principal bundles, connections, curvatures, Bianchi
    identities, Yang-Mills theory
    6. Topological field theories: Chern-Simons Theory, BF theory, sigma models, graded
    geometry, AKSZ formalism.
    7. Quantization of gauge systems: ghosts/antighosts, BRST & Fradkin-Batalin-Vilkoviski
    formalism, gerstenhaber & BV algebras, classical and quantum master equations.
    8. Scattering processes: S-matrix, amplituhedron, L∞-algebras.
    I propose to advance at a steady pace following a physically informed mathematical path.
    I would not focus on the logico-deductive process of mathematical proofs but rather on the
    physical ideas that led to the invention of these notions. I intend to write as many lecture notes
    as possible, and would hopefully put them on my website every week.

  • Занятия по четвергам в ПОМИ, 18:00, 311 ауд. Первое занятие 04.03.2021. Просьба регистриоваться

    Мы продолжаем серию курсов, целью которых является попытка довести
    объем математических знаний и уровень общей математической культуры
    студентов и выпускников нематематических специальностей вузов до того,
    который считался нормальным 30-40 лет назад, и фактически является
    минимально необходимым для работы инженеров во многих
    высокотехнологических отраслях промышленности (скажем, в разработке
    сложного программного обеспечения, робототехнике, анализе больших
    данных). В этом семестре мы сосредоточимся на обыкновенных
    дифференциальных уравнениях, уделив особое внимание исследованиям
    качественных свойств решений. Среди прочих будут разбираться задачи,
    возникающие в различных технических, физических и биомедицинских
    приложениях. Мы будем также обсуждать некоторые вопросы теории
    устойчивости и теории управления.
    Занятия могут быть полезны прежде всего студентам начальных курсов
    технических и смежных с ними специальностей вузов.

  • This is a research seminar focusing unrestrictedly on different subjects of modern combinatorial geometry. We are interested in: Tverberg-type theorems, local combinatorial formulas for characteristic classes, moduli spaces and Teichmueller spaces, universality theorems, combinatorial rigidity, etc.
    We meet partly offline (14 line 39, 120), partly on Zoom, usually on Mondays at 11-15.
    Zoom Meeting ID: 813 4428 8370
    Passcode: maximal number of acute angles in a pentagon

    If you want to (un)subscribe to announcements or give a talk, please contact Gaiane Panina at gaiane-panina@rambler.ru.

  • 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:


    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