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Theory of Riemann surfaces: methods and applications
(November 11–15, 2024, Sirius Mathemtical Center, Sochi)
The conference topic is the effective use of the function theory on Riemann surfaces and their families in various applications.
Riemann surface theory today is at the intersection of several mathematical disciplines: complex analysis, topology, geometry (algebraic, complex and hyperbolic) and number theory.
Despite its venerable age, this subject field continues to develop rapidly, which can be explained by its numerous applications. These applications arise in the most unexpected places, including mathematics itself, classical mechanics, theoretical physics, engineering, cryptography. Our goal is to bring together experts in the theory of Riemann surfaces and the theory of moduli spaces with specialists in scientific computing. The exchange of knowledge should inform analysts about the capabilities of modern computing and computational mathematicians about current problems in the theory of Riemann surfaces that are accessible for experimental study.
 Organizers
Bogatyrev Andrei Borisovich
Grinevich Petr Georgievich
Institutions
Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow |
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| Theory of Riemann surfaces: methods and applications, Sochi, November 11–15, 2024 |
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November 11, 2024 (Mon) |
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| 1. |
Opening
November 11, 2024 10:00–10:30, Sochi, Sirius Mathemtical Center
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| 2. |
Intersection theory on moduli spaces of curves I
S. K. Lando
November 11, 2024 10:30–11:25, Sochi, Sirius Mathemtical Center
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Intersection theory on moduli spaces of curves II
S. K. Lando
November 11, 2024 11:30–12:25, Sochi, Sirius Mathemtical Center
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KP2 solitons: a comparison between the combinatorial and the geometrical approach in the direct and inverse spectral problem
S. Abenda
November 11, 2024 12:45–13:30, Sochi, Sirius Mathemtical Center
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Hyperelliptic sigma functions and equations of mathematical physics. Lecture I. Weierstrass functions and their applications
V. M. Buchstaber
November 11, 2024 15:00–15:45, Sochi, Sirius Mathemtical Center
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Hyperelliptic sigma functions and equations of mathematical physics. Lecture II. Hyperelliptic sigma functions and their applications
V. M. Buchstaber
November 11, 2024 15:45–16:30, Sochi, Sirius Mathemtical Center
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Decompositions of Riemann surfaces into cylinders
G. B. Shabat
November 11, 2024 16:45–17:30, Sochi, Sirius Mathemtical Center
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Elliptic integrals and their generalizations
G. B. Shabat
November 11, 2024 17:30–18:15, Sochi, Sirius Mathemtical Center
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November 12, 2024 (Tue) |
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Holomorphic bundles over elliptic curves and integrable systems
A. V. Zotov
November 12, 2024 10:30–11:15, Sochi, Sirius Mathemtical Center
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Braid monodromy for a trinomial algebraic equation
S. Tanabé
November 12, 2024 11:15–12:00, Sochi, Sirius Mathemtical Center
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| 11. |
Diagonal complexes
G. Yu. Panina
November 12, 2024 12:15–13:00, Sochi, Sirius Mathemtical Center
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| 12. |
Squeezing function and related biholomorphic invariant functions
Tuen-Wai Ng
November 12, 2024 15:00–15:45, Sochi, Sirius Mathemtical Center
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On inversion of the Abel and Abel-Prym maps
O. K. Sheinman
November 12, 2024 15:45–16:30, Sochi, Sirius Mathemtical Center
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Connected components of Prym eigenform loci in genus five
M. S. Nenasheva
November 12, 2024 16:45–17:30, Sochi, Sirius Mathemtical Center
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Computation of Stiefel filtering function via genus 2 theta functions
E. A. Ladeishchikov
November 12, 2024 17:30–17:50, Sochi, Sirius Mathemtical Center
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November 14, 2024 (Thu) |
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Dynamic systems on two-dimensional surfaces and non-trivial conductivity regimes in metals
A. Ya. Mal'tsev
November 14, 2024 10:30–11:15, Sochi, Sirius Mathemtical Center
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Двумерные конечнозонные на одном уровне энергии операторы Шредингера как предел интегрируемых разностных операторов
A. E. Mironov
November 14, 2024 11:15–12:00, Sochi, Sirius Mathemtical Center
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Higher-order degenerations of Fay’s identities and applications to integrable equations
Ch. Klein
November 14, 2024 12:15–13:00, Sochi, Sirius Mathemtical Center
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Random holomorphic functions
A. I. Bufetov
November 14, 2024 15:00–15:45, Sochi, Sirius Mathemtical Center
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Algebraic Geometry for the Solitary Waves
Türkü Özlüm Çelik
November 14, 2024 15:45–16:30, Sochi, Sirius Mathemtical Center
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| 21. |
Multisoliton KP-2 solutions and degenerate M-curves
P. G. Grinevich, S. Abenda
November 14, 2024 16:45–17:30, Sochi, Sirius Mathemtical Center
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| 22. |
Elliptic in $t$ finite zone solutions of Toda lattice
A. O. Smirnov
November 14, 2024 17:30–18:10, Sochi, Sirius Mathemtical Center
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November 15, 2024 (Fri) |
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| 23. |
О структуре характеристического многочлена матрицы Лапласа циркулярных расслоений графов
I. A. Mednykh
November 15, 2024 10:30–11:00, Sochi, Sirius Mathemtical Center
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| 24. |
Efficient variational formulae for Schottky model of Riemann surfaces
A. B. Bogatyrev
November 15, 2024 11:00–11:45, Sochi, Sirius Mathemtical Center
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Inverse scattering method for holomorphic potentials
A. V. Domrin
November 15, 2024 12:00–12:45, Sochi, Sirius Mathemtical Center
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Solutions of Korteweg–de Vries hierarchy and Novikov's n-equations in terms of multidimensional sigma functions
E. Yu. Bunkova
November 15, 2024 12:45–13:30, Sochi, Sirius Mathemtical Center
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| 27. |
Возмущения конечнозонных решений: авторезонанс и диссипация
V. Yu. Novokshenov
November 15, 2024 15:00–15:45, Sochi, Sirius Mathemtical Center
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| 28. |
Комбинаторные и эргодические свойства некоторых отображений сдвигов отрезков
V. V. Chernyi
November 15, 2024 15:45–16:05, Sochi, Sirius Mathemtical Center
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| 29. |
Non-uniquely ergodic interval exchange transformations
A. N. Kobzev
November 15, 2024 16:10–16:30, Sochi, Sirius Mathemtical Center
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Quasi integrable and single appearance anomalous waves in multidimensions; a preliminary phenomenological perspective (joint work with F. Coppini)
P. M. Santini
November 15, 2024 16:45–17:30, Sochi, Sirius Mathemtical Center
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| 31. |
On the residue map
Q. Gendron
November 15, 2024 17:30–18:15, Sochi, Sirius Mathemtical Center
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| 32. |
Closing ceremony
November 15, 2024 18:15–18:15, Sochi, Sirius Mathemtical Center
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