Algebraic Curves with Symmetries, their Jacobians and Integrable Dynamical Systems

National University of “Kyiv-Mohyla Academy”
July 30 - August 1, 2014

To the memory of Professor Petro Holod, a head of the Department of physical and mathematical sciences of the National University of “Kyiv-Mohyla Academy”, passed away on 3 January 2014. He was a senior researcher of the Bogolyubov Institute for Theoretical Physics, a professor in the Department of theoretical physics of Taras Shevchenko National University of Kyiv, and an academician of the Academy of Science of the Ministry of Higher Education of Ukraine.

Overview

This meeting will focus on a special class of lower genera algebraic curves: both hyperellptic and non-hyperelliptic curves that cover elliptic or lower genera hyperelliptic curves. These curves have attracted significant attention because of their appearance in various problems surrounding integrable dynamical systems. These dynamical systems include three celebrated classical problems: Kowalewska's problem of the motion of the non-symmetric top, Clebsch's integrable case of the Kirchhoff problem of body motion in an ideal liquid, and the problem of the motion of 4-dimensional Euler top. The curves relevant to these problems are double cover ramified over four points. Other modern problems include Hitchin's description of non-abelian monopoles, where the cover is non-ramified, the integrable H'enon-Heiles system and its generalizations, where the double covers are ramified over two points, SU(3)-magnet and others. We will discuss the structure of the associated Prym varieties that naturally arise as subvarieties of Jacobians of the curves in question.

The Workshop will be held in the memorial part of Kiev - Podil, at the National University of `Kyiv-Mohyla Academy' .

Brief History of the University

The University traces its origins to 1615, when the noblewoman Galshka Gulevicheva donated land and money to build the Brotherhood Monastery School in Kiev. When Petro Mohyla (circa 1597-1647), the Metropolitan of Kyiv, Galich and all Rus, arrived in Kiev and decided to open a school at Kiev-Pechersk Lavra, the Brotherhood Monastery School appealed to Mohyla not to open a new school but to use the existing institution as the base. Mohyla agreed, and in 1632 the Brotherhood Monastery School was reorganized into the Kiev-Mohyla Collegium, in 1658 it obtained the status of an Academy. Under Mohyla's protection, the monastery and school received additional land and financial support. The aim of the Kyiv-Mohyla Academy was to master the intellectual skills and learning of contemporary Europe and apply them to education in Ukraine. The academy was open to young men from all social strata and attracted students and scholars from Ukraine and other European countries. It flourished at the end of the 17th century and enjoyed its golden age during the reign of Hetman Ivan Mazepa (1687-1709), when enrollment was more than 2,000. The academy's golden age came to an abrupt end with Mazepa's defeat at Poltava in 1709. The ban by Tsar Peter I on Ukrainian publications and religious texts in Ukrainian was a further heavy blow. The school revived for a time after Peter's death, but suffered again under Catherine the Great, whose abolition of the hetmanate in 1764 and secularization of the monasteries in 1786 deprived the academy of its chief sources of financial support. In 1817 the Kyiv-Mohyla Academy was closed down. In 1991, when Ukraine gained its independence, the academy was revived as National University of `Kyiv-Mohyla Academy'.

Organizing committee

Participants

Julia Bernatska National University of `Kyiv-Mohyla Academy' (Ukraine)
Yulia Bezvershenko Bogolyubov Institute for Theoretical Physics (Ukraine)
Harry W. Braden School of Mathematics, University of Edinburgh (United Kingdom)
Oleg Chalykh School of Mathematics, University of Leeds (United Kingdom)
Chris Eilbeck School of Mathematics, Heriot-Watt University (United Kingdom)
Victor Enolski School of Mathematics, University of Edinburgh (United Kingdom)
Allan P. Fordy School of Mathematics, University of Leeds (United Kingdom)
Dmitry Korotkin Concordia University (Canada)
Nikolai Iorgov Bogolyubov Institute for Theoretical Physics (Ukraine)
Atsushi Nakayashiki Tsuda College (Japan)
Andriy Panasyuk University of Warmia and Mazury (Poland)
Maxim Pavlov Lebedev Physical Institute RAS (Russian Federation)
Anatolij Prykarpatski The Ivan Franko State Pedagogical University (Ukraine)
Taras Skrypnyk Universita degli studi di Milano-Bicocca (Italia)
Yuriy Sydorenko Ivan Franko National University of Lviv (Ukraine)

Plenary Speakers

  • H. W. Braden (Edinburgh)
    Recent progress in the algebro-geometric construction of non-abelian monopoles

    Presentation

  • V. Enolski (Edinburgh)
    Two explicit examples of non-Abelian monopoles

    Presentation

  • J. C. Eilbeck (Edinburgh)
    Coble surfaces, heat equations, and Weierstrass functions in genus 2 and 3

    Presentation

  • D. Korotrin (Montreal)
    Bergman tau-function and Witten cycles in moduli spaces

    Presentation

  • A. Nakayashiki (Tokyo, Kodaira)
    An application of the theory of tau functions to Riemann's theta functions

    Presentation

  • A. Prykarpatski (Drohobych)
    On the factorized spectral problems and related integrable dynamical systems

    Presentation

  • J. Bernatska (Kyiv)
    SU(3) magnet and generalized theta-functions of trigonal curve

    Presentation

  • Yu. Bezvershenko (Kyiv)
    Dynamics of Dicke model via generalized theta-functions

    Presentation

  • O. Chalykh (Leeds)
    KP hierarchy for a cyclic quiver

    Presentation

  • N. Iorgov (Kyiv)
    Algebro-geometric solutions of the Schlesinger system from conformal field theory

    Presentation

  • A. Panasyuk (Olsztyn)
    On classification and applications of pencils of Lie algebras

    Presentation

  • M. Pavlov (Moscow)
    Integrable Dispersive Chains

    Presentation

  • T. Skrypnyk (Milano)
    Elliptic and higher genus curves, classical r-matrices and integrable systems

    Presentation

  • Yu. Sydorenko (Lviv)
    Extended KP hierarchies with self-consistent sources and binary Darboux transformations

    Presentation

Schedule

July 30, Wednesday
9:30 - 10:00 Opening Ceremony
Morning session
Chairman: A. P. Fordy
10:00 - 10:50 H. Braden
10:50 - 11:00 Coffee break
11:00 - 11:50 V. Enolski
11:50 - 12:00 Coffee break
12:00 - 12:50 J. Bernatska
 
13:00 - 14:00 Lunch
14:00 - 15:00 Excursion to the Kyiv-Mohyla Academy
Afternoon session
Chairman: H. Braden
15:00 - 15:50 O. Chalykh
15:50 - 16:00 Coffee break
16:00 - 16:30 C. Eilbeck
16:30 - 17:00 N. Iorgov
July 31, Thursday
 
Morning session
Chairman: V. Enolski
10:00 - 10:50 A. Nakayashiki
10:50 - 11:00 Coffee break
11:00 - 11:50 A. Prykarpatski
11:50 - 12:00 Coffee break
12:00 - 12:50 T. Skrypnyk
 
13:00 - 14:00 Lunch
 
15:00 - 18:00 Boat trip
 
 
 
 
 
19:00 - 20:00 Conference dinner
August 1, Friday
 
Morning session
Chairman: A. Nakayashiki
10:00 - 10:50 D. Korotrin
10:50 - 11:00 Coffee break
11:00 - 11:50 M. Pavlov
11:50 - 12:00 Coffee break
12:00 - 12:50 A. Panasyuk
13:00 - 13:30 Yu. Bezvershenko
13:30 - 14:00 Closing Ceremony
 
14:00 - 15:00 Lunch
 
 
 
 
 
 

Program

The program in a pdf-file is located here.

Abstracts are available.

Besides scientific talk we are planning a small trip along Dniper river and a social relaxation time in the Mariyinski park in one from evenings when we will be able to discuss our scientific subjects.

How to get