Algebraic Curves, Integrable Systems,
and Cryptography

National University of Kyiv-Mohyla Academy
August 24 - 25, 2018

Overview

The goal of this workshop is to explore applications of algebro-geometric methods in cryptography. We will focus on different aspects of the theory of algebraic curves (hyperelliptic and nonhyperelliptic, and some particular cases): fields of Abelian functions and addition laws in these fields, multivariative entire functions which generate the Abelian functions. We are interested in algebraic curves over finite fields.

The Workshop will be held in Podil, the memorial part of Kiev, at the National University of Kyiv-Mohyla Academy.
There is no registration fee.
Please note, that we do not provide any financial support or reimbursement of travel and living expenses.
We suggest to stay at Vozdvyzhensky Hotel, which is located near the University.

 

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

Christopher Athorne University of Glasgow (UK)
Julia Bernatska National University of Kyiv-Mohyla Academy (Ukraine)
Igor Burban University of Paderborn (Germany)
Adam Doliwa University of Warmia and Mazury (Poland)
Yuriy Drozd Institute of Mathematics of the NASU (Ukraine)
John Christopher Eilbeck Heriot-Watt University (UK)
Victor Enolski National University of Kyiv-Mohyla Academy (Ukraine)
Yury Fedorov Politechnic University of Catalonia (Spain)
Jaime Gutierrez University of Cantabria (Spain)
Nikolai Iorgov Bogolyubov Institute for Theoretical Physics (Ukraine)
Shigeki Matsutani National Institute of Technology, Sasebo College (Japan)
Alexander Mikhailov University of Leeds (UK)
Shuichi Otake Waseda University (Japan)
Andriiana Plakosh Institute of Mathematics of NAS of Ukraine
Anatolij Prykarpatsky Cracov University of Technology (Poland)
Iryna Raievska Institute of Mathematics of NAS of Ukraine
Maryna Raievska Institute of Mathematics of NAS of Ukraine
Mukhayo Rasulova Institute of Nuclear Physics of AS of Uzbekistan
Tanush Shaska Oakland University (USA)
Taras Skrypnyk University of Milano-Bicocca (Italy)
Olena Vaneeva Institute of Mathematics of NAS of Ukraine

Plenary Speakers

  • C. Athorne
    Counting relations for curves
  • J. Bernatska
    On degenerate hyperelliptic sigma functions

    Presentation

  • I. Burban
    Algebraic geometry of the classical Yang-Baxter equation

    Presentation

  • A. Doliwa
    Algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve

    Presentation

  • Yu. Drozd
    Vector bundles on singular curves of genus 1

    Presentation

  • J. C. Eilbeck
    Heat equations in the non-Weierstrass case

    Presentation

  • V. Enolski
    On the modular representation for periods of hyperelliptic integrals

    Presentation

  • Yu. Fedorov
    Inversion of an `impossible' Abel-Prym map in the linearization of the Clebsch system

    Presentation

  • J. Gutierrez
    Predicting the linear congruential generator on elliptic curves

    Presentation

  • N. Iorgov
    On solutions of the Fuji-Suzuki-Tsuda system

    Presentation

  • S. Matsutani
    Abelian functions of a curve given by Weierstrass normal form: Jacobi inversion formulae and sigma of singular curves

    Presentation

  • A. Mikhailov
    Integrable Hamiltonian systems, naturally defined by symmetric powers of algebraic curves

    Presentation

  • S. Otake
    Bezoutians and the discriminant of certain quadrinomials

    Presentation

  • A. Prykarpatsky
    On the solutions to the topological field theory Witten-Dijgraaf-Verlinde-Verlinde associative equations and their geometric properties

    Presentation

  • M. Rasulova
    The solution of quantum kinetic equation with delta potential and its application for cryptology

    Presentation

  • T. Shaska
    Abelian varieties and their applications to cryptography

    Presentation

  • T. Skrypnyk
    Separation of variables and classical r-matrices: `magic recipe' revisited

Schedule

August 24, Friday
 
Morning session
Chairman: V. Enolski
9:30 - 9:40 Opening
9:40 - 10:40 T. Shaska
10:40 - 11:40 Yu. Drozd
11:40 - 12:10 Coffee break
12:10 - 12:50 J. Gutierrez
12:50 - 13:30 S. Otake
 
13:30 - 14:30 Lunch
 
Afternoon session
Chairman: T. Shaska
14:30 - 15:10 S. Matsutani
15:10 - 15:50 J.C. Eilbeck
15:50 - 16:30 C. Athorne
16:30 - 17:00 Coffee break
17:00 - 17:40 J. Bernatska
17:40 - 18:20 V. Enolski
 
19:00 - 20:00 Conference dinner
August 25, Saturday
 
Morning session
Chairman: J.C. Eilbeck
9:20 - 10:20 A. Mikhailov
10:20 - 11:00 I. Burban
11:00 - 11:40 N. Iorgov
11:40 - 12:10 Coffee break
12:10 - 12:50 A. Doliwa
12:50 - 13:30 M. Rasulova
 
13:30 - 14:30 Lunch
 
Afternoon session
Chairman: A. Mikhailov
14:30 - 15:10 Yu. Fedorov
15:10 - 15:50 T. Skrypnyk
15:50 - 16:30 A. Prykarpatsky
16:30 - 16:40 Closing
 
 
 
 

Program

The program in a pdf-file is located here.

here Abstracts are available.

How to get