Tropical geometry and integrable cellular automata II - Bilinear form and Tropical Fay's identity

40 mins 56 secs, 233.48 MB, QuickTime 384x288, 25.0 fps, 44100 Hz, 778.78 kbits/sec

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Description:	Takenawa, T (Tokyo Uni of Marine Science) Tokyo University of Marine Science and Technology Geometric Aspects of Discrete and Ultra-discrete Integrable Systems

Created:

2011-03-14 09:54

Collection:

Discrete Integrable Systems

Publisher:

Isaac Newton Institute

Tomoyuki Takenawa

Language:

eng (English)

Credits:

Author:	Tomoyuki Takenawa
Producer:	Jonathan Nimmo
Director:	David Johnstone
Editor:	Steve Greenham


Abstract:	A seminar from the Geometric Aspects of Discrete and Ultra-discrete Integrable Systems conference in association with the Newton Institute programme: Discrete Integrable Systems http://www.gla.ac.uk/departments/mathematics/research/isamp/events/gadudis/programme/ The ultra-discrete Toda lattice (UD-Toda) is essentially equivalent to the in-tegrable Box and Ball system, and considered to be a fundamental object in ultra-discrete integrable systems. In this talk, we construct the general solution of the UD-Toda with periodic boundary condition, by using the tropical theta function and the bilinear form. For the proof, we introduce a tropical analogue of Fay's trisecant identity for the tropical spectral curves of the periodic UD-Toda. As a result, we can also prove that the general isolevel set of the periodic UD-Toda is isomorphic to the tropical Jacobian.

Abstract:

A seminar from the Geometric Aspects of Discrete and Ultra-discrete Integrable Systems conference in association with the Newton Institute programme: Discrete Integrable Systems

http://www.gla.ac.uk/departments/mathematics/research/isamp/events/gadudis/programme/

The ultra-discrete Toda lattice (UD-Toda) is essentially equivalent to the in-tegrable Box and Ball system, and considered to be a fundamental object in ultra-discrete integrable systems. In this talk, we construct the general solution of the UD-Toda with periodic boundary condition, by using the tropical theta function and the bilinear form. For the proof, we introduce a tropical analogue of Fay's trisecant identity for the tropical spectral curves of the periodic UD-Toda. As a result, we can also prove that the general isolevel set of the periodic UD-Toda is isomorphic to the tropical Jacobian.

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