»ã±¨±êÌâ (Title)£ºDeautonomisation of integrable mappings and degree growth£ºI, II, III £¨¿É»ýϵͳµÄ·Ç×ÔÖλ¯ÓëìØÔö³¤£©

»ã±¨ÈË (Speaker)£ºAlexander Stokes ²©Ê¿£¨Ôçµ¾Ìï´óѧ£¬ÈÕ±¾£©

»ã±¨¹¦·ò (Time)£º(I): 2024Äê9ÔÂ20ÈÕ 15:40-17:10

         (II): 2024Äê9ÔÂ21ÈÕ 14:00-15:30

         (III): 2024Äê9ÔÂ21ÈÕ 15:40-17:10

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÕÅÐÛʦ

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In discrete integrable systems, the idea of taking an integrable birational mapping of the plane and cooking up a ¡®non-autonomous version¡¯ of it with integrability properties preserved is best known as a path from QRT maps to discrete Painlev¨¦ equations. This is often done using singularity confinement, which can be formulated in terms of the geometry of rational surfaces. The aim of these talks is to give a pedagogical introduction to several topics under the theme of deautonomisation, beginning with how to perform deautonomisation by singularity confinement of a mapping of the plane on the level of geometry. We will then discuss the relation between parameter evolution and degree growth when deautonomisation by singularity confinement is performed on non-integrable mappings. Time permitting, we will also introduce a novel example of elliptic nature with links to algebraic dynamics and some examples beyond dimension two.