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DynamIC Seminars
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Title
Date
Time
Room
Mauricio Garay (Institute Fibonacci and Johannes Gutember Universitat-Mainz)
A new quasi-analytic class (joint work with Duco van Straten)
Abstract:
Holomorphic functions are uniquely defined by their Taylor expansion at any point. If a sheaf has this property then it is called quasi-analytic. At the beginning of the XIX^th century, Emile Borel introduced the concept of monogenic functions which are holomorphic functions defined on locally closed subsets, say X. Such functions arose in number theory already in the work of Euler but there was no analytic treatment of them. Spaces of monogenic functions are in general not quasi-analytic. Borel was probably the first to put conditions on the set X to preserve quasi-analyticity. Restriction to real lines inside the set X led Denjoy and Carleman to define a simpler quasi-analytic class. All these have a defect: they do not contain even the elementary examples of number theory (q-hypergeometric functions) or of dynamical systems. In his 1954 talk at the ICM, Kolmogorov asked for the existence of a quasi-analytic class to which perturbative expansion. For a long time such a class was unknown. In the talk, I will introduce a new quasi-analytic class in the spirit of Borel which has the property to englobe many and probably most perturbative expansions of mathematical physics. In particular, I will explain why the KAM perturbative expansions belong to this class.
Tuesday, 19 May 2026
11:00
HXLY 144
Francisco de Melo Viríssimo (London School of Economics)
TBD
Abstract:
TBD
Tuesday, 26 May 2026
14:00
HXLY 145
DynamIC Workshops and Mini-Courses
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One-day workshop on Random Dynamical Systems and Ergodic Theory
Tuesday, 9 September 2025
HXLY 340, Imperial College London
CHAOS (Homoclinic Bifurcations, Strange Attractors, Arnold Diffusion, Fermi Acceleration, Solitons)
Sunday, 24 September 2023 – Friday, 29 September 2023
Nesin Math Village, Izmir, Turkey
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