2012 Stanisław Łojasiewicz Lecture

Preparatory Workshop

Kraków, 12 May 2012 (Saturday)

Schedule

9.00-9.45	Wiesław Pawłucki (UJ) On the Malgrange-Ehrenpreis Theorem and the Malgrange Preparation Theorem Abstract: These two theorems reflect two main domains of research of Bernard Malgrange: differential equations and singularities of functions. We shall present the theorems indicating how they are connected with some papers of Stanisław Łojasiewicz.
10.00-10.45	Teresa Crespo (Barcelona University) The origins of differential Galois theory Abstract: In this talk we shall present Picard-Vessiot theory of linear differential equations. This theory is an exact counterpart of the classical Galois theory of algebraic equations and the starting point for more general Galois theories.
10.45-11.15	Coffee break
11.15-12.00	Teresa Crespo (Barcelona University) The work of Ellis Kolchin and beyond Abstract: Nonlinear differential Galois theories begun with Kolchin's strongly normal extensions. In this talk we shall report on Kolchin's work and further developments of nonlinear theories by Hiroshi Umemura.
12.00-13.00	Lunch break
13.00-13.45	Zbigniew Hajto (UJ) Recent progress in differential Galois theory Abstract: We shall present generalizations of differential Galois theory to differential fields with non algebraically closed fields of constants. The interesting relations of differential algebra with model theory and differential geometry will also be discussed.
14.00-14.45	Zbigniew Hajto (UJ) Malgrange's nonlinear differential Galois theory Abstract: The notion of D-groupoid, as a generalization of the differential Galois group, was introduced and developed by Bernard Malgrange. In this talk we shall recall Malgrange's definitions of D-groupoid and D-Lie algebra and present the main highlights of his theory.
14.45-15.15	Coffee break
15.15-16.00	Henryk Żołądek (UW) Non-integrability of the Painlevé equations Abstract: The Painlevé equations can be written in Hamiltonian form with polynomial and time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous systems in C⁴. We shall prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.

All lectures will take place in Room 1016 of the Department of Mathematics and Computer Science of Jagiellonian University (New Campus, Kraków).

Please contact Wiesław Pawłucki for further details.

Odpowiedzialni:

treść:: Marcin Pitera
kod:
edytor:
aktualizacja:: So, 14 kwi 2012 01:28:26 +0000