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Poisson [P,P]=0 Seminar - varying dates 14hs - at SYMCREA
Poisson [P,P]=0 Seminar - varying dates 14hs - at SYMCREA
see more details at the seminar's page
Special Lecture Isaac Ramos Reina- April 7, FME, room 101 at 16h
Special Lecture Isaac Ramos Reina- April 7, FME, room 101 at 16h
Title: The geometry of mathematical billiards: from integrable to undecidable systems.
Abstract: Mathematical billiards are simple dynamical systems in which a point particle moves in straight lines and reflects at the boundary of a table. Despite this simple definition, the behavior of billiards depends strongly on the geometry of the table. In this talk, we will see examples ranging from integrable billiards to polygonal billiards, which can be studied through unfolding, and to dispersive billiards, where chaotic behavior appears.
In the second part, we will introduce the idea of undecidability via the halting problem and explain how computational complexity can be built into billiard systems. This shows that billiards connect geometry, dynamics, and computation in a surprising way.
Special Lecture Professor Eckhard Meinrenken- March 17, FME, room 101 at 16h
Special Lecture Professor Eckhard Meinrenken- March 17, FME, room 101 at 16h
Title: Normal form results in differential geometry
Abstract: A vector field on R^n is "Euler-like" if it is equal to the Euler vector field, up to higher order terms. Euler-like vector fields
can always be linearized, by an essentially unique change of coordinates. This basic fact gives rise to quick proofs of various
normal form results in geometry, such as the Morse lemma and the Darboux theorem. We shall also discuss linearizability of Euler-like vector fields along submanifolds N of a manifolds M, and some of its consequences. This will involve tubular neighborhood embeddings of normal bundles, and deformation spaces.
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