401-4530-23L  Introduction to Hofer's Geometry

SemesterSpring Semester 2023
LecturersJ.‑P. Chassé
Periodicitynon-recurring course
Language of instructionEnglish
CommentNumber of participants limited to 12.



Courses

NumberTitleHoursLecturers
401-4530-23 SIntroduction to Hofer's Geometry2 hrs
Wed14:15-16:00ML J 37.1 »
J.‑P. Chassé

Catalogue data

AbstractFrom the point of view of classical mechanics, the group of Hamiltonian diffeomorphisms is the set of admissible motions on a given phase space. In that context, it is natural to ask what is the least amount of energy necessary to generate such a given motion. In 1990, Hofer formalized this notion through tools from symplectic topology, leading to his eponymous metric.
ObjectiveThe purpose of this seminar is to introduce the participants to the field of symplectic topology and the questions it asks, specifically those related to Hamiltonian diffeomorphisms. They will be able to see how the geometry of the (infinite dimensional Lie) group of Hamiltonian diffeomorphisms compares and contrasts to the finite dimensional case, and how that is related to classical mechanics; all this whilst getting to learn the less technical tools of symplectic topology.
ContentThe seminar—seperated in 12 instances—will start by covering general facts on symplectic manifolds and will then move on to more and more specific statements on Hofer's geometry. Eventually, this will all circle back to some dynamical applications and will give a taste of modern symplectic topology.
LiteratureL. Polterovich: The geometry of the group of symplectic diffeomorphisms.
D. McDuff & D. Salamon: Introduction to symplectic topology
Prerequisites / NoticeThe participant should know all the basic facts of differential geometry, specifically forms, their integration, and their differentiation. However, no prior knowledge on symplectic topology or dynamics will be assumed.
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesfostered
Problem-solvingfostered
Social CompetenciesCommunicationassessed
Personal CompetenciesAdaptability and Flexibilityfostered
Creative Thinkingfostered
Critical Thinkingfostered
Integrity and Work Ethicsfostered
Self-awareness and Self-reflection fostered
Self-direction and Self-management fostered

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersJ.-P. Chassé
Typeungraded semester performance
Language of examinationEnglish
RepetitionRepetition only possible after re-enrolling for the course unit.

Learning materials

 
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Groups

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Restrictions

PlacesLimited number of places. Special selection procedure.
Beginning of registration periodRegistration possible from 02.01.2023
PriorityRegistration for the course unit is only possible for the primary target group
Primary target groupMathematics BSc (404000) starting semester 05
Mathematics MSc (437000)
Applied Mathematics MSc (437100)
Mathematics (Mobility) (448000)
Waiting listuntil 27.02.2023
End of registration periodRegistration only possible until 17.02.2023

Offered in

ProgrammeSectionType
Mathematics BachelorSeminarsWInformation
Mathematics MasterSeminarsWInformation