Pédagogie > summer school
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Sat, 31 Oct 2020 14:34:40 GMTGiovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 1)Sun, 14 Jun 2015 22:00:00 GMTIn
these lectures I will first recall the basic notions and results that
are needed to study minimal surfaces in the smooth setting (above all
the area formula and the first variation of the area), give a short
review of the main (classical) techniques for existence results, and
then outline the theory of Finite Perimeter Sets, including
the main results of the theory (compactness, structure
of distributional derivative, rectifiability). If time allows, I
will conclude with a few applications.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22067
oai:canal-u.fr:22067URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22067 ]]>Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 5)Wed, 17 Jun 2015 22:00:00 GMTIn these lectures I will first
recall the basic notions and results that are needed to study minimal
surfaces in the smooth setting (above all the area formula and the first
variation of the area), give a short review of the main (classical)
techniques for existence results, and then outline the theory of Finite
Perimeter Sets, including the
main results of the theory (compactness, structure of distributional
derivative, rectifiability). If time allows, I will conclude with a few
applications.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22129
oai:canal-u.fr:22129URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22129 ]]>Nicholas Alikakos - On the structure of phase transition maps : density estimates and applicationsWed, 01 Jul 2015 22:00:00 GMTindisponible
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22133
oai:canal-u.fr:22133URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22133 ]]>Lars Andersson - Geometry and analysis in black hole spacetimes (Part 1)Sun, 15 Jun 2014 22:00:00 GMTBlack holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22339
oai:canal-u.fr:22339URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22339 ]]>Lars Andersson - Geometry and analysis in black hole spacetimes (Part 2)Mon, 16 Jun 2014 22:00:00 GMTBlack holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22341
oai:canal-u.fr:22341URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22341 ]]>Lars Andersson - Geometry and analysis in black hole spacetimes (Part 3)Tue, 17 Jun 2014 22:00:00 GMTBlack holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22345
oai:canal-u.fr:22345URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22345 ]]>Lars Andersson - Symmetry operators and energiesTue, 01 Jul 2014 22:00:00 GMTBlack holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22353
oai:canal-u.fr:22353URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22353 ]]>Alain Bachelot - Waves in the Anti-de Sitter space-time AdsThu, 03 Jul 2014 22:00:00 GMTIn this talk we address some issues concerning the wave propagation in the 4D+1 anti de Sitter space time : the role of the conformal boundary, the representation of the fields in term of Kaluza Klein tower, the existence of new dynamics associated with a family of novel boundary conditions, the linear stability of a De Sitter brane.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22567
oai:canal-u.fr:22567URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22567 ]]>Thomas Backdahl - Symmetry operators, conserved currents and energy momentum tensorsThu, 03 Jul 2014 22:00:00 GMTConserved quantities, for example energy and momentum, play a fundamental role in the analysis of dynamics of particles and fields. For field equations, one manifestation of conserved quantities in a broad sense is the existence of symmetry operators, i.e. linear differential operators which take solutions to solutions. A well known example of a symmetry operator for the scalar wave equation is provided by the Lie derivative along a Killing vector field. It is important to note that other kinds of objects can generate symmetry operators. For waves in the Kerr spacetime there is a symmetry operator associated with Carter's constant. This symmetry, which is "hidden" in the sense that it arises from a Killing spinor, satisfying a generalization of the Killing vector equation, rather than a Killing vector, was an essential ingredient in a proof of decay of scalar waves on the Kerr background by Andersson and Blue. In this talk we will consider what conditions on a spacetime are necessary for existence of symmetry operators for the conformal wave equation, the Dirac Weyl equation, and the Maxwell equation, i.e. for massless test fields of spins 0, 1/2 and 1. We will investigate how the conditions for the symmetry operators for the different field equations are related, and how they are related to existence of conserved currents. Furthermore, these tools lead to the construction of a new energy momentum tensor for a Maxwell field on a Kerr background. This will provide a powerful tool for the study of decay of Maxwell fields on the Kerr spacetime.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22569
oai:canal-u.fr:22569URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22569 ]]>Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 4)Wed, 17 Jun 2015 22:00:00 GMTIn these lectures I will first
recall the basic notions and results that are needed to study minimal
surfaces in the smooth setting (above all the area formula and the first
variation of the area), give a short review of the main (classical)
techniques for existence results, and then outline the theory of Finite
Perimeter Sets, including the
main results of the theory (compactness, structure of distributional
derivative, rectifiability). If time allows, I will conclude with a few
applications.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22121
oai:canal-u.fr:22121URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22121 ]]>