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Kommende Vorträge

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Ausführliche Liste aller demnächst stattfindenden Vorträge und Seminare. Für eine Übersicht konsultieren Sie bitte auch den Kalender.

Seminar on Kac-Moody algebras and related topics

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Organiser(s): 
Giovanni Faonte, Benjamin Hennion, Lin Weng
Datum: 
Fre, 2017-02-10 13:30 - Son, 2017-12-31 15:00
Location: 
MPIM Lecture Hall

The Globalization Theorem for the Curvature-Dimension Condition

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Speaker: 
Emanuel Milman
Zugehörigkeit: 
Technion - Israel Institute of Technology
Datum: 
Mon, 2017-09-25 09:30 - 10:30
Location: 
MPIM Lecture Hall

The Lott-Sturm-Villani Curvature-Dimension condition provides a synthetic notion for a metric-measure space to have Ricci-curvature bounded from below and dimension bounded from above.

Differential calculus on RCD spaces - part 1

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Speaker: 
Nicola Gigli
Zugehörigkeit: 
SISSA
Datum: 
Mon, 2017-09-25 11:00 - 11:40
Location: 
MPIM Lecture Hall

In the lecture I will survey recent advances on calculus on RCD spaces. I shall start recalling how the concept of `L2-normed L1 module' allows to give a reasonable de finition of
(co)tangent space and to build a first-order theory on abstract metric measure spaces. The Bochner inequality, which properly interpreted de fines RCD spaces, will then allow
to build a second order calculus in such setting: we shall review it and, if time permits, see some applications to the study of geometry of RCD spaces.

Non-commutative transport metrics, gradient flow and functional inequalities - part 2

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Speaker: 
Eric Carlen
Zugehörigkeit: 
Rutgers University
Datum: 
Mon, 2017-09-25 15:20 - 16:00
Location: 
MPIM Lecture Hall

The space of positive semi-definite $n\times n$ matrices with unit trace, or more generally, the space of states on a $C^*$ algebra can be made into a metric space using constructions that a analogous to the transportation-theoretic constructions that make  spaces of probability measures into metric spaces.

A categorical approach to universal knot invariants

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Speaker: 
Danica Kosanovic
Zugehörigkeit: 
MPIM
Datum: 
Mon, 2017-09-25 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Quantitative Isoperimetry à la Levy-Gromov

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Speaker: 
Fabio Cavalletti
Zugehörigkeit: 
SISSA
Datum: 
Die, 2017-09-26 09:30 - 10:30
Location: 
MPIM Lecture Hall

On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of a round sphere of suitable radius. The deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise.

Harmonic maps between Riemannian manifolds

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Speaker: 
Maria Bertozzi
Zugehörigkeit: 
U. Bonn
Datum: 
Die, 2017-09-26 10:00 - 11:00
Location: 
MPIM Seminar Room
Parent event: 
Extra talk

Differential calculus on RCD spaces - part 2

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Speaker: 
Nicola Gigli
Zugehörigkeit: 
SISSA
Datum: 
Die, 2017-09-26 11:00 - 11:40
Location: 
MPIM Lecture Hall

In the lecture I will survey recent advances on calculus on RCD spaces. I shall start recalling how the concept of `L2-normed L1 module' allows to give a reasonable de finition of
(co)tangent space and to build a first-order theory on abstract metric measure spaces. The Bochner inequality, which properly interpreted de fines RCD spaces, will then allow
to build a second order calculus in such setting: we shall review it and, if time permits, see some applications to the study of geometry of RCD spaces.

Isometry groups of spaces with lower ricci curvature bounds

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Speaker: 
Jaime Santos Rodríguez
Zugehörigkeit: 
Universidad Autónoma de Madrid
Datum: 
Die, 2017-09-26 15:00 - 15:30
Location: 
MPIM Lecture Hall

Isometric actions on Riemannian manifolds have been a usefu tool to investigate the interaction between the topology and the Riemannian metric a manifold might admit. A major result in the area is the theorem of Myers-Steenrod [4] stating that the isometry group of a Riemannian manifold is a Lie group. Later this result has been extended to a wider class of spaces with certain synthetic notions of curvature bounds such as Alexandrov spaces by Fukaya-Yamaguchi [2] and limits of manifolds with lower Ricci curvature bounds by Cheeger-Colding [1].

Markovian representation of the continuity equation

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Speaker: 
Nicolas Juillet
Zugehörigkeit: 
Université de Strasbourg
Datum: 
Die, 2017-09-26 15:30 - 16:00
Location: 
MPIM Lecture Hall

It has been established by Lisini that absolutely continuous curves (of order 2) $\mu:t ↦ \mu_t$ in the Wasserstein space over a metric space $X$ can be represented by an action-minimizing probability measure on the space of absolutely continuous curves. We will show that in the basic case of the real line ($X=\mathbb{R}$), this measure can moreover be asked to be Markovian. This is a special case of a more general result, with other consequences, where no continuity assumptions are made on the family $\mu$. (joint work with Charles Boubel)

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