Old and New on Diffeomorphism Groups Too. 50th Seminar ''Sophus Lie''. 25 September - 1 October 2016, Bedlewo, Poland

Infinite dimensional Lie groups: Diffeomorphism groups. MIT Lie Groups Seminar. Cambridge, USA. September 14, 2016.

Infinite dimensional manifolds.
(Not all slides were presented).

A series of 4.5 hours of lectures at:
XXV International Fall Workshop on Geometry and Physics.
Instituto de Estructura de la Materia (CSIC) Madrid, Spain.
August 29 - September 02, 2016.

Invariance and Geometry of the Fisher--Rao metric on the space of smooth densities. Workshop: Geometria we Fisica, a geometrical vision of physics. Celebrating 70th birthday of Giuseppe Marmo July 11-13, 2016, San Rufo, Campania, Italia.

Uniqueness of the Fisher--Rao metric on the space of smooth densities. IGAIA IV: Information Geometry and its Applications IV, June 12-17, 2016, Liblice, Czech Republic.

Uniqueness of the Fisher--Rao metric on the space of smooth densities. Conference: Geometric Analysis in Control and Vision Theory. 8-14 May, 2016. Bergen/Voss, Norway.

Infinite dimensional differential geometry: The space of all Riemannian metrics on a compact manifold and several natural weak Riemannian metrics on it. Mathematical Physics and Combinatorics Seminar, Brunel University, London. February 23, 2016

Overview on Convenient Calculus and Differential
Geometry in Infinite dimensions, with Applications
to Diffeomorphism Groups and Shape Spaces.

A series of 5 lectures, held at the
ESI Programme: Infinite-Dimensional Riemannian Geometry
with Applications to Image Matching and Shape Analysis.
January 19-23, 2015.

Content:

- A short introduction to convenient calculus in infinite dimensions.
- Manifolds of mappings (with compact source) and diffeomorphism groups as convenient manifolds.
- A zoo of diffeomorphism groups on $\mathbb R^n$.
- A diagram of actions of diffeomorphism groups.
- Riemannian geometries of spaces of immersions and shape spaces.
- Right invariant Riemannian geometries on Diffeomorphism groups.
- Arnold's formula for geodesics on Lie groups.
- Solving the Hunter-Saxton equation.
- Riemannian geometries on spaces of Riemannian metrics and pulling them back to diffeomorphism groups.
- Approximating Euler's equation of fluid mechanics on the full diffeomorphism group of $\mathbb R^n$.
- Robust Infinite Dimensional Riemannian manifolds, Sobolev Metrics on Diffeomorphism Groups, and the Derived Geometry of Shape Spaces.

Uniqueness of the Fisher-Rao metric on the space of smooth densities.

Workshop on "Infinite-dimensional Riemannian geometry".
ESI Programme:
Infinite-Dimensional Riemannian Geometry
with Applications to Image Matching and Shape Analysis.
Vienna, Austria.
January 12-16, 2015.

Overview on Geometries of Diffeomorphism Groups.

Workshop: Variational methods in imaging.
RICAM, Linz.
October 27-31, 2014.
My lecture here was a subset of the Pisa-lectures.

Overview on Geometries of Shape Spaces and Diffeomorphism Groups.

Workshop: Geometric Models in Vision.
Institut Henri Poincare, Paris.
October 22-24, 2014.
My lecture here was a subset of the Pisa-lectures.

Frölicher spaces as a setting for tree spaces and stratified spaces

Mini-Workshop: Asymptotic statistics on stratified spaces.
Oberwolfach,
September 29 - October 4, 2014.

Overview on Convenient Calculus and Differential
Geometry in Infinite dimensions, with Applications
to Diffeomorphism Groups and Shape Spaces, or

Geodesic evolution equations on shape spaces and diffeormorphism groups.

A series of 6 lectures, held at the
ERC School on Geometric Evolution Problems,
Centro De Giorgi, Pisa
June 23-27, 2014.

An newer version of these lecture was held at ESI in
January 19-23, 2015. See there for the slides.

Approximating Euler's equation on the full diffeomorphism group,
and soliton-like solutions.

Geometrical Aspects of Hydrodynamics workshop.
Simons Center for Geometry and Physics.
Stony Brook University.
May 19 - 23, 2014.

Video of the Lecture on the SCGP-webpage.

Overview on
Convenient Calculus and Differential Geometry in Infinite dimensions, with
Applications to
Diffeomorphism Groups and Shape Spaces
.

Workshop: Infinite dimensional geometry.
MSRI and UC Berkeley, USA, December 7-8, 2013.

Convenient Calculus and Differential Geometry in Infinite Dimensions
.

Norwegian Summer School on Analysis and Geometry,
Bergen,
Norway, June 24-28, 2013.

Overview on geometries of shape spaces, diffeomorphism groups, and
spaces of Riemannian metrics
.

Norwegian Summer School on Analysis and Geometry,
Bergen,
Norway, June 24-28, 2013.

Robust Infinite Dimensional Riemannian manifolds,
Sobolev Metrics on Diffeomorphism Groups,
and the Derived Geometry of Shape Spaces
.

Conference: Differential Geometry and its Applications
Brno, Czech Republic,
August 23, 2013.

Euler's equation of fluids and $\text{Diff}_{H^\infty}(\mathbb R^n)$
.

Norwegian Summer School on Analysis and Geometry,
Bergen,
Norway, June 24-28, 2013.

On the Hunter-Saxton equation on $\textrm{Diff}_{\mathcal A}(\mathbb R)$
.

Norwegian Summer School on Analysis and Geometry,
Bergen,
Norway, June 24-28, 2013.