# Implicit Function

# Theorems

# in

# Geometry

# and Dynamics

## February 19–22, 2020

## Schloß Rauischholzhausen

The winter school will present two incarnations of the implicit function theorem to master and PhD students: the implicit function theorem of Nash and Moser, and the implicit function theorem in scale calculus and polyfold-theory as developed by Hofer, Wysocki and Zehnder.

There will be two mini-courses on the theoretical framework of each incarnation which will be complemented by talks on classical and current applications to analysis and geometry.

## Lecture courses

### Massimiliano Berti

Nash-Moser implicit function theorems and applications in dynamics

### Zhengyi Zhou

Implicit function theorems in scale-calculus and polyfold theory

## Additional talks

### Alberto Abbondandolo

TBA

### Pietro Baldi

TBA

### Lucas Dahinden

TBA

### Filippo Giuliani

Proof of the KAM theorem by a Nash-Moser approach

### Colin Guillarmou

Marked length spectrum local rigidity

### Irene Seifert

Finding periodic delay orbits via the Polyfold-IFT

### Thibault Lefeuvre

Local rigidity of the boundary distance function

*boundary distance function*is the map assigning to each pair of points on the boundary, the Riemannian distance between the two points. It is conjectured that under some mild assumptions on the metric and/or on the topology of the manifold (that I will detail), one can reconstruct the metric up to isometries. This theoretical question naturally arises in seismic tomography, where one tries to reconstruct the inner structure of the crust from the knowledge of travel times of seismic P- and S-waves from the earthquake to seismic stations. I will explain some partial results on this question, involving (in two different steps) an implicit function theorem. Some tools will be reinvested in a subsequent talk by C. Guillarmou in order to deal with a rather similar problem on closed manifolds.

### Dingyu Yang

TBA

## Practical information

### VENUE

Schloßpark 1

35085 Ebsdorfergrund

Germany

### Arrival:

February, 19 – before lunch

### Departure:

February, 22 – after lunch

### Registration:

Please send an e-mail to Petra Kuhl.

### Arrival:

February 19, before lunch

We will organise shuttle buses that will bring you up to the castle. The meeting point for the shuttle is in front of the main station Marburg (Lahn).

### Departure:

February 22, after lunch

We will drive together at 1:45 pm with a bus to the main train station Marburg (Lahn), which will be reached by 2:20 pm at the latest.

### Observe:

Lodging and meals will be provided by the castle. All local costs are covered by us. All lectures will take place at the castle.