Floer Lectures 2020

FCG

Floer Lectures 2020

June 25-26, Bochum

We are delighted to have Alessio Figalli (ETH) and Gigliola Staffilani (MIT) as our two speakers. They will each give two talks.

This is a workshop hosted by the Floer Center of Geometry and funded by the Bochum-Cologne SFB collaboration program CRC/TRR 191 "Symplectic Structures in Geometry, Algebra and Dynamics”.

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SCHEDULE:


Thursday

15:15-16:15 G. Staffilani - "How much math do you need to know to solve an initial value problem? I"

16:15-17:00 Coffee break

17:00-18:00 A. Figalli - "Regularity of interfaces in phase transitions via obstacle problems I"



Friday

15:15-16:15 A. Figalli - "Regularity of interfaces in phase transitions via obstacle problems II"

16:15 - 17:00 Coffee break

17:00-18:00 G. Staffilani - "How much math do you need to know to solve an initial value problem? II"


ABSTRACTS:

G. Staffilani - "How much math do you need to know to solve an initial value problem?"

In these lectures I will present some recent results concerning periodic solutions to nonlinear Schrodinger equations, and in doing so I will introduce a variety of mathematical techniques that range from harmonic and Fourier analysis to dynamical systems, from number theory to probability.
I will start with a derivation of the nonlinear Schrodinger equation from a many body system, and I will discuss how Hamiltonian structures can now be mapped through this derivation process. I will then move to the study of the dynamics of associated initial value problems for long time and for time near zero, and I will show how deep elements of Fourier analysis and more soft ideas from dynamical systems are fundamental to work through this analysis. I will finish by introducing a more probabilistic approach, that goes back to work of Lebowitz-Rose-Speer and Bourgain, that will allow us to view the initial value problem as a statistical ensemble of infinite dimension with an invariant Gibbs measure. This type of approach has opened new and exciting directions that are connecting ideas from stochastic PDE with the more deterministic ones from dispersive PDE.



A. Figalli - "Regularity of interfaces in phase transitions via obstacle problems"

The so-called Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase change, for example ice melting to water. An important goal is to describe the structure of the interface separating the two phases. In its stationary version, the Stefan problem can be reduced to the classical obstacle problem, which consists in finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. The aim of these lectures is to give a general overview of the classical theory of the obstacle problem, and then discuss recent developments on the structure of interfaces, both in the static and the parabolic settings.



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Anyone is welcome to attend!

There is no formal registration, but please send an email to Frau Minzlaff (Corina Minzlaff) so that we can estimate the number of participants. Everyone is welcome to join us for a dinner on Thursday evening. In this case plase contact Corina Minzlaff before 8th June 2020.

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HOTELS:

Here are some of the hotels in Bochum, please contact Frau Minzlaff if you would like assistance with booking a room.

Mercure Hotel Bochum City - conveniently located next to central station, large rooms, but not cheap (ca. 92 Euro incl. breakfast).

Hotel Claudius - a central but quiet location in Bochum, only about 700 m away from central station, this modern hotel offers stylish rooms, a varied breakfast buffet and a terrace.(ca. 85 Euro incl. breakfast).

Ibis Styles und Ibis Bochum Zentrum - next to central station, small rooms, good price but nothing special - Ibis Bochum Zentrum is probably a bit more quiet (ca. 67 incl. breakfast).

Art Hotel Tucholsky in the "Bermuda triangle" (party mile), can be noisy at night, but if you reserve a room to the back yard it's very fine, art hotel with funny accessoires - great breakfast, probably the most interesting hotel in the list (ca. 75 Euros incl. breakfast)

Hotel Ostmeier - a little further from central station but it is a hotel with a family atmosphere, warm hospitality and even with a wellness area and swimming pool (ca. 75 Euros for single rooms incl. breakfast).

Jugendherberge (youth hostel) Bochum again in the "Bermuda triangle", it is supposed to be very good and has differnet kinds of rooms (ca. 62 Euros for single rooms incl. breakfast)


General directions including a map of the campus can be found here .

For assistance or questions please contact Corina Minzlaff.

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We hope to see you there!



Coffee breaks will take place at the reception of the main entrance building IB, floor 01.