Tomorrow I departure for the next destination - Valladolid (Spain) for a French-Spanish Workshop on Evolution Problems (FSWEP16). This meeting will be hosted by imUVa and Universidad de Valladolid. The Programme can be seen here. I would like to thank the organizers for giving me an opportunity to speak there. My talk will be devoted to the derivation of Galilean invariant and energy-consistent long wave models.
During these two weeks (1st – 14th of April 2016) I will be in Curitiba, Brazil to deliver some lectures on the Numerical Analysis at a PhD school in PUCPR University. I found on YouTube a short video presenting this University:
The Lecture notes are already available. They will be probably updated in the nearest future to the latest version (including some minor corrections and perhaps some new material):
Otherwise, recently with Didier Clamond we submitted a new mauscript where we report the multi-symplectic structure for the Green-Naghdi-type system describing long internal waves evolution. It seems that this system was derived for the first by E. Barthélémy (1989) in his PhD thesis done at the University of Grenoble. For simplicity, we adopt the rigid lid approximation, but the multi-symplectic structure can be generalized to the free surface case as well. The preprint is already freely available to download:
Any comments and suggestions are welcome!
Finally, yesterday with my collaborators from the University of Nice we submitted our manuscript on the construction of singular solitary wave solutions using the classical Phase Plane Analysis (PPA) and some methods from effective Algebraic Geometry.
This work was presented in many seminars from Japan (Yokohama) to Russia (Novosibirsk) and Austria (Linz). So, now you can find all the details about computations in our preprint available at all popular preprints servers:
Recently I had to travel from Bucharest to Lyon (with a connecting flight at Istanbul). Arguably the best thing to do during a flight is to read. So, during my recent flights I read the following interesting article that I am pleased to recommend to you:
The reference is a little bit long, but it includes a lot of interesting historical information. Finally, I can say that after reading it I have an impression to have understood something about Quantum Chaos (QC)! :) In particular, you will learn that QC appears in three different kinds. I also had an impression that this research topic is essentially open. Very little is known about genuine QC.
Currently there is a general excitement (both among the scientists and in mass media) about the detection of gravity waves. Certainly it is an important breakthrough in technology and also in Signal Processing (yes, signal processing is responsible at least for half of the detection success, the description of employed algorithms can be found here). However, for me this event is another confirmation of a tremendous gap which exists between the theoretical and experimental physics today (and possibly until forever). The state of the art in experimental physics today (2016) corresponds to the state of the art of theoretical physics in 1916. Theoretical physicists work today on the structure of space and time on Planck’s scales (i.e. ~ 10^{-33} cm / 10^{-44} s). There are some reasons to think that most probably we shall never be able to access experimentally to these scales.
On a more positive side, I would like to share another article from Inference Review, devoted to Alexander Grothendieck. This person for me is a symbol of the scientific revolution. The article is available both in French and in English for your convenience:
P. Cartier. Alexander Grothendieck. Un pays dont on ne connaîtrait que le nom, Inference Review, 1(1), 2014
P. Cartier. Alexander Grothendieck. A Country Known Only by Name, Inference Review, 1(1), 2014
Many fields of Mathematics (and of Science in general) wait for their A. Grothendieck!