Men despise religion; they hate it, and they fear it is true.
by Pascal, Blaise (1623-1662)

Computational Complexity Reading List?

I’m trying to learn a bit (or maybe more than just a bit) about computational complexity. I could download a few books which looked interesting to me:

* Agrawal & Arvind (Perspectives) 2014

* Arora & Barak (A modern approach) 2009 (I’ve read half of this book so far, and found it really very . . . → Read More: Computational Complexity Reading List?

Đại hội bố già tổ chức ở đâu (bài toán vui)?

Liên đoàn bố già Việt Nam chuẩn bị tổ chức đại hội thường kỳ, với sự tham dự của tất cả các bố già. Quy định của liên đoàn là địa điểm tổ chức phải ở một thành phố sao cho tổng độ dài các quãng đường của các bố già từ các thành . . . → Read More: Đại hội bố già tổ chức ở đâu (bài toán vui)?

A general approach to the problem of action-angle variables (new version)

Here is the new version of my invited talk

“A general approach to the problem of action-angle variables” (PDF File: AATalk2014, version 26/10/2014)

to be presented et the conference in honour of Charles Michel Marle’s 70th birthday in November 2014 in Paris.

Here is the website of the conference: http://www.imcce.fr/Equipes/ASD/person/albouy/Marle2014.html

 

 

A general approach to the problem of action-angle variables

These are the slides (preliminary version, to be revised) for a talk that I’ll give in Paris (24/11/2014) in the Conference in honour of the 80th birthday of C-M Marle. It contains  a conceptual approach to the problem of action-angle variables, with some new results (a paper is in preparation based on an old . . . → Read More: A general approach to the problem of action-angle variables

Stratified affine spaces

These are quick notes for a joint work with Ch. Wacheux

Here, by an affine manifold, we mean a paracompact manifold with a locally flat affine structure. If the manifold is of dimension n, then near each point we have a chart whose coordinate functions are affine functions, and any local affine function is . . . → Read More: Stratified affine spaces

Three lectures on singular foliations

For those who might be interested: This PDF file contains the slides of my 3-hour minicourse on singular foliations, given in the Workshop “GAP XII: Geometric Mechanics”, Internatinal Mathematical Forum of Tsing Hua University, Sanya, 10-14/March/2014:

http://zung.zetamu.net/Maths/Talks/FoliationsSanya2014.pdf

The main topic of this minicourse is the correspondence Singular Foliations <–> Nambu structures, and how . . . → Read More: Three lectures on singular foliations

Notes on random systems 2

What is a random fixed point ?

A reference: Ochs – Oseledets: Examples of  RDS on a closed unit ball without random fixed points. (So the topological fixed point theorem is NOT valid for RDS)

Definition. A random fixed point of a RDS \Phi over noise space (\Omega, \theta) (theta is the dynamics in . . . → Read More: Notes on random systems 2

Monodromy can kill global convexity!

We just got a rather surprising result in our joint research project with Christophe Wacheux (currently post-doc at EPFL) about the intrinstic convexity of singular affine spaces.

The problem is to study the intrinsic local and global convexity of the affine structure of the base space of integrable Hamiltonian systems whose singularities are nondegenerate . . . → Read More: Monodromy can kill global convexity!

Thuật toán của người mất trí nhớ

Có một bài toán “khá đơn giản” sau về vấn đề thuật toán, tôi biết chắc chắn là giải được (vì có định lý về vấn đề này), có điều tôi thử tự tìm lời giải mà loay hoay mãi chưa ra:

Có một người ở một làng bị mất trí và được cho . . . → Read More: Thuật toán của người mất trí nhớ

Geometry and Physics XII, Hainan (China), 10-14/03/2014

Next year I’ll come to Sanya, Hainan, China to attend “GAP XII”, an international conference on geometry and physics.

The organizers said they would have money to cover local expenses for a number of participants, so if anyone is interested in visiting Sanya, please contact them (or contact me if you don’t know them)

. . . → Read More: Geometry and Physics XII, Hainan (China), 10-14/03/2014

Integrable p-vector fields and singular foliations

There seems to be a lot of confusion (among my colleagues, and also of myself) concerning the relationships between singular foliations and integrable p-vector fields (a.k.a. Nambu structures). The aim of this note is to make some clarifications.

1) How to construct a singular foliation from an integrable p-vector field ?

The obvious (but . . . → Read More: Integrable p-vector fields and singular foliations

Talk at AlanFest 07/2013

 

This week I’m at the AlanFest in EPFL, Switzerland, on the occasion of Alan Weinstein’s 70th birthday. I gave  a talk on Thursday entitled:

A normalization toolbox, with applications to singular foliations

Here are the slides of my talks (with some typographical errors), for people who might be interested:

NTZ_AlanFest2013

. . . → Read More: Talk at AlanFest 07/2013

Linearization of smooth integrable systems

I’m writing down here the ideas for proving that smooth nondegenerate integrable dynamical systems are smoothly linearizable. The analytic case can be proved using analytic torus actions (my paper about that will appear in Ergodic Th Dyn Sys). I think the smooth case is also true, but the proof is much more complicated than . . . → Read More: Linearization of smooth integrable systems