The job of a citizen is to keep his mouth open.
by Günter Grass

Thơ con cóc

Trong lúc chưa viết xong bài về giao ban năm con rồng, tạm chưng ra đây 1 bài thơ con cóc cho vui:

Mấy cụ ăn trên ngồi trốc

Mặc cho dân tình kêu than đói khổ

Công lao là của các cụ

Bon cu li kia được tích sự gì

Viện Toán sẽ thành viện … Toán Sơ Cấp !

Anh ĐNH gửi cho tôi xem cái này, không nhịn được cười, nên post lại đây:

http://vietnamnet.vn/vn/giao-duc/57527/gs-ngo-bao-chau-va–bai-toan–vuc-day-nen-toan.html co doan trich loi anh Trung: ==================== GS Ngô Việt Trung,Viện trưởng Viện Toán học:“Tương lai con em chúng ta sẽ không ra nước ngoài làm” Ngày xưa chúng ta chỉ có một Viện, nay có thêm . . . → Read More: Viện Toán sẽ thành viện … Toán Sơ Cấp !

Chết vì môn toán

Tin buồn về một cô bé học lớp 12 nhảy lầu tự tử sau khi bị cô giáo trẻ dạy toán sỉ vả liên tục 10 phút:

http://quechoa.info/2012/01/15/co-giao-qua-l%E1%BB%9Di-n%E1%BB%AF-sinh-t%E1%BB%AD-n%E1%BA%A1n/

Ở bên Tây cũng có những chuyện học sinh tự tử, hay thậm chí giáo viên tự tử, khi bị hành hạ quá mức chịu đựng . . . → Read More: Chết vì môn toán

Rn-actions on n-dimensional manifolds

last updated: 18/jan/2012

This is a particular case of integrable non-Hamiltonian systems that my student Minh is working on with me for this thesis. We want to study such systems topologically. A real integrable system of type is nothing but a -action (generated by a family of commuting vector fields) on a -dimensional manifold.

. . . → Read More: Rn-actions on n-dimensional manifolds

A* journals in mathematics, according to Aussies

(updated 21/06/2013)

While looking for journals to submit my new preprints (I prefer to submit to places where I have not published before, in order to “collect” the journals :-)), I came across the following list of A* journals in mathematics, according to the Australian Mathematical Society. I don’t know which are their selection . . . → Read More: A* journals in mathematics, according to Aussies

Smooth linearization of sl(2,R) and SL(2,R) actions ?

This is a particular case of a larger problem of linearization of Lie group and Lie algebra actions. The case of sl(2,R) and SL(2,R) is already non-trivial.

Guillemin and Sternberg gave an example of a smooth sl(2,R) action on R3 which is not linearizable.

Cairns and Ghys gave an example of a smooth SL(2,R) . . . → Read More: Smooth linearization of sl(2,R) and SL(2,R) actions ?

Tin nhanh: kiều hối 2011 đạt 9 tỷ USD ?

Số liệu lấy từ bài báo này: http://www.vietnamplus.vn/Home/Luong-kieu-hoi-nam-2011-uoc-dat-khoang-9-ty-USD/20121/121779.vnplus

Tính nhẩm ra là 1/2 sự phát triển kinh tế VN là do kiều hối mang lại !

Vì sao: Tạm cho là GDP tăng thêm 6 tỷ trong năm qua.

Với tỷ lệ ICOR = 3 cho những đầu tư tốt (và hy vọng là . . . → Read More: Tin nhanh: kiều hối 2011 đạt 9 tỷ USD ?

Applications of Nash-Moser normal form theorem ?

Project with Eva Miranda and Philippe Monnier

We have invented a “hammer” called “abstract Nash-Moser normal form theorem” and now are looking for “nails” :-)

We used our hammer for the problem of rigidity of Hamiltonian actions on Poisson manifolds (see paper in Advances Math 2012). We don’t know yet to what problems (beyond . . . → Read More: Applications of Nash-Moser normal form theorem ?

Second-order models for asset prices

I’m doing this project about 2nd-order pricing models with a PhD student of mine. The project is quite ambitious. It aims to to be better than known models (Black-Scholes, stochastic volatility, 1st-order jump models, equilibrium, etc.) and be able to explain things that can’t be explained by previous models. Potential applications include investing & . . . → Read More: Second-order models for asset prices

Topology of integrable non-Hamiltonian systems

This is the research project of a PhD student of mine. Actually the general project is sufficiently large for a number of PhD theses. There are lots of open questions in the non-Hamiltonian case.

What my student is doing is to study simplest (mostly low-dimensional) cases, and with only nondegenerate singularities:

– Systems of . . . → Read More: Topology of integrable non-Hamiltonian systems

Geometric proof of Whitehead’s lemma ?

Whitehead’s lemma says that and where is a simple Lie algebra and is a linear representation of it. I know an algebraic proof which gives an explicit formula for the homotopy operator. I’m looking for a more geometric proof (using, for example, an averaging formula). Why ? Because the explicit homotopy operator in the . . . → Read More: Geometric proof of Whitehead’s lemma ?

Nondegeneracy of simple Lie algebras of real rank 1

Work in progress with Philippe Monnier

Conn showed that compact simple Lie algebras are smoothly nondegenerate.

Weinstein showed that simple Lie algebras of real rank >= 2 are smoothly degenerate.

What about the case of real rank 1 ?

There are only 3 series of real rank 1: so(n,1), su(n,1) and sp(n,1)

(orthogonal, unitary . . . → Read More: Nondegeneracy of simple Lie algebras of real rank 1

Computation of entropy

This is a small research project that I intend to give to some master students for their memoir:

– Examples of geometric structures of zero entropy. In particular, write down the proof of the fact that linear Poisson structures have zero entropy.

– Example of positive entropy. Explicit computations. Comparison with Lyapunov exponents, Godbillon-Vey . . . → Read More: Computation of entropy