My Training

I followed the French-German bilingual School LFA in Buc, where I got a french Baccalauréat as well as a German Abitur. Then I choosed to go to Paris-Sud University in Orsay, hesitating between Mathematics, Physics and Sport. After that I was accepted at the École Normale Supérieure, where I followed the double formation in Mathematics and Physics. After my Master 2, I prepared with success the Agrégation in Mathematics, which is the highest Teaching competitive exam in France. I started my PhD in Pure Mathematics at the Ecole Polytechnique in 2001. During this period I was Teaching Assistant in Paris-Sud University. For my great pleasure, I then spent 2 years as Post-doc at the EPFL, living right at the boarder of Geneva lake.

My Current Position

Since 2007, I have a permanent position at Lille University as Assistant Professor in the Department of Mathematics, in the subgroup of Mathematical Physics.

You can write me at the following address :

Alice Barbara Tumpach
UMR CNRS 8524
UFR de mathématiques 
Laboratoire Paul Painlevé
59655 Villeneuve d’Ascq
France
									

You can also find me at my office M3 226, which is located in the Math. building M3, second floor, but you may first want to consult my Schedule or write me an email at :

barbara.tumpach “at” math.univ-lille1.fr

My Skills

I’m a specialist in Infinite Dimensional Geometry, which is a subject at the intersection of Geometry, Functional Analysis and Algebra, and a fundamental backstage subject for finite dimensional Geometry, Optimization, Probability and Physics. I work on the Theory as well as on Applications in Form Recognition and Garment Design.

Teaching is one of my most intense pleasure, and I’m quite disappointed that the french system gives so few recognition to Teaching Skills.

Having 3 Kids and a lot of Projects, I developed Managerial Skills for Group dynamics, Walking Around Techniques and Time optimization.

My new paper is online! On the Bruhat-Poisson structure of the restricted Grassmannian, generalized Poisson-Lie groups and the Korteweg-de Vries hierarchy. It took me 6 years of gestation, so please have a look here! See also my Research.

Garment Design

Understanding how the stretch of fabric influences the design of a pattern is one of my goal in life. Mathematically this is related to quasi-conformal maps.

Banach Poisson Lie-Groups

Finite-dimensional Poisson Lie-groups come into pairs, one acting on the other. In the infinite-dimensional context the landscape is full of mines...See here.

Queer Poisson Brackets

In the infinite dimensional context, the Leibniz rule does not imply the existence of a Poisson tensor for a Poisson bracket. Weird, isn't it? See here

Form recognition

Using Riemannian geometry to classify automatically surfaces by grouping together the surfaces that are close is a nice application of infinite-dimensional geometry. See here

Some talks I gave recently. See also my Schedule.

Banach Poisson Lie groups, the KdV equation and the restricted Grassmannian

The talk is at the interface of Analysis, Geometry and Fonctional Analysis. There is a link between the KdV hierarchy, the restricted Grassmanian, and the triangular truncation of an operator acting on an Hilbert space. The KdV equation is a completely integrable system, and the link to the restricted Grassmannian is known since the work of Segal and Wilson in 1985. The restricted Grassmannian is a Hilbert manifold, analogous to the space of p-dimensional subspace in an n-dimensional ambient space. The Poisson structure of the latter, with symplectic leaves the Schubert cells, has been explained by Lu and Weinstein in 1990 via the action of a Poisson-Lie group. It is therefore natural to ask whether the KdV equation comes from the action of a Banach Poisson-Lie group on the restricted Grassmannian. This infinite-dimensional context raise problems from Functional Analysis related to triangular truncations of trace class operators. See here.

Riemannian metrics on Shape Spaces of curves and surfaces

The talk is directed to a large audience of scientists, with some background in basic differential geometry. The Shape space of (unparameterized) curves (or surfaces) can be interpreted either as a quotient space or as a section of the Preshape space of parameterized curves (or surfaces). Starting from a diffeomorphism-invariant Riemannian metric on Preshape space, these two different interpretations lead to different Riemannian metrics on Shape space. Another possibility is to start with a degenerate Riemannian metric on Preshape space, with degeneracy along the orbits of the diffeomorphism group. This leads to a framework where the length of a path of curves (or surfaces) does not depend on the parameterizations of the curves (or surfaces) along the path.

How to make a computer read our lips using infinite-dimensional Geometry

The talk is directed to high school student. Observing the movement of the outline of our lips when we are talking, and trying to guess the words we are saying without hearing them is at the base of lip-reading. Make a computer lip-read is a challenging mathematical problem, that invites us to a trip in an infinite-dimensional world. But the trip can not be carried out without effort! In order to take part in it, one has to climb the ladder of abstraction : rung after rung new worlds are discovered, build with so familiar objects...Each of these worlds has a surprise in store, triangles whose sum of angles is greater than 180 degree, spaces where two different points are at distance 0 of each other... After this trip, we will be quite happy to recover our familiar 3-dimensional space (or 4-dimensional?)

Some places I visited during my studies. See also my CV.

Ecole Polytechnique, Palaiseau, France.

The Ecole Polytechnique is an engineering school under military status, with an important research centre. Among former students, one count the mathematicians Cauchy, Coriolis, Poincaré, Poisson and Mandelbrot, the physicists Becquerel, Carnot, Fresnel, 3 Nobel Prizes, 1 Fields Medals and 3 Presidents.

Paris-Sud University, Orsay, France

Paris-Sud University is probably the best French University for education and research. But aside of its training level, I was attracted by the large number of sports facilities at the disposal of students : a university swimming pool, a horse-riding centre, 2 professional dance studios, tennis courts, a 300m2 dojo, 2 gyms with the latest weightlifting equipment, many sports halls, and outdoor sports grounds. All this in a green environment not far from Paris…

EPFL, Lausanne, Switzerland

The École polytechnique fédérale de Lausanne (EPFL) is a research institute and university in Lausanne, Switzerland, that specializes in natural sciences and engineering. It is one of the two Swiss Federal Institutes of Technology, and it has three main missions: education, research and technology transfer at the highest international level. EPFL is widely regarded as a world leading university. The QS World University Rankings ranks EPFL 12th in the world across all fields in their 2017/2018 ranking, whilst Times Higher Education World University Rankings ranks EPFL as the worlds 11th best school for Engineering and Technology.

Some useful links…