Homepage of Alice Barbora TUMPACH

tumpach"at"math.cnrs.fr

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 2021, I am an independant researcher working at Institut CNRS Pauli, UMI 2842, Vienna where I am PI of FWF Project I-5015N ``Banach_poisson lie Groups and integrable systems'' (306 768 EUR) and PAT 1179524`` Geometric Green Learning on Groups and Quotient spaces'' (420 887 EUR). I'm am also Maître de conférence at Lille University since 2007 in the Department of Mathematics, in the subgroup of Mathematical Physics. Currently on leave from Lille University.

You can write me an email at :

tumpach"at"math.cnrs.fr

or

alice-barbora.tumpach“at”univ-lille.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.

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?)