tumpach"at"math.cnrs.fr
My Habilitation Defense took place on December, 9, 2022, at 14:30 in Lille University, Laboratoire Painlevé, Bâtiment M3, salle de visioconférence.
Lectures on Infinite-dimensional Geometry Slides Exercises Lecture Notes
financed by FWF Mozart Grant I-5015 N and WPI
On April 13, 2021, I gave a talk on Banach Poisson-Lie groups in Delft Analysis Colloquim and Seminar. In the first part of this talk, we introduced the theory of Poisson-Lie groups and related objects. It was addressed to a wide audience and do not required specialized background. The example of the unitary group U(n) served as our reference example. The second part of the talk is devoted to the study of particular examples of Banach Poisson-Lie groups related to the Korteweg-de-Vries hierarchy.
We are given a talk on Infinite-dimensional Geometry : Theory and Applications at 15th International Young Researchers Workshop on Geometry, Mechanics, and Control on December 1, 2 and 3, 2020. If you want to learn about Nash-Moser Theorem, register here
Our paper on Banach Poisson-Lie groups has been published in Communication in Mathematical Physics. See here.
The theory of Banach Poisson--Lie groups that we intend to explore is a new concept in the context of infinite-dimensional geometry. Extension to the Fréchet context will allow to study Hamiltonian systems coming from gauge theories. The analysis of Poisson structures and new integrable systems associated to the restricted Grassmannian using modern geometrical tools is part of the project. This study will allow to increase the understanding of Poisson geometry in the infinite-dimensional setting, and find new links to other known problems. See here.
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.
I'm an 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, I am working at Institut CNRS Pauli, UMI 2842, Vienna where I am PI of FWF Project I-5015N.
You can write me an email at :
tumpach"at"math.cnrs.fr
or
alice-barbora.tumpach“at”univ-lille.fr
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.
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.
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.
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
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
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.
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.
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?)
The École Normale Supérieure, is a French grande école, and a constituent college of PSL Research University, a collegiate university based in the Latin Quarter of Paris. Among former students of the École Normale Supérieure, one counts 13 Nobel Prizes, 11 Fields Medals, 2 Abel Prizes, 27 Gold Medals of the CNRS Institution, as well as a President and many Ministers and Prime Ministers.
Picture credit: © Ahmed Ben Cheikh
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 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…
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.
