Related papers: Christiaan Huygens and contact geometry
We consider a three dimensional liquid drop sitting on a rough and chemically heterogeneous substrate. Using a novel minimization technique on the free energy of this system, a generalized Young's equation for the contact angle is found. In…
This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September…
Notes from a course given at Oujda university, Morocco, october 2002 - march 2003 within the support of a fellowship from the Agence Universitaire de la Francophonie. These notes present a brief introduction to Connes' non commutative…
These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.
We present a picture of Lagrangean mechanics, free of some unnatural features (such as complete divergences). As a byproduct, a completely natural U(1)-bundle over the phase space appears. The correspondence between classical and quantum…
This is a survey on contact open books and contact Dehn surgery. The relation between these two concepts is discussed, and various applications are sketched, e.g. the monodromy of Stein fillable contact 3-manifolds, the Giroux-Goodman proof…
Lecture notes on Finsler Geometry
These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is…
Talk given at the First Workshop on Forward Physics and Luminosity Determination at the LHC, Helsinki, Finland, November 2000. 12 pages, 9 figures
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
Lecture notes from the Third International School on Geometry and Physics at the Centre de Recerca Matematica in Barcelona, March 26--30, 2012.
This is an expanded and updated version of a lecture series I gave at Seoul National University in September 1997. It is in some sense an update of the 1979 Griffiths and Harris paper with a similar title. I discuss: Homogeneous varieties,…
These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight…
The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…
We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the one dominating in the literature, serves also for non-trivial contact structures. In this approach Hamiltonians are no longer functions on the contact…
Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…
This survey article on Hilbert's first and second problems is adapted from a one-hour colloquium lecture given at the University of Auckland in May, 2000, just three months before the 100th anniversary of Hilbert's lecture. It includes an…
Opening Lecture at the Second Rencontres du Vietnam, October 21-28, 1995.
These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.
This paper records my opening remarks at Nobel Symposium 148, on Graphene and Quantum Matter, at Saltsj\"obaden, Sweden, in June 2010. After some broad comments on the quantum theory of matter as a frontier of physics, and some slightly…