Related papers: Lecture notes on topological recursion and geometr…
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.
In a paper presented a few years ago, De Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes (Phys. Rev. D 56, 3329 (1997)). The purpose of this present work is to go a step…
The aim of these notes (which were partially covered in lectures given at the Peyresq Summer School on 17--22 June, 2002) is to give an introduction to some mathematical aspects of supersymmetry. Some (hopefully) original point of view are…
In the Gromov-Witten theory of a target curve we consider descendent integrals against the virtual fundamental class relative to the forgetful morphism to the moduli space of curves. We show that cohomology classes obtained in this way lie…
Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'' month at CIRM in 2004.
This is an extended abstract for a talk given at the mini-workshop "Cohomology rings and fundamental groups of hyperplane arrangements, wonderful compactifications, and real toric varieties", held in Oberwolfach, September 30-October 6,…
Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures,…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
We derive recursive equations for the characteristic numbers of rational nodal plane curves with at most one cusp, subject to point conditions, tangent conditions and flag conditions, developing techniques akin to quantum cohomology on a…
These notes are based on a series of lectures given by the author at the Centre Bernoulli (EPFL) in July 2016. They aim at illustrating the importance of the mod-$\ell$ cohomology of Deligne--Lusztig varieties in the modular representation…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
This informal introduction is an extended version of a three hours lecture given at the 6th Peyresq meeting ``Integrable systems and quantum field theory''. In this lecture, we make an overview of some of the mathematical results which…
This text is an introduction to a few selected areas of Alain Connes' noncommutative geometry written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It is an expanded version of my lectures which…
This text gives some results about quantum torsors. Our starting point is an old reformulation of torsors recalled recently by Kontsevich. We propose an unification of the definitions of torsors in algebraic geometry and in Poisson…
The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4-manifolds. In addition, we provide topological sphere theorems for compact…
The Eynard-Orantin topological recursion relies on the geometry of a Riemann surface S and two meromorphic functions x and y on S. To formulate the recursion, one must assume that x has only simple ramification points. In this paper we…
Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise,…
In this lecture we address some topological questions connected with the existence on a general spacetime manifold of diffeomorphisms connected to the identity which reverse the time-orientation.