A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Notes on a theorem with broad applications in dynamical systems.
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 to sketch a proof of Giroux correspondence between open book decompositions of t…
This paper surveys a few aspects of the global theory of wave equations. This material is structured around the contents of a minicourse given by the second author during the CMI/ETH Summer School on evolution equations during the Summer of 2008.
Survey on non-positively curved cube complexes and geometric group theory.
Lectures given at the summer school on Algebraic Groups, Goettingen, June 27 - July 15 2005
This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.
The source of these notes is a series of lectures given at the CIMPA's summer school "Recent Topics in Geometric Analysis".
Course on market microstructure models for students.
These notes from the 2014 summer school Quantum Topology at the CIRM in Luminy attempt to provide a rough guide to a selection of developments in Khovanov homology over the last fifteen years.
Survey on curvature bounds and isoperimetric inequalities.
These are lecture notes from a series of lectures at the SMF summer school on "Geometric and Quantum Topology in Dimension 3", June 2014. The focus is on Heegaard Floer homology from the perspective of sutured Floer homology.
These notes have been prepared as reading material for the mini-course that the author gave at IMS, National University of Singapore, as part of the "Summer school on the moduli space of Higgs bundles".
The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional Topology, Trieste Italy 2001
Lectures on using randomness in numerical linear algebra.
Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their central extensions, and positive energy representations.
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop "Quantum Groups and Gravity" at the University of Waterloo, April 2016.
The goal of this article is to give an elementary introduction to Dirac geometry and group-valued moment maps, via pure spinors. The material is based on my lectures at the summer school on 'Poisson geometry in Mathematics and Physics' at Keio University, June 2006.
These notes briefly summarize the lectures for the Summer School "Optimal transportation: Theory and applications" held by the second author in Grenoble during the week of June 22-26, 2009. Their goal is to describe some recent results on Brenier's variational models for incompressible Euler equation.
Survey on complex Monge-Ampère equations in Hermitian contexts.
These notes are based on a series of five lectures given at the 2009 Villa de Leyva Summer School on Geometric and Topological Methods for Quantum Field Theory. The purpose of the lectures was to give an introduction to differential-geometric methods in the study of holomorphic vector bundles on a compact connected Rie…
Heat semigroups used to solve geometric inequalities on manifolds.
Study on spheres in simply-connected 4-manifolds with abelian complements.
We present a short overview on the strongest variational formulation for gradient flows of geodesically -convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer…
These are lecture notes of the Summer school on the geometry of differential equations held in Nordfjordeid, Norway in 1996. They cover geometric structures related to scalar second order ODEs, the construction of the associated Cartan connection, techniques for computing invariants of differential equations starting f…
Lecture notes on advanced geometry equations and subvarieties.
The materials accompany a lecture short course presented at the 2011 Park City Mathematics Institute, Graduate Summer School on Moduli Spaces of Riemann Surfaces. The lectures were part of/coordinated with an overall program, including lectures by Ursula Hamenstadt on Teichmueller Theory, Andy Putman on Mapping Class a…
Notes on harmonic maps between manifolds, existence and regularity covered.
These lecture notes, which were designed for the Summer School "Heegaard-Floer Homology and Khovanov Homology" in Marseilles, 29th May - 2nd June, 2006, provide an elementary introduction to Khovanov homology. The intended audience is graduate students with some minimal background in low-dimensional and algebraic topol…
Explains optimal functional inequalities, focusing on Sobolev and fractional Sobolev.
Lecture notes on gauge theory for manifold invariants.
Teaches Dirac operators for geometry and topology.
These are the lecture notes for my course at the 2011 Park City Mathematics Graduate Summer School. The first two lectures covered the basics of the Torelli group and the Johnson homomorphism, and the third and fourth lectures discussed the second cohomology group of the level p congruence subgroup of the mapping class…
These are notes from lectures given at the Clay Institute Summer School on "Floer homology, gauge theory and low-dimensional topology" (Budapest, 2004). The first part describes as background some of the geometry of symplectic fibre bundles and their monodromy. The second part, overviewing joint work with Paul Seidel, …
Kempe discusses NTK approach to machine learning problems.
Introduces supermanifolds and supersymmetry for mathematicians.
Solla discusses neural processing using statistical physics and Bayesian methods.
Lectures on link homology and its algebraic/geometric models.
Lecture notes on a conjecture about affine manifolds' Euler characteristics.
The following are expanded lecture notes for the course of eight one hour lectures given by the second author at the 2014 summer school Asymptotic Analysis in General Relativity held in Grenoble by the Institut Fourier. The first four lectures deal with conformal geometry and the conformal tractor calculus, taking as p…
This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the following aspects of integrable non-Hamiltonian systems: local and semi-local normal …
These notes are adapted from two talks given at the 2004 Clay Institute Summer School on Floer homology, gauge theory, and low dimensional topology at the Alfred Renyi Institute. We will quickly review what we do and do not know about the existence and uniqueness of smooth and symplectic structures on closed, simply-co…
The quantum differential equations can be regarded as examples of equations with certain universal properties which are of wider interest beyond quantum cohomology itself. We present this point of view as part of a framework which accommodates the KdV equation and other well known integrable systems. In the case of qua…
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 1-10, 1997. In the published version, an epilogue of recent developments and many ne…
These lecture notes, based on a course given at the Zurich Clay Summer School (June 23-July 18, 2008), review our current mathematical understanding of the global behaviour of waves on black hole exterior backgrounds. Interest in this problem stems from its relationship to the non-linear stability of the black hole spa…
Lectures on deep learning properties in infinite and large-width networks.
Explains Higgs bundles and their applications in gauge theory.
Witten-Helffer-Sjöstrand theory is an addition to Morse theory and Hodge-de Rham theory for Riemannian manifolds and considerably improves on them by injecting some spectral theory of elliptic operators. It can serve as a general tool to prove results about comparison of numerical invariants associated to compact manif…
This paper explains a 2-form on moduli spaces using quasi-Hamiltonian and Dirac geometry.