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.
Improve exposition and explain metric bundle equivalence.
This is an exposition of a proof of the Madsen-Weiss Theorem, which asserts that the homology of mapping class groups of surfaces, in a stable dimension range, is isomorphic to the homology of a certain infinite loopspace that arises naturally when one applies the "scanning method". The proof given here utilizes simpli…
The exposition has been significantly altered, hopefully improved.
The aim of this text is to provide an elementary and self-contained exposition of Gromov's argument on topological overlap (the presentation is based on Gromov's work, as well as two follow-up papers of Matousek and Wagner, and of Dotterrer, Kaufman and Wagner). We also discuss a simple generalization in which the vert…
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
Minor changes in the exposition and small corrections on the previous version.
An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.
A natural occurrence of shift equivalence in a purely algebraic setting constitutes the subject matter of the following short exposition.
This is an exposition of the homological classification of actions of surface groups on the plane, in every degree of smoothness.
We give an exposition of the work of Bigelow and Krammer who proved that the Artin braid groups are linear.
This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.
This is an exposition of the theory of differentiable structures on metric measures spaces, in the sense of Cheeger and Keith.
New proof shows exotic 4-manifolds exist without complex calculations.
The goal of this paper is to offer a comprehensive exposition of the current knowledge about Heegaard splittings of exteriors of knots in the 3-sphere. The exposition is done with a historical perspective as to how ideas developed and by whom. Several new notions are introduced and some facts about them are proved. In …
A 2018 paper by A. Levine and T. Lidman outlines a proof of the following interesting result in topology of manifolds: there is a compact smooth 4-manifold with boundary such that is homotopy equivalent to but there does not exist an embedding which is a homotopy equivalence and is simplicial f…
We present a short exposition of the following results by S. Parsa. Let be a graph such that the join (i.e. the union of three cones over along their common bases) piecewise linearly (PL) embeds into . Then admits a PL embedding into such that any two disjoint cycles…
We give an exposition of Delzant's ideas extending the notion of Scott complexity of finitely generated groups to surjective homomorphisms of finitely presented groups to finitely generated groups.
Proves h-principle for loose Legendrian embeddings in contact topology.
We give an exposition of a theorem of Hirzebruch, Kodaira and Yau which proves the uniqueness of the Kahler structure of complex projective space, and of Yau's resolution of the Severi Conjecture.
These notes provide an introductory exposition of the Seiberg-Witten gauge theory. They collect the material presented in a series of seminars given by the author at the University of Milano.
Higher topos theory applied to physics.
This is a condensed exposition of the results of a future work, based on a talk of the second author at the Oberwolfach workshop "Poisson Geometry", April 30--4 May 2007.
This is an exposition of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The original work appeared in [1].
Simplified proof for Cheeger's isoperimetric constant.
In these notes we give an exposition of a result of G. Tian, which says that a Fano surfaces admits a Kahler-Einstein metric precisely when the Lie algebra of holomorphic vector fields is reductive.
In the present work we are going to give a formal exposition of the ribbon graphs topic based on notes of Labourie \cite{Lab}, since is difficult to find as such in the literature.
After a detailed introduction including new examples, we give an exposition focusing on the Riemannian cases of the positive mass, Penrose, and ZAS in- equalities of general relativity, in general dimension.
This is an exposition of aspects of the result of Daskalopoulos and Sesum that any 2-dimensional complete noncompact ancient solution to Ricci flow with bounded positive scalar curvature and finite width must be the cigar soliton.
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are discussed.
We give an exposition, following joint works with J.-C. Zambrini, of the link between Euclidean Quantum Mechanics, Bernstein processes and isovectors for the heat equation. A new application to Mathematical Finance is then discussed.
This note is an exposition of Waldhausen's proof of Waldhausen's Theorem: the three-sphere has a single Heegaard splitting, up to isotopy, in every genus. As a necessary step we also give a sketch of the Reidemeister-Singer Theorem.
This paper has been withdrawn by the authors, because it has been made obsolete by the detailed expositions in our papers in arXiv:0812.4885 (the mathematics part) and arXiv:0812.4737 (the economics part).
We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on their scalar curvatures
We give an exposition of a formula of Daskalopoulos, Hamilton and Sesum for solutions to the Ricci flow on the 2-sphere. This is one of several estimates used by them to classify ancient solutions on the 2-sphere.
This paper will be an exposition of the Kauffman bracket polynomial model of the Jones polynomial, tangle methods for computing the Jones polynomial, and the use of these methods to produce non-trivial links that cannot be detected by the Jones polynomial.
This is a short, elementary survey article about taut submanifolds. In order to simplify the exposition, we restrict to the case of compact smooth submanifolds of Euclidean or spherical spaces. Some new, partial results concerning taut 4-manifolds are discussed at the end of the text.
These notes are based on a series of lectures given by the first author at the school of `Poisson 2010', held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded manifolds, cohomological vector fields, graded symplectic structures, reduction and the AKSZ-formalism.
This paper provides an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. The exposition is designed to be comprehensible to people without any prior knowledge of the subject.
We present an axiomatic/synthetic account of the Huygens Principle of wave fronts. The primitive notions are "touching", and (a weak notion of ) metric. The paper simplifies some of the exposition of the author's "Metric spaces and SDG", Theory and Appl. of Categories 32 (2017), 803-822
We develop the theory of Berezin-Toeplitz operator on any compact symplectic prequantizable manifold from scratch. Our main inspiration is the Boutet de Monvel-Guillemin theory, that we simplify in several ways to obtain a concise exposition. A comparison with the spin-c Dirac quantization is also included.
Poisson and symplectic structures discussed in lecture notes.
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary con…
The goal of the paper is an exposition of the simplest -TQFTs in a sense following a pictorial approach. In the end, we fell short on details in the later sections where new results are stated and proofs are outlined. Comments are welcome and should be sent to the 4th author.
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing open problems given in problem sessions in the workshop and seminars on `Invariants of Knots and 3-Manifolds' held at Kyoto in 2001.
This is primarily an exposition, combining work of several authors (Curtis, Hsiang, Freedman, Stong, Matveyev, and Bizaca), of the proof that a smooth 5-dimensional h-cobordism between simply connected 4-manifolds is a product off of a contractible piece which itself is diffeomorphic to the 5-ball.
The adaptive processing of graph data is a long-standing research topic which has been lately consolidated as a theme of major interest in the deep learning community. The snap increase in the amount and breadth of related research has come at the price of little systematization of knowledge and attention to earlier li…
A simplified proof of the Alexander-Conway polynomial exists.
This paper is an exposition of heuristics related to Witten's functional integral, relating it to Vassiliev invariants and to the Kontsevich integrals that can be used to produce Vassiliev invariants of knots and links.In particular, we give a simplified version of the appearance of the Kontsevich integrals in the pert…