Related papers: Notes on motivic infinite loop space theory
Waldhausen's algebraic K-theory machinery is applied to motivic homotopy theory, producing an interesting motivic homotopy type. Over a field F of characteristic zero, its path components receive a surjective ring homomorphism from the…
The goal of this paper is to study non-$\mathbb{A}^1$-invariant motivic cohomology, recently defined by Elmanto, Morrow, and the first-named author, for smooth schemes over possibly non-discrete valuation rings. We establish that the cycle…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
An important open question in fundamental physics concerns the nature of spacetime at distance scales associated with the Planck length. The widespread belief that probing such distances necessitates Planck-energy particles has impeded…
Spaces in the genus of infinite quaternionic projective space which admit essential maps from infinite complex projective space are classified. In these cases the sets of homotopy classes of maps are described explicitly. These results…
These notes provide an introduction toward Wilson loops in N=4 supersymmetric Yang-Mills theory with a focus toward their integrability properties. In addition to a brief discussion of exact results for the circular Wilson loop and the cusp…
Three lectures on effective field theory given at the Seventh Summer School in Nuclear Physics, Seattle June 19-30 1995.
These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this…
This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…
These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.
You may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT gravity, cohomological field theory, free…
The 1-loop effective potential in a scalar theory with quartic interaction on the space $M^{4} \times T^{n}$ for $n=2$ is calculated and is shown to be unbounded from below. This is an indication of a possible instability of the vacuum of…
These are the notes for some lectures given by this author at Harish-Chandra Research Institute, Allahabad in March 2014 for a workshop on Schur multipliers. The lectures aimed at giving an overview of the subject with emphasis on groups of…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
We evaluate one-loop finite-time amplitudes for graviton scattering in Matrix theory and compare to the corresponding amplitudes in supergravity. We find agreement for arbitrary time intervals at leading order in distance, providing a…
The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
We study finite-dimensional spaces of rational one-forms on a projective manifold by means of their integrable locus.
In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Past research on iterative learning analyzed for example many important…
These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…