Related papers: Kolmogorov and Aleksandrov in Sevan Monastery, Arm…

This is a sequel to our previous paper of oriented bivariant theory [14]. In 2001 M. Levine and F. Morel constructed algebraic cobordism $\Omega_*(X)$ for schemes $X$ over a field $k$ in an abstract way and later M. Levine and R.…

These are (not updated) notes from the lectures I gave in St.Petersburg in July of 2001. Their goal is to give an expository account of the proof of Kontsevich's combinatorial formula for intersections on moduli spaces of curves following…

I arrived in Berkeley in 1957, at which time Leo was an Acting Assistant Professor of Mathematics here. He had recently proven the "individual ergodic theorem of information theory"---a triumph---and since this was becoming central to my…

We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points and which are not conjugated to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen…

We use point contact spectroscopy (PCS) to probe the superconducting properties of electron doped $\rm{Ba(Fe_{1-x}Co_x)_2As_2}$ ($\rm{x = 0.05, 0.055, 0.07, 0.08}$) and hole doped $\rm{Ba_{0.8}K_{0.2}Fe_2As_2}$. PCS directly probes the low…

A sentence from Carl Boyer's A History of Mathematics can be interpreted so that the full brothers Nicolaus II (02/06/1695 - 07/31/1726) and Daniel Bernoulli (02/08/1700 - 03/17/1782) are the authors of the St. Petersburg paradox. The…

Given any complex Laurent polynomial $f$, $\mathrm{Amoeba}(f)$ is the image of its complex zero set under the coordinate-wise log absolute value map. We give an efficiently constructible polyhedral approximation, $\mathrm{ArchtTrop}(f)$, of…

We give here the Table of Contents and clickable links to papers of the proceedings from the workshop "Asteroseismology of Stellar Populations in the Milky Way", held in Sesto, 22-26 July 2013. The aim of this workshop was to foster…

This is expanded text of a lecture delivered by the author at the conference "Mat\'eriaux pour l'Histoire des Math\'ematiques au XX\`eme si\`ecle", which took place in Nice in January 1996. The task was to describe one area in the…

We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where…

The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov complexity with the discrete universal distribution. There are conditional versions referred to in several publications but as yet there exist no written proofs in…

The results of Iv. Prodanov on abstract spectra and separative algebras were announced in the journal "Trudy Mat. Inst. Steklova", 154, 1983, 200--208, but their proofs were never written by him in the form of a manuscript, preprint or…

The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…

We give a characterization of those Alexandrov spaces admitting a cohomogeneity one action of a compact connected Lie group $G$ for which the action is Cohen--Macaulay. This generalizes a similar result for manifolds to the singular setting…

Recently, Kolmogorov-Arnold Networks (KANs) have been proposed as an alternative to multilayer perceptrons, suggesting advantages in performance and interpretability. We study a typical binary event classification task in high-energy…

We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample…

We investigate the skew-zigzag algebras introduced by Huerfano and Khovanov. In particular, we relate moduli spaces of such algebras with the cohomology of the corresponding graph.

Professor M. C. Polivanov and I met only a few times, during my infrequent visits to the-then Soviet Union in the 1970's and 1980's. His hospitality at the Moscow Steclov Institute made the trips a pleasure, while the scientific environment…

In this paper we shall give two-sided sharp estimates of Kolmogorov numbers of embeddings of the Besov spaces with dominating mixed smoothness $S^t_{p,q}B((0,1)^d)$ into $ L_{\infty}((0,1)^d)$.

We study the relations between the notions of highness, lowness and logical depth in the setting of complexity theory. We introduce a new notion of polylog depth based on time bounded Kolmogorov complexity. We show polylog depth satisfies…