Related papers: Topological Complexity of omega-Powers : Extended …
This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.
We analyse omega-categorical precompact expansions of particular omega-categorical structures from the viewpoint of amenability of their automorphism groups. The main result of the paper corrects and simplifies Section 3.2 of the first…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
This is an update on, and expansion of, our paper Open problems on $\beta\omega$ in the book Open Problems in Topology.
Let $\Omega$ be a smooth real analytic submanifold of a complex manifold $X$. We establish and study the link between the following 3 subjects: 1) topological properties of smooth families of attached analytic discs, the manifold $\Omega$…
We use the Sigma^1_3 absoluteness theorem to show that the complexity of the statement "(omega,E)$ is isomorphic to an initial segment of the core model" is Pi^1_4, and that the complexity of the statement "(omega,E)$ is isomorphic to a…
We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
This is an informal survey of progress in Weihrauch complexity (cf arXiv:1707.03202) in the period 2018-2020. Open questions are emphasised.
This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.
We develop a theory of k-partitions of the set of infinite words recognizable by classes of finite automata. The theory enables to complete proofs of existing results about topological classifications of the (aperiodic) omega-regular…
This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…
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.
This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichm\"uller Theory and Mapping Class Groups", 2…
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
This paper presents a method to analyze the powers of a given trilinear form (a special kind of algebraic constructions also called a tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication. Compared with…