Related papers: Integrable Combinatorics
This is a survey of open problems in different parts of combinatorial and additive number theory. The paper is based on lectures at the Centre de Recerca Matematica in Barcelona on January 23 and January 25, 2008.
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
These are the lecture notes of a course given by the first author on December 27, 2012 - January 4, 2013, held at the Academy of Mathematics and Systems Science Chinese Academy of Sciences in Beijing.
In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.
The plenary presentations of the conference are summarised, highlighting some aspects that were of particular interest and attempting to link a few of the topics covered. Particular emphasis is placed on the problem of deep-inelastic…
The constraints arising for a general set of causal relations, both classically and quantumly, are still poorly understood. As a step in exploring this question, we consider a coherently controlled superposition of "direct-cause" and…
We survey several problems related to logical aspects of quantum structures. In particular, we consider problems related to completions, decidability and axiomatizability, and embedding problems. The historical development is described, as…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
Further formulas are presented involving quantum mechanics, thermodynamics, and integrable systems. Modifications of dispersionless theory are developed.
These notes illustrates the power of formulating ideas of commutative algebra in a homotopy invariant form. They can then be applied to derived categories of rings or ring spectra. These ideas are powerful in classical algebra, in…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were…
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…
This article, intended for a general mathematical audience, is an informal review of some of the many interesting links which have developed between quantum cohomology and "classical" mathematics. It is based on a talk given at the Autumn…
This review article discusses recent progress in understanding of various families of integrable models in terms of algebraic geometry, representation theory, and physics. In particular, we address the connections between soluble many-body…