Workshop on New Directions for the Tutte Polynomial: Extensions, Interrelations, and Applications

Tutte多项式是一个与图形相关的多项式，它以代数方式编码图形的结构信息。近年来，图多项式领域的新发展激增，其中许多发展是由数学内外的其他科学研究领域的应用所驱动的。图特多项式无疑是所有图多项式中研究最深入和最重要的，而且许多（如果不是大多数的话）其他图多项式在某种程度上与图特多项式有关。Tutte多项式有大量与之相关的工作，涉及多个领域，在图论、拓扑学、几何、结理论、生物学、物理学甚至社会学等领域都有广泛的应用。有整本书都是关于图特多项式的单个面；例如，在专业领域，如色多项式、流动和可靠性，以及Tutte多项式的其他公式，如Potts模型，物理学中重要的统计力学模型。本次研讨会的目的是汇集专家在许多广泛的性质和应用的Tutte多项式。这一领域的进展往往是独立发展的，每一个都有自己的特定应用，但是，因为Tutte多项式是所有这些研究的核心，所以当技术转移时，经常会在一个领域取得成果，然后在另一个领域取得突破。本次研讨会将提供一个论坛，有效地分享有关的想法、技术和应用。它还将通过交流一系列开放的问题和基于应用的目标来关注该领域，以促进未来对Tutte多项式及其跨学科应用的研究。

The Tutte polynomial is a polynomial associated with a graph that algebraically encodes structural information about the graph. Recent years have seen a surge of new developments in the area of graph polynomials, with many of these developments being driven by applications to other areas of scientific research, both within mathematics and outside of it. The Tutte polynomial is unquestionably the most heavily studied and important of all graph polynomials, and many, if not most, other graph polynomials are related to the Tutte polynomial in some way.The Tutte polynomial has a vast body of work associated with it, across multiple fields, with applications in a wide range of other areas encompassing graph theory, topology, geometry, knot theory, biology, physics, and even sociology. There are entire books on just single facets of the Tutte polynomial; for example, on specialisations such as the chromatic polynomial, flows, and reliability, as well as on other formulations of the Tutte polynomial such as the Potts model, an important statistical mechanics model in physics. The purpose of this workshop is to bring together experts in the many wide-ranging properties and applications of the Tutte polynomial. Advances in this area tend to develop independently, each for their own particular application, but, because the Tutte polynomial is at the heart of all these various investigations, very frequently results in one field then lead to breakthroughs in another when the techniques are transferred. This workshop will provide a forum for effective sharing of related ideas, techniques and applications. It will also focus the field by communicating a set of open problems and applications-based objectives for future research on the Tutte polynomial and its applications across disciplines.