European Companies Search Engine
UK funding (£206,085): Polyhedral perspectives on combinatorial Hodge theory Ukri17 Apr 2025 UK Research and Innovation, United Kingdom
Overview
Text
Polyhedral perspectives on combinatorial Hodge theory
| Abstract | The Hodge theory of matroids (also known as combinatorial Hodge theory) provides new approaches to old combinatorial problems, by leveraging ideas that previously proved useful in algebraic geometry. Many remarkable instances of this success lie at the core of June Huh's work on matroid inequalities. The polyhedral perspective on matroids welcomes a new paradigm: how do polyhedra relate to the Hodge theory of matroids? Several problems regarding matroids, including positivity conjectures for Kazhdan-Lusztig polynomials of matroids and Speyer's fvector conjecture, can be phrased both in the language of polytopes and the language of Hodge theory. In the recent years, independently the fellow and the supervisor have been working on problems revolving around these two frameworks, but driven by different motivations. Part of this proposal is to train the fellow in new methods in this area such as the "tautological classes of matroids" and techniques in the K-theory of matroids such as equivariant localization. The goal of this proposal is to investigate the interplay between the Hodge-theoretic and the polyhedral frameworks, with specific aims towards certain open problems that lie in the core of both of them. Special attention will be paid to i) inequality-type results, which are a major motivation for problems regarding matroids, and ii) valuations and matroid polytope subdivisions, in particular because of the subtle and impactful interplay with the rapidly developing area of tropical geometry. |
| Category | Fellowship |
| Reference | EP/Z003008/1 |
| Status | Active |
| Funded period start | 01/08/2025 |
| Funded period end | 31/07/2027 |
| Funded value | £206,085.00 |
| Source | https://gtr.ukri.org/projects?ref=EP%2FZ003008%2F1 |
Participating Organisations
| Queen Mary University of London |
The filing refers to a past date, and does not necessarily reflect the current state. The current state is available on the following page: Queen Mary University of London, London.
The visualizations for "Queen Mary University of London - UK funding (£206,085): Polyhedral perspectives on combinatorial Hodge theory"
are provided by
North Data
and may be reused under the terms of the
Creative Commons CC-BY license.
