Innovating Works

CARPE

Financiado
Combinatorial Applications of Random Processes and Expansion
The concepts of Randomness and Expansion are pervasive throughout Mathematics and its applications to many areas of Science and Engineering. The mathematical study of Expansion can be traced back to the ancient Greeks and of Proba... The concepts of Randomness and Expansion are pervasive throughout Mathematics and its applications to many areas of Science and Engineering. The mathematical study of Expansion can be traced back to the ancient Greeks and of Probability to the analysis (e.g. by Fermat and Pascal) of games of chance. In the modern era, both concepts are influential in many areas of Mathematics (this proposal will emphasise Combinatorics and Probability, and also touch on Analysis, Geometry, Topology, Number Theory and Theoretical Computer Science). Within Science and Engineering, topics related to the mathematical problems covered in this proposal include Approximation Algorithms (Counting and Sampling), Statistical Physics (Magnetism, Lattice Gases, Polymer Models), Mathematical Biology (Epidemiology), Control Theory and Fluid Flow. My recent and ongoing research has generated several exciting new ideas and methods. The most recent of these, the Cluster Expansion Method (work with Matthew Jenssen), is a far-reaching program to apply a classical tool from Statistical Physics to developing methods for describing the typical structure of models such as random homomorphisms from a discrete torus. Another exciting recent technique, Global Hypercontractivity (work with Noam Lifshitz, Eoin Long and Dor Minzer), is a structural refinement of the classical hypercontractivity theorem; we will generalise many of its applications to Mathematics and Computer Science and give several new applications, e.g. in Extremal Combinatorics (via the Junta Method). I will also develop new Absorption techniques to answer constructive mathematical questions that seem beyond the reach of Randomised Algebraic Construction (a method I developed to solve Steiner's 1852 question on the Existence of Designs). ver más
30/06/2026
UOXF
2M€
Perfil tecnológico estimado
Duración del proyecto: 73 meses Fecha Inicio: 2020-05-06
Fecha Fin: 2026-06-30

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2020-05-06
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-2019-ADG: ERC Advanced Grant
Cerrada hace 5 años
Presupuesto El presupuesto total del proyecto asciende a 2M€
Líder del proyecto
THE CHANCELLOR MASTERS AND SCHOLARS OF THE UN... No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5