Innovating Works

ISCoURaGe

Financiado
Interplay of structures in conformal and universal random geometry
My overall goal is to provide novel conceptual understanding of persistent challenges in mathematical physics, in light of recent discoveries of myself and others. The emphasis is especially in finding connections between differen... My overall goal is to provide novel conceptual understanding of persistent challenges in mathematical physics, in light of recent discoveries of myself and others. The emphasis is especially in finding connections between different areas, making use of my expertise at their crossroads. The first two aims concern statistical mechanics (SM) and mathematical formulations of (logarithmic) conformal field theory (CFT), on the one hand algebraically and on the other hand probabilistically. The last two aims focus on connections and interplay of structures arising in SM, such as Schramm-Loewner evolutions (SLE), with algebro-geometric formulations of CFT. Gaining conceptual understanding is fundamental for progress towards deep results. Specifically, in Aim 1, I focus on CFT correlation functions and plan to reveal non-semisimple and logarithmic behavior, poorly understood even in the physics literature. For this, e.g. hidden symmetries from my earlier work will be exploited. Aim 2 combines this with probability theory: investigations of non-local quantities in critical SM models, relating to specific CFT correlation functions and to SLE. In Aim 3, I investigate the interplay of SLE, CFT, and Teichmueller theory in terms of generalizations of so-called Loewner energy of curves. The main objective is to shed light on the hidden geometric interpretation of Loewner energy from the point of view of formulations of CFT in terms of Riemann surfaces, and eventually also to find its role within geometric quantization. To elaborate the latter goal, Aim 4 combines these ideas with related structures in the theory of isomonodromic deformations. My starting point is the observation that Loewner energy minima and semiclassical limits of certain CFT correlations are both described by isomonodromic systems. I plan to make these connections explicit and implement them in order to discover intrinsic features of the interplay of the aforementioned structures. ver más
31/12/2027
AALTO
1M€
Perfil tecnológico estimado
Duración del proyecto: 61 meses Fecha Inicio: 2022-11-07
Fecha Fin: 2027-12-31

Línea de financiación: concedida

El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2022-11-07
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-2021-STG: ERC STARTING GRANTS
Cerrada hace 3 años
Presupuesto El presupuesto total del proyecto asciende a 1M€
Líder del proyecto
AALTO KORKEAKOULUSAATIO SR No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5