## Error message

• Notice: Undefined offset: 0 in include() (line 36 of /home/it/www/www-icts/sites/all/themes/riley/templates/views/views-view-fields--related-file-field-collection-view.tpl.php).
• Notice: Undefined offset: 0 in include() (line 36 of /home/it/www/www-icts/sites/all/themes/riley/templates/views/views-view-fields--related-file-field-collection-view.tpl.php).
• Notice: Undefined offset: 0 in include() (line 36 of /home/it/www/www-icts/sites/all/themes/riley/templates/views/views-view-fields--related-file-field-collection-view.tpl.php).
• Notice: Undefined offset: 0 in include() (line 36 of /home/it/www/www-icts/sites/all/themes/riley/templates/views/views-view-fields--related-file-field-collection-view.tpl.php).
• Notice: Undefined offset: 0 in include() (line 36 of /home/it/www/www-icts/sites/all/themes/riley/templates/views/views-view-fields--related-file-field-collection-view.tpl.php).
Infosys-ICTS Ramanujan Lectures
Speaker
Hugo Duminil-Copin (Institut des Hautes Études Scientifiques, France & University of Geneva, Switzerland)
Date & Time
09 January 2023 to 13 January 2023
Venue
Ramanujan Lecture Hall
Resources

Lecture 1

Date and time: 9 January 2023, 15:30 - 16:30

Title: Critical Phenomena Through the Lens of the Ising Model

Abstract: The Ising model is one of the most classical lattice models of statistical physics undergoing a phase transition. Initially imagined as a model for ferromagnetism, it revealed itself as a very rich mathematical object and a powerful theoretical tool to understand cooperative phenomena. Over one hundred years of its history, a profound understanding of its critical phase has been obtained. While integrability and mean-field behavior led to extraordinary breakthroughs in the two-dimensional and high-dimensional cases respectively, the model in three and four dimensions remained mysterious for years. In this talk, we will present recent progress in these dimensions based on a probabilistic interpretation of the Ising model relating it to percolation models.

Lectures 2-5

Dates and time: 10 & 11 January 2023, 11:15 - 12:05

Dates and time: 12 & 13 January 2023, 10:00 - 10:50

Title: Marginal triviality of the scaling limits of critical 4D Ising

Abstract: We will discuss the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian and its implications from the point of view of Euclidean Field Theory. Similar statements will be proven for the $λϕ^4$ fields over $R^4$ with a lattice ultraviolet cutoff, in the limit of infinite volume and vanishing lattice spacing. The proofs are enabled by the models' random current representation, in which the correlation functions' deviation from Wick's law is expressed in terms of intersection probabilities of random currents with sources at distances which are large on the model's lattice scale. Guided by the analogy with random walk intersection amplitudes, the analysis focuses on the improvement of the so-called tree diagram bound by a logarithmic correction term, which is derived here through multi-scale analysis.