Statistical Physics of Generative Diffusion
Generative models, in which one trains an algorithm to generate samples ‘similar’ to those of a data base, is a major new direction developed in machine learning in the recent years. In particular, generative models based on diffusion equations have become the state of the art, notably for image generation. However, the reasons for this spectacular technological success are not well understood, and neither are its limitations.
After an introduction to this topic, the talk will focus on the behavior of generative diffusion in the high-dimensional limit, where data are formed by a very large number of variables. Using methods from statistical physics, we explain the various dynamical regimes that occur during the generation.
Friday, 2nd February 2024, 14:30, Aula Magna
Decoding Primordial Fluctuations
I will review our current understanding of the initial conditions of the universe, and describe what information is available from current and future measurements of cosmological correlation functions. Then I will describe a new method developed to compute and constrain the possible shapes of those correlation functions. This ``cosmological bootstrap” draws much inspiration from the modern scattering amplitudes program in flat space, and also from the conformal bootstrap of phase transitions. A thorough understanding of the fluctuations will give us insight into particle physics at very high energy scales and may provide a window into the nature of spacetime itself. Time permitting, I will describe a toy example of emergent time in cosmological correlations.
Friday, 15th December 2023, 14:30, Aula Magna
Saturons and their role in particle physics and cosmology
"Saturons" are macroscopic objects that saturate the field theoretic upper bound on microstate degeneracy. Due to this feature, saturons and black holes belong to the same universality class with common key properties. However, as opposed to black holes, saturons can emerge in renormalizable gauge theories, in the form of solitons, baryons and other bound states. After reviewing the general properties of saturons, we discuss their potential implications for particle physics and cosmology. In particular, saturons are interesting candidates for dark matter. Due to the maximal microstate entropy, the saturon dark matter can form as a result of a direct quantum transition from the radiation thermal bath. Correspondingly, they can form a superheavy dark matter at very low temperatures. Saturons can provide a new type of source for primordial black holes. They also serve as a theoretical laboratory for understanding and predicting new features of black holes that can be imprinted in gravitational radiation from black hole mergers.
Friday, 17th November 2023, 14:30, Aula C