Colloquium, Dept. of Mathematics and Applied Math. -- Γενικό Σεμινάριο

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Colloquium

Statistical optics of complex systems: From beam propagation through atmospheric turbulence to thermalization and thermodynamics

Abstract: We present a statistical-optics view of light in complex media, ranging from structured beam transport through atmospheric turbulence to thermodynamics and thermalization of weakly nonlinear multimode optical systems. The complexity arises either from the fluctuations of the refractive index in atmospheric turbulence or from the combination of nonlinearity with the presence of a large number of modes in optical thermodynamics.

Abstract: Generative Adversarial Networks (GANs) represent one of the most influential families of generative models. This talk will introduce the core principles of GANs and their formulation as divergence minimization problems. By employing variational (duality-based) representations of divergences, the intractable optimization problem can be reframed as a tractable two-player zero-sum game. While GANs have achieved remarkable success, training instability and convergence issues remain major challenges. To address these, we propose a general framework for constructing tailored divergences that bridge $f$-divergences and integral probability metrics, combining the stability properties of both. I will highlight key results demonstrating improved convergence and performance in challenging scenarios, such as heavy-tailed distributions and image generation. Finally, I will discuss a novel variant of GANs that naturally gives rise to Generative Gradient Flows and a corresponding Generative Particle Algorithm.