Prof. Dr. Edriss S. Titi, University of Cambridge, Texas A&M University and
Weizmann Institute of Science
Title: Turbulent Flows and the Navier-Stokes Enigma: A Mathematical Challenge
Abstract: Turbulence is one of the most complex and captivating phenomena in classical physics - an enduring challenge that has fascinated mathematicians, physicists, engineers, and computational scientists alike. While chaos theory emerged in the late 20th century to study seemingly unpredictable behavior across various scientific fields, turbulence has remained the ultimate, elusive prize.
The ability to understand, predict, and control turbulence has profound economic and industrial implications. From reducing drag in cars and airplanes to designing more efficient engines and improving weather and climate forecasts, the stakes are high.
At the heart of turbulence lies the Navier-Stokes equations, which govern the fluid motion. In regimes of high Reynolds numbers - where nonlinear advective forces overwhelm viscous effects - these equations describe the turbulent behavior of fluids. Despite their central role in modeling everything from jet streams to climate systems, the question of whether smooth solutions to the three-dimensional Navier-Stokes equations persist for all time remains unresolved.
Even today, accurate simulations of turbulent flows lie far beyond the reach of the most advanced supercomputers. In this talk, I will introduce the major hurdles faced by various scientific communities in tackling this grand challenge, with a particular focus on the rigorous mathematical foundations of turbulence - explained in accessible, layman-friendly terms.

Prof. Dr. Robert Denk, University of Konstanz
Title: $L^p$-Perspectives on Deterministic and Stochastic Evolution Equations
Abstract: Nonlinear parabolic partial differential equations can often be studied effectively through the analysis of associated operators on $L^p$-Sobolev spaces.
In this talk, we describe how techniques from function space theory and harmonic analysis yield fundamental properties of linearized operators, including maximal $L^p$-regularity and a bounded $H^\infty$-calculus. These tools provide a robust framework for proving well-posedness and regularity for both deterministic and stochastic partial differential equations. We begin with simple examples to illustrate the main concepts and then discuss applications from mathematical physics, such as free boundary problems in fluid mechanics and the stochastic primitive equations.