Beyond the horizon: navigating turbulence, irregularity, and stochasticity in fluid dynamics

Fluid is one of the most omnipresent substances on the planet. Mathematical analysis of the fundamental partial differential equations of fluid dynamics such as the Navier-Stokes equations was pioneered by Leray in 1934. Gaining insights into the behaviour of the solutions to such equations is crucial for our understanding of the physical phenomena that we experience in our daily lives. Very recently, multiple breakthrough works such as the blow-up of three-dimensional Euler equations, the development of the convex integration technique, and the solution theory of singular stochastic partial differential equations, have intensified the research on the partial differential equations of fluid dynamics. Many long-standing conjectures from physicists and mathematicians have come to a resolution. This interdisciplinary conference served as a forum for leading experts, emerging early-career researchers, and under-represented groups with complementary strength to explore recent developments, exchange insights, and address key challenges in the pursuit of better understanding of various issues. Through collaborative engagement and discussions, we aspired to deepen our understanding of the intricate interplay within the phenomena of irregularity, turbulence, and stochasticity in fluid dynamics.