Previous Conferences & Workshops

Training a predictor to minimize a loss function fixed in advance is the dominant paradigm in machine learning. However, loss minimization by itself might not guarantee desiderata like fairness and accuracy that one could reasonably expect from a...

Blockchains that support a general contract layer (e.g., Ethereum) export the functionality of a general-purpose, ownerless, and open-access computer that can enforce property rights for digital data.  How is such functionality implemented?  Using a...

For any regularity exponent $\beta<\frac 12$, we construct non-conservative weak solutions to the 3D incompressible Euler equations in the class $C^0_t (H^{\beta} \cap L^{\frac{1}{(1-2\beta)}})$.  By interpolation, such solutions belong to $C^0_tB^{s}_{3,\infty}$ for $s$ approaching $\frac 13$ as $\beta$ approaches $\frac 12$.  Hence this result provides a new proof of the flexible side of the Onsager conjecture, which is independent from that of Isett.  Of equal importance is that the intermittent nature of our solutions matches that of turbulent flows, which are observed to possess an $L^2$-based regularity index exceeding $\frac 13$.  The proof employs an intermittent convex integration scheme for the 3D incompressible Euler equations.  We employ a scheme with higher-order Reynolds stresses, which are corrected via a combinatorial placement of intermittent pipe flows of optimal relative intermittency.

Abstract:In his seminal work, Leray demonstrated the existence of global weak solutions, with nonincreasing energy, to the Navier-Stokes equations in three dimensions. In this talk we exhibit two distinct Leray solutions with zero initial velocity...

Abstract: Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. The presence of vortex stretching is the primary source of a potential finite-time singularity...