56 PD13 Abstracts IP0 Hence the need to develop a partial regularity theory: is The SIAG/Analysis of Partial Differential Equa- it true that solutions are always smooth outside a ”small” tions Prize Lecture: Weak Solutions of the Euler singular set? The aim of this talk is first to review the Equations: Non-Uniqueness and Dissipation classical regularity theory, and then to describe some re- cent results about partial regularity. There are two aspects of weak solutions of the incompress- ible Euler equations which are strikingly different to the Alessio Figalli behaviour of classical solutions. Weak solutions are not Department of Mathematics unique in general and do not have to conserve the en- The University of Texas at Austin ergy. Although the relationship between these two aspects fi
[email protected] is not clear, both seem to be in vague analogy with Gro- movs h-principle. In the talk I will explore this analogy in light of recent results concerning both the non-uniqueness, IP3 the search for selection criteria, as well as the dissipation Waves in Honeycomb Structures anomaly and the conjecture of Onsager. I will discuss the propagation of waves in honeycomb- L´aszl´oSz´ekelyhidi, Jr. structured media. The (Floquet-Bloch) dispersion rela- Universit¨at Leipzig tions of such structures have conical singularities which
[email protected] occur at the intersections of spectral bands for high- symmetry quasi-momenta. These conical singularities, also Camillo De Lellis called Dirac points or diabolical points, are central to the Institut f¨ur Mathematik remarkable electronic properties of graphene and the light- Universitat Zurich, Switzerland propagation properties in honeycomb structured dielectric
[email protected] media.