### Outlook on Lambda-convexity

Analysis and Geometry Seminar

23rd January 2018, 3:00 pm – 4:00 pm

Howard House, 2nd Floor Seminar Room

De Lellis and Szekelyhidi demonstrated that the method of convex integration, so fruitful in differential topology and nonlinear elasticity, also had the potential to elucidate some of the most important questions in the mathematical theory of fluid turbulence. In the first half of this talk I will illustrate the kind of results, falling under the name of the h-principle, that convex integration establishes. In the second half I will talk about recent results, in collaboration with Ben Pooley, on the geometric content of one of the convex integration schemes devised by De Lellis and Szekelyhidi. These results pertain to what is called Lambda-convexity, which can be seen as a relaxed notion of classical convexity but has very peculiar properties which I will comment on.

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