School of Mathematics

Recent gluing constructions in Geometry and the gluing methodology

Nicos Kapouleas
Brown University; Member, School of Mathematics
November 7, 2018

Abstract: I will first concentrate on doubling gluing constructions for minimal surfaces, including a recent construction for free boundary minimal surfaces in the unit ball (with D. Wiygul: arXiv:1711.00818).

 

I will then discuss the Linearized Doubling methodology and its applications so far (J.  Differential Geom. 106:393-449, 2017; and with P. McGrath: arXiv:1707.08526),

and some further ongoing work expanding the scope of these methods to new cases.

 

Sunflowers and friends

Shachar Lovett
University of California San Diego
November 5, 2018
The Erdos-Rado sunflower conjecture is one of the tantalizing open problems in combinatorics. In my talk, I will describe several attempts on how to get improved bounds for it. These will lead to surprising connections with several other combinatorial structures, such as randomness extractors, intersecting families and DNFs.

Based on joint works with Xin Li, Noam Solomon and Jiapeng Zhang.

Weyl Law for the phase transition spectrum and density of limit-interfaces

Marco Mendez Guaraco
Member, School of Mathematics
November 5, 2018

Abstract: The Allen-Cahn equation behaves as a desingularization of the area functional.  This allows for a PDE approach to the construction of minimal hypersurfaces in closed Riemannian manifolds. After presenting and overview of the subject, I will discuss recent results regarding a Weyl Law and its consequences for the density of minimal hypersurfaces in generic metrics. This is joint work with P. Gaspar.