World Disorder Lecture Series: Latin America: Walls or Bridges?

Jeffrey Davidow
Retired US Ambassador to Mexico, Venezuela, and Zambia; Cohen Group
March 1, 2017
Latin America’s move in recent decades to greater levels of democracy and economic development are undermined by weak institutions, corruption and the lure of populism. While it is a zone of peace with no international hostilities or significant internal insurrections at this time, the nations of the region must deal with complicated futures, which can impact the United States. Cuba, Mexico and Venezuela all face potential profound change.

Canonical coordinates for Calabi Yau manifolds I

Sean Keel
University of Texas, Austin; Member, School of Mathematics
March 1, 2017
In the two talks, aimed at a broad mathematical audience, I'll explain my conjecture, joint with Gross, Hacking, and Siebert, which says, informally, that if you live on a Calabi Yau, your world comes with an intrinsic global positioning system. More precisely: that the coordinate ring comes with a canonical vector space basis, such that the structure constants for the multiplication rule are given by counts of rational curves (on the mirror).

Structural and computational aspects of Brascamp-Lieb inequalities

Avi Wigderson
Herbert H. Maass Professor, School of Mathematics
February 28, 2017
The celebrated Brascamp-Lieb (BL) inequalities are an important mathematical tool, unifying and generalizing numerous inequalities in analysis, convex geometry and information theory, with many used in computer science. I will survey the well-understood structural theory of BL inequalities, and then discuss their computational aspects. Far less was known about computing their main parameters, and I will discuss new efficient algorithms (via operator scaling) for those, which also inform structural questions.

New insights on the (non)-hardness of circuit minimization and related problems

Eric Allender
Rutgers University
February 27, 2017
The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deals with time-bounded Kolmogorov complexity are prominent candidates for NP-intermediate status. We present new results relating the complexity of various approximation problems related to MCSP and MKTP. We show that, under modest cryptographic assumptions, some of these approximation problems must have intermediate complexity: they have no solution in P/poly and are not NP-hard under P/poly reductions.

Folding papers and turbulent flows

Camillo De Lellis
University of Zürich
February 24, 2017
In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. A couple of decades later Gromov showed how Nash's ideas can be used to reinterpret other known counterintuitive facts in geometry and to discover many new ones. Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics.

Folding papers and turbulent flows

Camillo De Lellis
University of Zürich
February 23, 2017
In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. A couple of decades later Gromov showed how Nash's ideas can be used to reinterpret other known counterintuitive facts in geometry and to discover many new ones. Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics.

Symplectic homology for cobordisms

Alexandru Oancea
Université Pierre et Marie Curie; Member, School of Mathematics
February 23, 2017
Symplectic homology for a Liouville cobordism (possibly filled at the negative end) generalizes simultaneously the symplectic homology of Liouville domains and the Rabinowitz-Floer homology of their boundaries. I intend to explain a conceptual framework within which one can understand it, and give a sample application which shows how it can be used in order to obstruct cobordisms between contact manifolds. Based on joint work with Kai Cieliebak and Peter Albers.