## Combinatorics of the amplituhedron

Lauren Williams

University of California, Berkeley; von Neumann Fellow, School of Mathematics

January 23, 2017

Yve-Alain Bois

Pablo Picasso did not speak often about abstraction, but when he did, it was either to dismiss it as complacent decoration or to declare its very notion an oxymoron. The root of this hostility is to be found in the impasse that the artist reached in the summer 1910, when abstraction suddenly appeared as the logical development of his previous work, a possibility at which he recoiled in horror. But though he swore to never go again near abstraction, he could not prevent himself from testing his... Read more

Lauren Williams

University of California, Berkeley; von Neumann Fellow, School of Mathematics

January 23, 2017

Shachar Lovett

University of California, San Diego

January 23, 2017

An active learning algorithm for a classification problem has access to many unlabelled samples. The algorithm asks for the labels of a small number of samples, carefully chosen, such that that it can leverage this information to correctly label most of the unlabelled samples. It is motivated by many real world applications, where it is much easier and cheaper to obtain access to unlabelled data compared to labelled data. The main question is: can active learning algorithms out-perform classic passive learning algorithms?

David Treumann

Boston College; von Neumann Fellow, School of Mathematics

January 20, 2017

I will survey the coherent-constructible correspondence of Bondal, which embeds the derived category of coherent sheaves on a toric variety into the derived category of constructible sheaves on a compact torus. The tools of the first lecture turn this into a homological mirror theorem -- a pretty strong one, after recent results of Ike and Kuwagaki.

David Treumann

Boston College; von Neumann Fellow, School of Mathematics

January 18, 2017

I will give an introduction to the microlocal theory of sheaves after Kashiwara and Schapira, and some of its recent applications in symplectic topology. I'll start with the basics, but target applications for the 75 minutes are Tamarkin's proof of nondisplaceability, and Shende's proof that a Legendrian isotopy between conormals of knots implies a smooth isotopy between the knots.

Jordan Ellenberg

University of Wisconsin

January 17, 2017

Jake Solomon

Hebrew University of Jerusalem; Visitor, School of Mathematics

December 16, 2016

I'll begin with a leisurely introduction to Fukaya A-infinity algebras and their bounding chains. Then I'll explain how to use bounding chains to define open Gromov-Witten invariants. The bounding chain invariants can be computed using an open analog of the WDVV equations. This leads to an explicit understanding of the homotopy type of certain Fukaya A-infinity algebras. Also, the bounding chain invariants generalize Welschinger's real enumerative invariants. A nice example is real projective space considered as a Lagrangian submanifold of complex projective space.

Jake Solomon

Hebrew University of Jerusalem; Visitor, School of Mathematics

December 14, 2016

I'll begin with a leisurely introduction to Fukaya A-infinity algebras and their bounding chains. Then I'll explain how to use bounding chains to define open Gromov-Witten invariants. The bounding chain invariants can be computed using an open analog of the WDVV equations. This leads to an explicit understanding of the homotopy type of certain Fukaya A-infinity algebras. Also, the bounding chain invariants generalize Welschinger's real enumerative invariants. A nice example is real projective space considered as a Lagrangian submanifold of complex projective space.

Frank van den Bosch

Yale University

December 13, 2016

Pravesh Kothari

Member, School of Mathematics

December 13, 2016

Nathaniel Bottman

Member, School of Mathematics

December 12, 2016

The Fukaya category of a symplectic manifold is a robust intersection theory of its Lagrangian submanifolds. Over the past decade, ideas emerging from Wehrheim--Woodward's theory of quilts have suggested a method for producing maps between the Fukaya categories of different symplectic manifolds. I have proposed that one should consider maps controlled by compactified moduli spaces of marked parallel lines in the plane, called "2-associahedra".