Algebra and geometry of the scattering equations

Peter Goddard
Professor Emeritus, School of Natural Sciences
April 3, 2017
Four years ago, Cachazo, He and Yuan found a system of algebraic equations, now named the "scattering equations", that effectively encoded the kinematics of massless particles in such a way that the scattering amplitudes, the quantities of physical interest, in gauge theories and in gravity could be written as sums of rational functions over their solutions.

A time-space lower bound for a large class of learning problems

Ran Raz
Princeton University
April 3, 2017

We prove a general time-space lower bound that applies for a large class of learning problems and shows that for every problem in that class, any learning algorithm requires either a memory of quadratic size or an exponential number of samples. As a special case, this gives a new proof for the time-space lower bound for parity learning [R16].

Rigid holomorphic curves are generically super-rigid

Chris Wendl
Humboldt-Universität zu Berlin
March 31, 2017
I will explain the main ideas of a proof that for generic compatible almost complex structures in symplectic manifolds of dimension at least 6, closed embedded J-holomorphic curves of index 0 are always "super-rigid", implying that their multiple covers are never limits of sequences of curves with distinct images. This condition is especially interesting in Calabi-Yau 3-folds, where it follows that the Gromov-Witten invariants can be "localized" and computed in terms of Euler classes of obstruction bundles for a finite set of disjoint embedded curves.

Speculations about homological mirror symmetry for affine hypersurfaces

Denis Auroux
University of California, Berkeley; Member, School of Mathematics
March 31, 2017
The wrapped Fukaya category of an algebraic hypersurface $H$ in $(C*)^n$ is conjecturally related via homological mirror symmetry to the derived category of singularities of a toric Calabi-Yau manifold $X$, whose moment polytope is determined by the tropicalization of $H$. (The case of the pair of pants discussed in the first talk is a special case of this construction).

Galois Representations for the general symplectic group

Arno Kret
University of Amsterdam
March 30, 2017

In a recent preprint with Sug Woo Shin (https://arxiv.org/abs/1609.04223) I construct Galois representations corresponding for cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields under the local hypothesis that there is a Steinberg component. In this talk I will explain some parts of this construction that involve the eigenvariety.