In this talk we will consider the question of defining descendant invariants in open Gromov-Witten theory. In the closed Gromov-Witten theory, descendant invariants are constructed from Chern classes of certain tautological lines bundles which live on the moduli space of stable curves. The intersection numbers obtained from those classes (and other classes) can be incorporated in a generating function that satisfies various partial differential equations reflecting recurrence relations and which can sometimes be used to calculate the numbers explicitly.

Suppose Z/n acts on a manifold, then if it has a fixed point, the natural homomorphism Z/n --> Out(π) (π = the fundamental group) lifts to Aut(π). If π is centreless, and the aspherical manifold is locally symmetric and the action is isometric, the converse holds. We shall discuss the extent to which this observation is geometric and to what extent it's topological. (It will depend on M and it will depend on n).
לאירוע הזה יש שיחת וידאו.
הצטרף: https://meet.google.com/mcs-bwxr-iza

Monodromy of linear differential and difference equations is a very old and classical object, which may be seen as a far-reaching generalization of the exponential map of a Lie group. While general properties of this map may studied abstractly, for certain very special equations of interest in enumerative geometry, representation theory, and also mathematical physics, it is possible to describe the monodromy "explicitly", in certain geometric and algebraic terms. I will explain one such recent set of ideas, following joint work with M. Aganagic and R. Bezrukavnikov.

Since the 1970's, Physicists and Mathematicians who study random matrices in the standard models of GUE or GOE, are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces. We establish a new aspect of this theory: for random matrices sampled from the group U(n) of Unitary matrices. The group structure of these matrices allows us to go further and find surprising algebraic quantities hidden in the values of these integrals. The talk will be aimed at graduate students, and all notions will be explained.

Mirror symmetry is a far reaching duality relating symplectic geometry on a given manifold to complex geometry on a completely different manifold - its mirror. Toric Calabi Yau manifolds are a large family of examples which which have served as a testing ground for numerous ideas in the study of mirror symmetry. I will prove homological mirror symmetry when the symplectic side is a toric Calabi-Yau 3-fold. I will aim to explain geometrically why the mirror of a toric Calabi Yau takes the particular form it does.

Being the gradient flow of the area functional, the mean curvature flow can be thought of as a greedy algorithm for simplifying embedded shapes. But how successful is this algorithm?
In this talk, I will describe three examples for how mean curvature flow, as well as its variants and weak solutions, can be used to achieve this desired simplification.
The first is a short time smoothing effect of the flow, allowing to smooth out some rough, potentially fractal initial data.

By a Fourier quasicrystal we mean a pure point measure in R^d,
whose Fourier transform is also a pure point measure. This notion
was inspired by the experimental discovery of quasicrystalline
materials in the middle of 80's.
The classical example of such a measure comes from Poisson's
summation formula. Which other measures of this type may exist?
I will give the relevant background on this problem and present
our recent results obtained in joint work with Alexander Olevskii.

The Continuum Problem is whether there is a set of reals whose cardinality is strictly between the cardinality of the integers and the reals.

I will survey various approximation properties of finitely generated groups and explain how they can be used to prove various longstanding conjectures in the theory of groups and group rings. A large class of groups (no group known to be not in the class) is presented that satisfy the Kervaire-Laudenbach Conjecture about solvability of non-singular equations over groups. Our method is inspired by seminal work of Gerstenhaber-Rothaus, which was the key to prove the Kervaire-Laudenbach Conjecture for residually finite groups.

The inverse Galois problem (over number fields k) is one of the central problems in algebraic number theory. A classical approach to it is via specialization of Galois coverings: Hilbert’s irreducibility theorem guarantees the existence of infinitely many specialization values in k such that the Galois group of the specialization equals the Galois group of the covering. I will consider problems related to the inverse Galois problem which can be attacked using the specialization approach.

A classical result of Goldman states that character variety of an oriented surface is a
symplectic algebraic variety, and that the Goldman Lie algebra of free loops on the surface
acts by Hamiltonian vector fields on the character variety. I will describe a vast
generalization of these results, including to higher dimensional manifolds where the role of
the Goldman Lie algebra is played by the Chas-Sullivan string bracket in the string topology
of the manifold. These results follow from a general statement in noncommutative geometry.

Several well-known open questions (such as: are all groups sofic or hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)?
In the case of U(n), the question can be asked with respect to different metrics andnorms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which arenot approximated by U(n) with respect to the Frobenius (=L_2) norm.

I will give the structure of the hypoelliptic Laplacian. I will also describe a natural construction of the hypoelliptic Laplacian as a nonstandard Hodge Laplacian, and explain its connections with dynamical systems and an equation by Langevin.

Given a family of complex algebraic varieties parameterized by a base variety B there is an associated period mapping, which (at least locally) goes from B to a certain flag variety. However, although both the source and target are algebraic varieties,
this period map is of a transcendental nature.
I will explain joint work with Brian Lawrence which shows how the transcendence of the period mapping