Abstract: For a toric Fano manifold $X$ denote by $Crit(X) \subset (\mathbb{C}^{\ast})^n$ the solution scheme of the Landau-Ginzburg system of equations of $X$. Examples of toric Fano manifolds with $rk(Pic(X)) \leq 3$ which admit full strongly exceptional collections of line bundles were recently found by various authors. For these examples we construct a map $E : Crit(X) \rightarrow Pic(X)$ whose image $\mathcal{E}=\left \{ E(z) \vert z \in Crit(X) \right \}$ is a full strongly exceptional collection satisfying the M-aligned property.

Abstract: In the paper "Formal noncommutative symplectic geometry'', Maxim Kontsevich introduced three versions of cochain complexes GCCom, GCLie and GCAs "assembled from'' graphs with some additional structures. The graph complex GCCom (resp. GCLie, GCAs) is related to the operad Com (resp. Lie, As) governing commutative (resp. Lie, associative) algebras. Although the graphs complexes GCCom, GCLie and GCAs (and their generalizations) are easy to define, it is hard to get very much information about their cohomology spaces.

Abstract: I will review a beautiful construction of an infinite collection of monotone Lagrangian tori in the projective plane (and other del Pezzo surfaces) due to Renato Vianna. These tori are obtained from a single one by a procedure called mutation, and I will talk about the wall-crossing formula which relates this geometric procedure to algebraic mutation known from cluster algebra. A proof of the wall-crossing formula is work in progress.

Abstract: This Riemann-Hurwitz type inequality for non proper holomorphic maps between Riemann surfaces gives a geometric version of value distribution theory. I'll explain a proof of it.

Abstract:
Although the Ricci flow with surgery has been used by Perelman to solve the Poincaré and Geometrization Conjectures, some of its basic properties are still unknown. For example it has been an open question whether the surgeries eventually stop to occur (i.e. whether there are finitely many surgeries) and whether the full geometric decomposition of the underlying manifold is exhibited by the flow as t→∞.

Abstract:
In this pair of talks I will discuss how to obtain fixed-point expressions
for open Gromov-Witten invariants. The talks will be self-contained,
and the second talk will only require a small part of the first talk,
which we will review.
The Atiyah-Bott localization formula has become a valuable tool for
computation of symplectic invariants given in terms of integrals on
the moduli spaces of closed stable maps. In contrast, the moduli spaces
of open stable maps have boundary which must be taken into account

Abstract: A Hamiltonian isotopy class of positive Lagrangians in an almost Calabi-Yau manifold admits a natural Riemannian metric. This metric has a Levi-Civita connection, and hence, it gives rise to a notion of geodesics. The geodesic equation is fully non-linear degenerate elliptic, and in general, it is yet unknown whether the initial value problem and boundary problem are well-posed. However, results on the existence of geodesics could shed new light on special Lagrangians, mirror symmetry and the strong Arnold conjecture.

Abstract: We will give a beginner's introduction to simple homotopy theory and explain how it applies to prove the s-cobordism theorem, a generalization of the h-cobordism theorem for non-simply-connected h-cobordisms.

Abstract:
Over a decade ago Welschinger defined invariants of real symplectic manifolds of complex dimensions 2 and 3, which count $J$-holomorphic disks with boundary and interior point constraints. Since then, the problem of extending the definition to higher dimensions has attracted much attention.

Abstract: Joyce and others have used shifted symplectic geometry to define Donaldson-Thomas Invariants. This kind of geometry naturally appears on derived moduli stacks of perfect complexes on Calabi-Yau varieties. One wonderful feature of shifted symplectic geometry (developed by Pantev, Toën, Vaquié and Vezzosi) is that fibre products (i.e. intersections) of Lagrangians automatically carry Lagrangian structures. Using a strange property of triple intersections from arXiv:1309.0596, this extra structure can be organized into a 2-category.

To every topological group, one can associate a unique universal
minimal flow (UMF): a flow that maps onto every minimal flow of the
group. For some groups (for example, the locally compact ones), this
flow is not metrizable and does not admit a concrete description.
However, for many "large" Polish groups, the UMF is metrizable, can be
computed, and carries interesting combinatorial information. The talk
will concentrate on some new results that give a characterization of
metrizable UMFs of Polish groups. It is based on two papers, one joint

Speaker: Arie Levit
Weizmann Institute
Title: Local rigidity of uniform lattices
Abstract: A lattice is topologically locally rigid (t.l.r) if small deformations of it are isomorphic lattices. Uniform lattices in Lie groups were shown to be t.l.r by Weil [60']. We show that uniform lattices are t.l.r in any compactly generated topological group.

Abstract:
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.