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.

Abstract: We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the quintic threefold. Our approach to the orientability problem is based entirely on the topology of real bundle pairs over symmetric surfaces. This allows us to endow the uncompactified moduli spaces of real maps from symmetric surfaces of all topological types with natural orientations and to verify that they extend across the codimension-one boundaries of these spaces.

Title: Invariants of Random Knots.
Abstract:
Random curves in space and how they are knotted give an insight into the behavior of "typical" knots and links, and are expected to introduce the probabilistic method into the mathematical study of knots. They have been studied by biologists and physicists in the context of the structure of random polymers. There have been many results obtained via computational experiment, but few explicit computations.

Abstract:

Abstract: We use a geometric idea to give an analytic estimate for the word-length in the pure braid group of S^2. This yields that the L^1-norm (and hence each L^p-norm, including L^2) on the group of area-preserving diffeomorphisms of S^2 is unbounded. This solves an open question arising from the work of Shnirelman and Eliashberg-Ratiu. Joint work in progress with Michael Brandenbursky.

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.

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

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

INTRODUCTION TO MEAN DIMENSION AND THE EMBEDDING PROBLEM OF DYNAMICAL SYSTEMS (Part 1)

Speaker: Oren Becker
Title: Locally testable groups
Abstract:
Arzhantseva and Paunescu [AP2015] showed that if two permutations X and Y in Sym(n) nearly commute (i.e. XY is close to YX), then the pair (X,Y) is close to a pair of permutations that really commute.