2016 Jun 15

Topology & geometry, Vasily Dolgushev (Temple University), "The Intricate Maze of Graph Complexes"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2016 Mar 02

Topology & geometry, Dmitry Tonkonog (University of Cambridge), "Monotone Lagrangian tori and cluster mutations"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2015 Dec 09

Topology & geometry: Julien Duval (Université Paris Sud), "Ahlfors inequality for surfaces"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2016 May 25

Topology & geometry, Richard Bamler (UC Berkeley), "There are finitely many surgeries in Perelman's Ricci flow"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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→∞.
2016 Mar 30

Topology & geometry, Amitai Zernik (Hebrew University), "Fixed-point Expressions for Open Gromov-Witten Invariants - idea of the proof"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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
2015 Dec 30

Topology & geometry, Amitai Yuval (HUJI), " Geodesics of symmetric positive Lagrangians"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2015 Nov 18

Topology & geometry: Lara Simone Suárez (HUJI), "Whitehead torsion and s-cobordism theorem"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2016 Mar 16

Topology & geometry, Sara Tukachinsky (Hebrew University), "Point-like bounding chains in open Gromov-Witten theory"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2015 Dec 23

Topology & geometry: Oren Ben-Bassat (Oxford University), "Multiple Lagrangian Intersections"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2016 Jan 13

Topology & geometry, Penka Vasileva (Paris Rive Gauche), "Real Gromov-Witten theory in all genera"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2015 Nov 04

Topology & geometry: Chaim Even Zohar (HUJI), "Invariants of Random Knots"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2016 Jun 08

Topology & geometry, Ailsa Keating (Columbia University), "Homological Mirror Symmetry for singularities of type Tpqr"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
Abstract:
2016 Jan 06

Topology & geometry, Egor Shelukhin (IAS), "The L^p diameter of the group of area-preserving diffeomorphisms of S^2"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
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.
2016 Feb 24

Topology & geometry, Mikhail Katz (Bar Ilan University), "Determinantal variety and bi-Lipschitz equivalence"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
Abstract: The unit circle viewed as a Riemannian manifold has diameter (not 2 but rather) π, illustrating the difference between intrinsic and ambient distance. Gromov proceeded to erase the difference by pointing out that when a Riemannian manifold is embedded in L∞, the intrinsic and the ambient distances coincide in a way that is as counterintuitive as it is fruitful. Witness the results of his 1983 Filling paper.
2015 Dec 02

Topology & geometry: Pavel Paták (HUJI), "Homological non-embeddability and a qualitative topological Helly-type theorem"

11:00am to 12:45pm

Location:

Ross building, Hebrew University (Seminar Room 70A)
Abstract: The classical theorem of Van Kampen and Flores states that the k-dimensional skeleton of (2k+2)-dimensional simplex cannot be embedded into R2k.
We present a version of this theorem for chain maps and as an application we prove a qualitative topological Helly-type theorem.
If we define the Helly number of a finite family of sets to be one if all sets in the family have a point in common and as the largest size of inclusion-minimal subfamily with empty intersection otherwise, the theorem can be stated as follows: