Eventss

2016 Mar 23

Topology & geometry, Amitai Zernik (Hebrew University), "Fixed-point Expressions for Open Gromov-Witten Invariants - overview and $A_{\infty}$ perspective"

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
2016 Jan 20

Topology & geometry, Matan Prasma (Radboud University), "Model-categorical cotangent complex formalism"

11:00am to 12:45pm

Location: 

Ross building, Hebrew University (Seminar Room 70A)
Abstract: One of the first applications of model categories was Quillen homology. Building on the notion of Beck modules, one defines the cotangent complex of an associative or commutative (dg)-algebras as the derived functor of its abelianization. The latter is a module over the original algebra, and its homology groups are called the (Andre'-)Quillen homology. The caveat of this approach is that the cotangent complex is not defined as a functor on the category of all algebras.
2015 Nov 11

Topology & geometry: Cy Maor (HUJI), "Limits of elastic energies of converging Riemannian manifolds"

11:00am to 12:45pm

Location: 

Ross building, Hebrew University (Seminar Room 70A)
Abstract: An elastic energy functional of a Riemannian manifold  is a function that measures the distance of an embedding u:→ℝd from being isometric. In many applications, the manifold in consideration is actually a limit of other manifolds, that is,  is a limit of n in some sense. Assuming that we have an elastic energy functional for each n, can we obtain an energy functional of  which is a limit of the functionals of n?
2016 Mar 09

Topology & geometry, Frol Zapolsky (University of Haifa), "On the contact mapping class group of the prequantization space over the Am Milnor fiber"

11:00am to 12:45pm

Location: 

Ross building, Hebrew University (Seminar Room 70A)
Abstract: The contact mapping class group of a contact manifold V is the set of contact isotopy classes of its contactomorphisms. When V is the 2n-dimensional (n at least 2) Am Milnor fiber times the circle, with a natural contact structure, we show that the full braid group Bm+1 on m+1strands embeds into the contact mapping class group of V. We deduce that when n=2, the subgroup Pm+1 of pure braids is mapped to the part of the contact mapping class group consisting of smoothly trivial classes. This solves the contact isotopy problem for V.
2015 Dec 16

Topology & geometry: Yochay Jerby (HUJI), " Exceptional collections on toric Fano manifolds and the Landau-Ginzburg equations"

11:00am to 2:30pm

Location: 

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

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