Seminars

2018 Jan 02

T&G: Shaofeng Wang (Hebrew University), GIT, symplectic reduction and the Kempf-Ness theorem

1:00pm to 2:30pm

Location: 

Room 63, Ross Building, Jerusalem, Israel
Let G be a group acting on a projective variety. If G is noncompact, the quotient space X/G is in general "bad". In this talk I will discuss two methods to make this quotient "good", i.e. GIT and symplectic reduction. Both methods include the idea of keeping "good orbits" and throwing away "bad orbits". Hilbert-Mumford criterion provides a way to distinguish good orbits (which are called stable orbits) and the Kempf-Ness theorem tells us two methods produce the same quotient space. I will use several examples to show how Hilbert-Mumford criterion and the Kempf-Ness theorem work.
2017 Oct 24

T&G: Asaf Shachar (Hebrew University), Riemannian embeddings of minimal distortion

12:00pm to 1:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
This talk revolves around the question of how close is one Riemannian manifold to being isometrically immersible in another. We associate with every mapping $f:(M,g) \to (N,h)$ a measure of distortion - an average distance of $df$ from being an isometry. Reshetnyak's theorem states that a sequence of mappings between Euclidean domains whose distortion tends to zero has a subsequence converging to an isometry. I will present a generalization of Reshetnyak’s theorem to the general Riemannian setting.
2017 Nov 07

T&G: Ran Tessler (ETH - ITS), Open (CP^1,RP^1) intersection theory: properties, calculations and open Gromov-Witten/Hurwitz corrspondence.

1:00pm to 2:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
We will start be explaining the difficulties in constructing enumerative open Gromov-Witten theories, and mention cases we can overcome these difficulties and obtain a rich enumerative structure. We then restrict to one such case, and define the full genus 0 stationary open Gromov-Witten theory of maps to CP^1 with boundary conditions on RP^1, including descendents, together with its equivariant extension. We fully compute the theory.
2017 Dec 26

T&G: Or Hershkovits (Stanford), Uniqueness of mean curvature flow through (some) singularities

1:00pm to 2:30pm

Location: 

Room 63, Ross Building, Jerusalem, Israel
Abstract: Given a smooth compact hypersurface in Euclidean space, one can show that there exists a unique smooth evolution starting from it, existing for some maximal time. But what happens after the flow becomes singular? There are several notions through which one can describe weak evolutions past singularities, with various relationship between them. One such notion is that of the level set flow.
2017 Aug 09

T&G: Peter Ozsvath (Princeton), Bordered methods in knot Floer homology

12:00pm to 1:00pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
Knot Floer homology is an invariant for knots in the three-sphere defined using methods from symplectic geometry. I will describe a new algebraic formulation of this invariant which leads to a reasonably efficient computation of these invariants. This is joint work with Zoltan Szabo.
2016 Jan 11

Zabrodsky lecture series: Peter Ozsváth (Princeton) "Bordered Floer homology"

12:00pm to 1:00pm

Location: 

Ross 70A
Abstract: Bordered Floer homology is an invariant for three-manifolds with boundary, defined in collaboration with Robert Lipshitz and Dylan Thurston. The invariant associates a DG algebra to a parameterized surface, and a module over that algebra to a three-manifold with boundary. I will explain how methods from bordered Floer homology can be used to give a tidy description of knot Floer homology. This is joint work with Zoltan Szabo.
2017 Sep 12

T&G: Liat Kessler (Cornell and Oranim), Extending Homologically trivial symplectic cyclic actions to Hamiltonian circle actions

12:00pm to 1:00pm

Location: 

Ross Building Room 70A
We ask whether every homologically trivial cyclic action on a symplectic four-manifold extend to a Hamiltonian circle action. By a cyclic action we mean an action of a cyclic group of finite order; it is homologically trivial if it induces the identity map on homology. We assume that the manifold is closed and connected. In the talk, I will give an example of a homologically trivial symplectic cyclic action on a four-manifold that admits Hamiltonian circle actions, and show that is does not extend to a Hamiltonian circle action.
2015 Nov 03

Dynamics & probability: Asaf Nachmias (Tel Aviv)

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
Title: Indistinguishability of trees in uniform spanning forests Abstract: The uniform spanning forest (USF) of an infinite connected graph G is the weak limit of the uniform spanning tree measure taken on exhausting finite subgraphs of G. It is easy to see that it is supported on spanning graphs of G with no cycles, but it need not be connected. Indeed, a classical result of Pemantle ('91) asserts that when G=Zd, the USF is almost surely a connected tree if and only if d=1,2,3,4.
2015 Dec 08

Dynamics & probability: Brandon Seward (HUJI): "Positive entropy actions of countable groups factor onto Bernoulli shifts"

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
Title: Positive entropy actions of countable groups factor onto Bernoulli shifts Abstract: I will prove that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well-known Sinai factor theorem from classical entropy theory. As an application, I will show that for a large class of non-amenable groups, every positive entropy free ergodic action satisfies the measurable von Neumann conjecture.

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