Symplectic geometry

Lefschetz manifold

In mathematics, a Lefschetz manifold is a particular kind of symplectic manifold , sharing a certain cohomological property with Kähler manifolds, that of satisfying the conclusion of the Hard Lefschetz theorem. More precisely, the strong Lefschetz property asks that for , the cup product be an isomorphism. The topology of these symplectic manifolds is severely constrained, for example their odd Betti numbers are even. This remark leads to numerous examples of symplectic manifolds which are not Kähler, the first historical example is due to William Thurston. (Wikipedia).

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A frontal view on Lefschetz fibrations I - Emmy Murphy

Augmentations and Legendrians at the IAS Topic: A frontal view on Lefschetz fibrations I Speaker: Emmy Murphy Date: Friday, February 12 In this series of two talks we will discuss Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. The main

From playlist Mathematics

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Lefschetz pencils and crossed homomorphisms - Bruno Kahn

Bruno Kahn March 13, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu

From playlist Mathematics

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Lefschetz Without Positivity: An Overview - Karim Alexander Adiprasito

Members' Colloquium Topic: Lefschetz Without Positivity: An Overview Speaker: Karim Alexander Adiprasito Affiliation: Hebrew University of Jerusalem, Member, School of Mathematics Date: February 6, 2023 2:00pm|Simonyi Hall 101 and Remote Access - see Zoom link below The Lefschetz propert

From playlist Mathematics

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Algebraic Structures Associated to Weinstein Manifolds - Eliashberg

Yasha Eliashberg Stanford University September 28, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Karim Alexander Adiprasito - 5/6 - Lefschetz, Hodge and combinatorics...

Lefschetz, Hodge and combinatorics: an account of a fruitful cross-pollination Almost 40 years ago, Stanley noticed that some of the deep theorems of algebraic geometry have powerful combinatorial applications. Among other things, he used the hard Lefschetz theorem to rederive Dynkin's t

From playlist Hadamard Lectures 2021 - Karim Alexander Adiprasito - Lefschetz, Hodge and combinatorics: an account of a fruitful cross-pollination

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Mark Hughes: Branched Coverings Over Surface Braids and (Broken) Lefschetz Fibrations

Mark Hughes, Brigham Young University Title: Branched Coverings Over Surface Braids and (Broken) Lefschetz Fibrations on Non- compact 4-Manifold In this talk I will discuss a construction of Lefschetz type fibrations on 4–manifolds via coverings branched over braided surfaces. When applied

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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A frontal view on Lefschetz fibrations II - Rodger Casals

Augmentations and Legendrians at the IAS Topic: A frontal view on Lefschetz fibrations II Speaker: Roger Casals Date: Friday, February 12 In this series of two talks we will discuss Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. The ma

From playlist Mathematics

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Karim Alexander Adiprasito - 2/6 - Lefschetz, Hodge and combinatorics...

Lefschetz, Hodge and combinatorics: an account of a fruitful cross-pollination Almost 40 years ago, Stanley noticed that some of the deep theorems of algebraic geometry have powerful combinatorial applications. Among other things, he used the hard Lefschetz theorem to rederive Dynkin's t

From playlist Hadamard Lectures 2021 - Karim Alexander Adiprasito - Lefschetz, Hodge and combinatorics: an account of a fruitful cross-pollination

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What is a Manifold? Lesson 6: Topological Manifolds

Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.

From playlist What is a Manifold?

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Karim Alexander Adiprasito - 1/6 - Lefschetz, Hodge and combinatorics...

Lefschetz, Hodge and combinatorics: an account of a fruitful cross-pollination Almost 40 years ago, Stanley noticed that some of the deep theorems of algebraic geometry have powerful combinatorial applications. Among other things, he used the hard Lefschetz theorem to rederive Dynkin's t

From playlist Hadamard Lectures 2021 - Karim Alexander Adiprasito - Lefschetz, Hodge and combinatorics: an account of a fruitful cross-pollination

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Subflexible symplectic manifolds - Kyler Siegel

Princeton/IAS Symplectic Geometry Seminar Topic: Subflexible symplectic manifolds Speaker: Kyler Siegel Date: Thursday, March 3 After recalling some recent developments in symplectic flexibility, I will introduce a class of open symplectic manifolds, called "subflexible", which are not fl

From playlist Mathematics

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Lefschetz Fixed Point Theorem example

Here we give an example of how to use the Lefschetz fixed point theorem. These notes were really useful as a graduate student, some of them are down now, but I think these notes I had came from here: http://mathsci.kaist.ac.kr/~jinhyun/useful.html

From playlist Riemann Hypothesis

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Axioms for the Lefschetz number as a lattice valuation

"Axioms for the Lefschetz number as a lattice valuation" a research talk I gave at the conference on Nielsen Theory and Related Topics in Daejeon Korea, June 28, 2013. Chris Staecker's internet webarea: http://faculty.fairfield.edu/cstaecker/ Nielsen conference webarea: http://open.nims.r

From playlist Research & conference talks

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Weil conjectures 5: Lefschetz trace formula

This talk explains the relation between the Lefschetz fixed point formula and the Weil conjectures. More precisely, the zeta function of a variety of a finite field can be written in terms of an action of the Frobenius group on the cohomology groups of the variety. The main problem is then

From playlist Algebraic geometry: extra topics

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Manifolds 1.3 : More Examples (Animation Included)

In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5

From playlist Manifolds

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Holomorphic Floer theory and the Fueter equation - Aleksander Doan

Joint IAS/Princeton University Symplectic Geometry Seminar Holomorphic Floer theory and the Fueter equation Aleksander Doan Columbia University Date: April 25, 2022  I will discuss an idea of constructing a category associated with a pair of holomorphic Lagrangians in a hyperkahler manif

From playlist Mathematics

Related pages

Compact space | De Rham cohomology | Poincaré duality | Kähler manifold | Mathematics | Symplectic manifold | Nilmanifold | William Thurston | Torus | Betti number