Symplectic geometry | Categories in category theory
In symplectic topology, a Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds of , and morphisms are Floer chain groups: . Its finer structure can be described in the language of quasi categories as an A∞-category. They are named after Kenji Fukaya who introduced the language first in the context of Morse homology, and exist in a number of variants. As Fukaya categories are A∞-categories, they have associated derived categories, which are the subject of the celebrated homological mirror symmetry conjecture of Maxim Kontsevich. This conjecture has been computationally verified for a number of comparatively simple examples. (Wikipedia).
Fukaya categories and variation of symplectic form - Chris Woodward
I hope to talk more about how to find generators for Fukaya categories using symplectic version of the minimal model program in examples such as symplectic quotients of products of spheres and moduli spaces of parabolic bundles. More videos on http://video.ias.edu
From playlist Mathematics
Generation criteria for the Fukaya category - Mohammed Abouzaid
Generation criteria for the Fukaya category Mohammed Abouzaid MIT May 11, 2011
From playlist Mathematics
James Pascaleff: Poisson geometry and monoidal Fukaya categories
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: Poisson manifolds are a generalization of symplectic manifolds, so one can ask in what sense Floer theory and the Fukaya category generalize to them. Whil
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Nicolò Sibilla: The topological Fukaya category and mirror symmetry for toric Calabi-Yau threefolds
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: The Fukaya category of open symplectic manifolds is expected to have good local-to-global properties. Based on this idea several people have developed she
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Toward a contact Fukaya category - Lenny Ng
Toward a contact Fukaya category Augmentations and Legendrians at the IAS Topic: Toward a contact Fukaya category Speaker: Lenny Ng Date: Thursday, February 11 I will describe some work in progress (maybe more accurately, wild speculation) regarding a version of the derived Fukaya categor
From playlist Mathematics
Winter School JTP: Introduction to Fukaya categories, James Pascaleff, Lecture 1
This minicourse will provide an introduction to Fukaya categories. I will assume that participants are also attending Keller’s course on A∞ categories. Lecture 1: Basics of symplectic geometry for Fukaya categories. Symplectic manifolds; Lagrangian submanifolds; exactness conditions;
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Computing maps between Fukaya categories via Morse trees -Nathaniel Bottman
Short talks by postdoctoral members Topic: Computing maps between Fukaya categories via Morse trees Speaker: Nathaniel Bottman Affiliation: Member, School of Mathematics Date: September 26, 2017
From playlist Mathematics
Calabi-Yau mirror symmetry: from categories to curve-counts - Tim Perutz
Tim Perutz University of Texas at Austin November 15, 2013 I will report on joint work with Nick Sheridan concerning structural aspects of mirror symmetry for Calabi-Yau manifolds. We show (i) that Kontsevich's homological mirror symmetry (HMS) conjecture is a consequence of a fragment of
From playlist Mathematics
Homological Mirror Symmetry - Nicholas Sheridan
Nicholas Sheridan Massachusetts Institute of Technology; Member, School of Mathematics February 11, 2013 Mirror symmetry is a deep conjectural relationship between complex and symplectic geometry. It was first noticed by string theorists. Mathematicians became interested in it when string
From playlist Mathematics
Winter School JTP: Introduction to Fukaya categories, James Pascaleff, Lecture 2
This minicourse will provide an introduction to Fukaya categories. I will assume that participants are also attending Keller’s course on A∞ categories. Lecture 1: Basics of symplectic geometry for Fukaya categories. Symplectic manifolds; Lagrangian submanifolds; exactness conditions;
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
We're The Fugawis: Fugs on Food | History
When it comes to eating, the Fugawis are professionals. Get the inside look into the other passion the Fugawis share besides riding. HISTORY®, now reaching more than 98 million homes, is the leading destination for award-winning original series and specials that connect viewers with histo
From playlist We're the Fugawis | History
Versality for the relative Fukaya category - Nick Sheridan
Speaker: Nick Sheridan Title: Versality for the relative Fukaya category Affiliation: IAS Date: November 9, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics
The Relative Fukaya Category, Symplectic and Quantum Cohomology - Nicolas Sheridan
Nicolas Sheridan Massachusetts Institute of Technology; Member, School of Mathematics October 3, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Open Gromov-Witten Invariants from the Fukaya Category - Kai Hugtenburg
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Open Gromov-Witten Invariants from the Fukaya Category Speaker: Kai Hugtenburg Affiliation: University of Edinburgh Date: February 10, 2023 Enumerative mirror symmetry is a correspondence between closed Grom
From playlist Mathematics
A geometric model for the bounded derived category of a gentle algebra, Sibylle Schroll Lecture 3
Gentle algebras are quadratic monomial algebras whose representation theory is well understood. In recent years they have played a central role in several different subjects such as in cluster algebras where they occur as Jacobian algebras of quivers with potentials obtained from triangula
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
A stable infinity-category of Lagrangian cobordisms - David Nadler
A stable infinity-category of Lagrangian cobordisms David Nadler Northwestern May 11, 2011
From playlist Mathematics
Partially wrapped Fukaya categories of symmetric products of marked disks, Gustavo Jasso
Partially wrapped Fukaya categories of symmetric products of marked surfaces were in- troduced by Auroux so as to give a symplecto-geometric intepretation of the bordered Heegaard-Floer homology of Lipshitz, Ozsv ́ath and Thurston. In this talk, I will explain the equivalence between the p
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Winter School JTP: Introduction to Fukaya categories, James Pascaleff, Lecture 3
This minicourse will provide an introduction to Fukaya categories. I will assume that participants are also attending Keller’s course on A∞ categories. Lecture 1: Basics of symplectic geometry for Fukaya categories. Symplectic manifolds; Lagrangian submanifolds; exactness conditions;
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"