On the Gromov width of polygon spaces - Alessia Mandini
Alessia Mandini University of Pavia October 31, 2014 After Gromov's foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold (M,ω)(M,ω) is a symplectic invariant that measures, roughly speaking, the siz
From playlist Mathematics
Lizhi Chen - Topological complexity of manifolds via systolic geometry
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Lizhi Chen, Lanzhou University Title: Topological complexity of manifolds via systolic geometry Abstract: We discuss homology and homotopy complexity of manifolds in terms of Gromov’s systolic inequality. The optimal const
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Lizhi Chen: Triangulation Complexity of Hyperbolic Manifolds and Asymptotic Geometry
Lizhi Chen, Lanzhou University Title: Triangulation Complexity of Hyperbolic Manifolds and Asymptotic Geometry The triangulation complexity is related to volume of hyperbolic manifolds via simplicial volume. On the other hand, Gromov showed that simplicial volume is related to topological
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Henry Adams (5/1/21): Bridging applied and quantitative topology
I will survey emerging connections between applied topology and quantitative topology. Vietoris-Rips complexes were invented by Vietoris in order to define a (co)homology theory for metric spaces, and by Rips for use in geometric group theory. More recently, they have found applications in
From playlist TDA: Tutte Institute & Western University - 2021
Urysohn width - Alexey Balitskiy
Short Talks by Postdoctoral Members Topic: Urysohn width Speaker: Alexey Balitskiy Affiliation: Member, School of Mathematics Date: September 21, 2021
From playlist Mathematics
Yevgeny Liokumovich (9/10/21): Urysohn width, isoperimetric inequalities and scalar curvature
There exists a positive constant c(n) with the following property. If M is a metric space, such that every ball B of radius 1 in M has Hausdorff n-dimensional measure less than c(n), then there exists a continuous map f from M to (n-1)-dimensional simplicial complex, such that every pre-im
From playlist Vietoris-Rips Seminar
Mikhail Gromov - 1/4 Old, New and Unknown around Scalar Curvature
Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove
From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature
Nicolò Zava (3/17/23): Every stable invariant of finite metric spaces produces false positives
In computational topology and geometry, the Gromov-Hausdorff distance between metric spaces provides a theoretical framework to tackle the problem of shape recognition and comparison. However, the direct computation of the Gromov-Hausdorff distance between finite metric spaces is known to
From playlist Vietoris-Rips Seminar
Systolic inequalities - Alexey Balitskiy
Short Talks by Postdoctoral Members Topic: Systolic inequalities Speaker: Alexey Balitskiy Affiliation: Member, School of Mathematics Date: September 28, 2022
From playlist Mathematics
Open Gromov–Witten theory, skein modules, duality, and knot contact homology – T. Ekholm – ICM2018
Geometry | Topology Invited Lecture 5.7 | 6.3 Open Gromov–Witten theory, skein modules, large N duality, and knot contact homology Tobias Ekholm Abstract: Large N duality relates open Gromov–Witten invariants in the cotangent bundle of the 3-sphere with closed Gromov–Witten invariants in
From playlist Geometry
Panagiotis Papasoglu - Asymptotic dimension of graphs of polynomial growth and systolic inequalities
Asymptotic dimension and n-Uryson width are useful notions of dimension in coarse and systolic geometry respectively. I will explain how using similar techniques one obtains: 1. Sharp estimates for the asymptotic dimension of graphs of polynomial growth 2. A new proof of a theorem of Guth
From playlist Geometry in non-positive curvature and Kähler groups
Positive loops—on a question by Eliashberg- Polterovich... - Albers
Princeton/IAS Symplectic Geometry Seminar Topic: Positive loops—on a question by Eliashberg- Polterovich and a contact systolic inequality Speaker: Peter Albers Date: Thursday February 25 In 2000 Eliashberg-Polterovich introduced the concept of positivity in contact geometry. The notion
From playlist Mathematics
Toward Enumerative Symplectic Topology - Aleksey Zinger
Aleksey Zinger SUNY, Stony Brook;Institute for Advanced Study February 6, 2012 Enumerative geometry is a classical subject often concerned with enumeration of complex curves of various types in projective manifolds under suitable regularity conditions. However, these conditions rarely hold
From playlist Mathematics
Introduction to h-principle by Mahuya Datta
DATE & TIME: 25 December 2017 to 04 January 2018 VENUE: Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex structure. The moduli space of these curves (
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Transversality and super-rigidity in Gromov-Witten Theory by Chris Wendl
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar 5/27/22
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Three 20-minute research talks Speaker: Daniel Rudolf (Ruhr-Universität Bochum): Viterbo‘s conjecture for Lagrangian products in ℝ4 We show that Viterbo‘s conjecture (for the EHZ-capacity) for convex Lagrangian pro
From playlist Mathematics
Transversality and super-rigidity in Gromov-Witten Theory (Lecture - 03) by Chris Wendl
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Transversality and super-rigidity in Gromov-Witten Theory (Lecture – 02) by Chris Wendl
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Facundo Mémoli: Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Title: Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius Abstract: The persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information from metric spaces. We consider a different, more geome
From playlist Vietoris-Rips Seminar