Lie derivatives of differential forms
Introduces the lie derivative, and its action on differential forms. This is applied to symplectic geometry, with proof that the lie derivative of the symplectic form along a Hamiltonian vector field is zero. This is really an application of the wonderfully named "Cartan's magic formula"
From playlist Symplectic geometry and mechanics
Isometry groups of the projective line (I) | Rational Geometry Math Foundations 138 | NJ Wildberger
The projective line can be given a Euclidean structure, just as the affine line can, but it is a bit more complicated. The algebraic structure of this projective line supports some symmetries. Symmetry in mathematics is often most efficiently encoded with the idea of a group--a technical t
From playlist Math Foundations
Introduction to Fiber Bundles part 1: Definitions
We give the definition of a fiber bundle with fiber F, trivializations and transition maps. This is a really basic stuff that we use a lot. Here are the topics this sets up: *Associated Bundles/Principal Bundles *Reductions of Structure Groups *Steenrod's Theorem *Torsor structure on arith
From playlist Fiber bundles
Symmetries show up everywhere in physics. But what is a symmetry? While the symmetries of shapes can be interesting, a lot of times, we are more interested in symmetries of space or symmetries of spacetime. To describe these, we need to build "invariants" which give a mathematical represen
From playlist Relativity
Exploring Symplectic Embeddings and Symplectic Capacities
Speakers o Alex Gajewski o Eli Goldin o Jakwanul Safin o Junhui Zhang Project Leader: Kyler Siegel Abstract: Given a domain (e.g. a ball) in Euclidean space, we can ask what is its volume. We can also ask when one domain can be embedded into another one without distorting volumes. These
From playlist 2019 Summer REU Presentations
Symplectic topology and the loop space - Jingyu Zhao
Topic: Symplectic topology and the loop space Speaker: Jingyu Zhao, Member, School of Mathematics Time/Room: 4:45pm - 5:00pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Constructions in symplectic and contact topology via h-principles - Oleg Lazarev
More videos on http://video.ias.edu
From playlist Mathematics
What is a Manifold? Lesson 12: Fiber Bundles - Formal Description
This is a long lesson, but it is not full of rigorous proofs, it is just a formal definition. Please let me know where the exposition is unclear. I din't quite get through the idea of the structure group of a fiber bundle fully, but I introduced it. The examples in the next lesson will h
From playlist What is a Manifold?
Symplectic geometry of surface group representations - William Goldman
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Symplectic geometry of surface group representations Speaker: William Goldman Affiliation: Member, School of Mathematics Date: February 28, 2022 If G is a Lie group whose adjoint representation preserves a nondegenerate sy
From playlist Mathematics
Jerzy Lewandowski: The quantum states and operators of the canonical LQG
Recording during the meeting "Twistors and Loops Meeting in Marseille" the September 02, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisua
From playlist Mathematical Physics
A panoramic view of Mathematics Research @ICTS by Varun Thakre and Anish Mallick
ICTS In-house 2019 Organizers: Adhip Agarwala, Ganga Prasath, Rahul Kashyap, Gayathri Raman, Priyanka Maity Date and Time: 23rd April, 2019 Venue: Ramanujan Lecture Hall, ICTS Bangalore inhouse@icts.res.in An exclusive day to exchange ideas and discuss research amongst members of ICTS.
From playlist ICTS In-house 2019
An introduction to spectral data for Higgs bundles.. by Laura Schaposnik
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
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
Recent developments in knot contact homology - Lenny Ng
Princeton/IAS Symplectic Geometry Seminar Topic: Recent developments in knot contact homology Speaker: Lenny Ng, Duke University Date: December 11, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Noah Arbesfeld: A geometric R-matrix for the Hilbert scheme of points on a general surface
Abstract: We explain how to use a Virasoro algebra to construct a solution to the Yang-Baxter equation acting in the tensor square of the cohomology of the Hilbert scheme of points on a generalsurface S. In the special case where the surface S is C2, the construction appears in work of Mau
From playlist Algebraic and Complex Geometry
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture - 3) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
An introduction to spectral data for Higgs bundles.. by Laura Schaposnik
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Hodge Structures in Symplectic Geometry - Tony Pantev
Tony Pantev University of Pennsylvania October 21, 2011 I will explain how essential information about the structure of symplectic manifolds is captured by algebraic data, and specifically by the non-commutative (mixed) Hodge structure on the cohomology of the Fukaya category. I will discu
From playlist Mathematics