MAST30026 Lecture 20: Hilbert space (Part 3)
I prove that L^2 spaces are Hilbert spaces. Lecture notes: http://therisingsea.org/notes/mast30026/lecture20.pdf The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I hold free public online office hours for this class, every week, all year. Drop in and say Hi! For
From playlist MAST30026 Metric and Hilbert spaces
Functional Analysis Lecture 12 2014 03 04 Boundedness of Hilbert Transform on Hardy Space (part 1)
Dyadic Whitney decomposition needed to extend characterization of Hardy space functions to higher dimensions. p-atoms: definition, have bounded Hardy space norm; p-atoms can also be used in place of atoms to define Hardy space. The Hilbert Transform is bounded from Hardy space to L^1: b
From playlist Course 9: Basic Functional and Harmonic Analysis
Lecture with Ole Christensen. Kapitler: 00:00 - Def: Hilbert Space; 05:00 - New Example Of A Hilbert Space; 15:15 - Operators On Hilbert Spaces; 20:00 - Example 1; 24:00 - Example 2; 38:30 - Riesz Representation Theorem; 43:00 - Concerning Physics;
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
algebraic geometry 12 Hilbert's finiteness theorem
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the proof of Hilbert's finiteness theorem for rings of invariants. (This is not the same as Hilbert's finiteness theorem for ideals, though the two theorems are
From playlist Algebraic geometry I: Varieties
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 2
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic diffe
From playlist Felix Klein Lectures 2022
The Heisenberg Algebra in Symplectic Algebraic Geometry - Anthony Licata
Anthony Licata Institute for Advanced Study; Member, School of Mathematics April 2, 2012 Part of geometric representation theory involves constructing representations of algebras on the cohomology of algebraic varieties. A great example of such a construction is the work of Nakajima and Gr
From playlist Mathematics
algebraic geometry 15 Projective space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry
From playlist Algebraic geometry I: Varieties
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 1
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic diffe
From playlist Felix Klein Lectures 2022
Summing Over Bordisms In 2d TQFT - Greg Moore
Black Holes and Qubits Meeting Topic: Summing Over Bordisms In 2d TQFT Speaker: Greg Moore Affiliation: Rutgers University Date: March 24, 2022 Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms betwee
From playlist Natural Sciences
MAST30026 Lecture 20: Hilbert space (Part 1)
I defined inner product spaces, proved the Cauchy-Schwartz inequality and that any inner product space gives rise to a normed space, defined Hilbert spaces and proved that in a Hilbert space given a vector and a closed, convex nonempty subset there is a closest point in the subset to the v
From playlist MAST30026 Metric and Hilbert spaces
The Riemann-Hilbert Correspondence in Nonarchimedean Geometry - Jacob Lurie
IAS/Princeton Arithmetic Geometry Seminar Topic: The Riemann-Hilbert Correspondence in Nonarchimedean Geometry Speaker: Jacob Lurie Affiliation: Member, School of Mathematics Date: March 13, 2023 Let X be a smooth projective variety over the field of complex numbers. The classical Rieman
From playlist Mathematics
Anthony Henderson: Hilbert Schemes Lecture 1
SMRI Seminar Series: 'Hilbert Schemes' Lecture 1 Introduction Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested in representa
From playlist SMRI Course: Hilbert Schemes
8ECM Invited Lecture: Špela Špenko
From playlist 8ECM Invited Lectures
Sukhendu Mehrotra: Hilbert schemes of points on K3 surfaces and deformations
Abstract: The Hilbert scheme of points of a K3 surface X admits a 21-dimensional space of deformations, while the moduli space of K3 surfaces is 20-dimensional. The goal of this talk is to provide an interpretation of this extra modulus of the deformation space of the Hilbert scheme X[n] i
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
André Henriques: "Various things acted on by fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Various things acted on by fusion categories" André Henriques - University of Oxford Abstract: Besides von Neumann algebras and C*-algebras, there exist a couple of other mathematical object for which can be acted upon by fusion categorie
From playlist Actions of Tensor Categories on C*-algebras 2021
Anthony Licata: Hilbert Schemes Lecture 7
SMRI Seminar Series: 'Hilbert Schemes' Lecture 7 Kleinian singularities 2 Anthony Licata (Australian National University) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students inter
From playlist SMRI Course: Hilbert Schemes
Robert Ghrist (5/1/21): Laplacians and Network Sheaves
This talk will begin with a simple introduction to cellular sheaves as a generalized notion of a network of algebraic objects. With a little bit of geometry, one can often define a Laplacian for such sheaves. The resulting Hodge theory relates the geometry of the Laplacian to the algebraic
From playlist TDA: Tutte Institute & Western University - 2021