Timo Richarz: Basics on Affine Grassmanianns
The aim is to give an introduction to the basic theory of affine Grassmannians and affine flag varieties. We put special emphasis on the utility of dynamic methods in sense of Drinfeld [D], and the utility of non-constant group schemes. We plan to adress the following aspects: • Affine Gra
From playlist Algebraic and Complex Geometry
How to Integrate over Grassmann Numbers in Quantum Field Theory? (Berezin Integral)
In this video, we will show you how to do integrals with Grassmann numbers. Grassmann numbers are an important concept in quantum field theory, where we use them to describe fermions. They are named after the German mathematician Hermann Grassmann. The special thing about Grassmann numbers
From playlist Mathematical Physics
Joel Kamnitzer: Symplectic duality and (generalized) affine Grassmannian slices
Abstract: Under the geometric Satake equivalence, slices in the affine Grassmannian give a geometric incarnation of dominant weight spaces in representations of reductive groups. These affine Grassmannian slices are quantized by algebras known as truncated shifted Yangians. From this persp
From playlist SMRI Algebra and Geometry Online
algebraic geometry 20 Grassmannians
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It is about Grassmannians and some of their applications.
From playlist Algebraic geometry I: Varieties
algebraic geometry 17 Affine and projective varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between affine and projective varieties, with some examples such as a cubic curve and the twisted cubic.
From playlist Algebraic geometry I: Varieties
algebraic geometry 5 Affine space and the Zariski topology
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of affine space and its Zariski topology.
From playlist Algebraic geometry I: Varieties
Geordie Williamson: Miraculous Treumann-Smith theory and geometric Satake
Abstract: This talk will be about geometric approaches to the representation theory of reductive algebraic groups in positive characteristic p. A cornerstone of the geometric theory is the geometric Satake equivalence, which gives an incarnation of the category of representations as a cate
From playlist Geordie Williamson: Representation theory and the Geometric Satake
Geordie Williamson: Parity sheaves and modular representations II
This is a talk of Gordie Williamson given at the Harvard CDM Conference of November 23, 2019.
From playlist Geordie Williamson: Parity sheaves and modular representations
(PP 6.5) Affine property, Constructing Gaussians, and Sphering
Any affine transformation of a (multivariate) Gaussian random variable is (multivariate) Gaussian. How to construct any (multivariate) Gaussian using an affine transformation of standard normals. How to "sphere" a Gaussian, i.e. transform it into a vector of independent standard normals.
From playlist Probability Theory
Jarosław Buczyński (6/29/17) Bedlewo: Constructions of k-regular maps using finite local schemes
A continuous map R^m → R^N or C^m → C^N is called k-regular if the images of any k distinct points are linearly independent. Given integers m and k a problem going back to Chebyshev and Borsuk is to determine the minimal value of N for which such maps exist. The methods of algebraic topolo
From playlist Applied Topology in Będlewo 2017
algebraic geometry 24 Regular functions
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers regular functions on affine and quasiprojective varieties.
From playlist Algebraic geometry I: Varieties
Ivan Mirkovic: Loop Grassmanians and local spaces
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Branched Holomorphic Cartan Geometries by Sorin Dumitrescu
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Ilya Dumanski - Schubert varieties in the Beilinson-Drinfeld Grassmannian
Ilya Dumanski (MIT) The Borel-Weil theorem states that the space of sections of a certain line bundle on the flag variety is isomorphic to the irreducible representation of the corresponding reductive group. The classical result of Demazure describes the restriction of sections to the Sch
From playlist Azat Miftakhov Days Against the War
First examples of cluster structures on coordinate algebras,... (Lecture 1) by Maitreyee Kulkarni
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
Michael Finkelberg: Irreducible equivariant perverse coherent sheaves on affine Grassmannians of...
Title: Irreducible equivariant perverse coherent sheaves on affine Grassmannians of type A and dual canonical bases Abstract: S. Cautis and H. Williams identified the equivariant K-theory of the affine Grassmannian of GL(n) with a quantum unipotent cell of LSL(2). Under this identificatio
From playlist Algebraic and Complex Geometry
algebraic geometry 19 The Veronese surface and the variety of lines in space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers two examples of projective varieties: the Veronese surface in 5-dimensional projective space, and the variety of all lines in 3-dimensional space.
From playlist Algebraic geometry I: Varieties
algebraic geometry 26 Affine algebraic sets and commutative rings
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between morphisms of affine algebraic sets and homomorphisms of commutative rings. As examples it describes some homomorphisms of commutative rings
From playlist Algebraic geometry I: Varieties