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
Positive Grassmannian and polyhedral subdivisions – Alexander Postnikov – ICM2018
Combinatorics Invited Lecture 13.2 Positive Grassmannian and polyhedral subdivisions Alexander Postnikov Abstract: The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and combinatorial structures. Its study involves interesting combinatorial objects, such as po
From playlist Combinatorics
(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
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
The GrassmannCalculus application, based on the work of Grassmann and Browne, is described. One example, the derivation of coordinate equations for lines and planes in n-dimensional space, is presented. This illustrates how smoothly Mathematica and Grassmann–Browne algebra merge to form a
From playlist Wolfram Technology Conference 2021
Martina Lanini: Totally nonnegative Grassmannians, Grassmann necklaces and quiver Grassmannians
30 September 2021 Abstract: Totally nonnegative (tnn) Grassmannians are subvarieties of (real) Grassmannians which have been widely investigated thanks to the several applications in mathematics and physics. In a seminal paper on the subject, Postnikov constructed a cellularisation of the
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Combinatorial affine sieve - Alireza Salehi Golsefidy
Speaker: Alireza Salehi Golsefidy (UCSD) Title: Combinatorial affine sieve Abstract: In this talk the general setting of affine sieve will be presented. Next I will explain the Bourgain-Gamburd-Sarnak method on proving affine sieve in the presence of certain spectral gap. Finally I will sa
From playlist Mathematics
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
Double Grassmannians and Coulomb branches of 3d 𝒩=4 quiver gauge theories – M. Finkelberg – ICM2018
Lie Theory and Generalizations Invited Lecture 7.7 Double affine Grassmannians and Coulomb branches of 3d 𝒩=4 quiver gauge theories Michael Finkelberg Abstract: We propose a conjectural construction of various slices for double affine Grassmannians as Coulomb branches of 3-dimensional
From playlist Lie Theory and Generalizations
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 12
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Nonlinear algebra, Lecture 4: "Linear Spaces and Grassmanians", by Mateusz Michalek
This is the fourth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
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
Generalized affine Grassmannian slices, truncated shifted Yangians, Hamiltonian... - Joel Kamnitzer
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Generalized affine Grassmannian slices, truncated shifted Yangians, and Hamiltonian reduction Speaker: Joel Kamnitzer Affiliation: University of Toronto Date: November 19, 2020 For more video please visit h
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory