In mathematics, Koszul duality, named after the French mathematician Jean-Louis Koszul, is any of various kinds of dualities found in representation theory of Lie algebras, abstract algebras (semisimple algebra) and topology (e.g., equivariant cohomology). The prototype example, due to Joseph Bernstein, Israel Gelfand, and Sergei Gelfand, is the rough duality between the derived category of a symmetric algebra and that of an exterior algebra. The importance of the notion rests on the suspicion that Koszul duality seems quite ubiquitous in nature. (Wikipedia).
K-Motives and Koszul Duality in Geometric Representation Theory - Jens Eberhardt
K-Motives and Koszul Duality in Geometric Representation Theory - Jens Eberhardt Geometric and Modular Representation Theory Seminar Topic: K-Motives and Koszul Duality in Geometric Representation Theory Speaker: Jens Eberhardt Affiliation: Max Planck Institute Date: April 07, 2021 For m
From playlist Mathematics
Koszul duality phenomenon for the Hecke category - Shotaro Makisumi
Short Talks by Postdoctoral Members Koszul duality phenomenon for the Hecke category Shotaro Makisumi Member, School of Mathematics Date: September 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Geordie Williamson. Some examples of Koszul duality via dg algebras
Seminar talk on CORONA GS: https://murmuno.mit.edu/coronags Abstract: I will explain the basics of Morita theory for derived categories and give some examples, including the classic BGG duality between symmetric and exterior algebras. This is standard stuff but should perhaps be better kn
From playlist CORONA GS
Commutative algebra 63: Koszul complex
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We define the Koszul complex of a sequence of elements of a ring, and show it is exact if the sequence is regular. This gives
From playlist Commutative algebra
Duality in Higher Categories-I by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Commutative algebra 64: Gorenstein rings
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give an informal introduction to Gorenstein local rings, which are informally those with good duality properties. We give s
From playlist Commutative algebra
Alexandru Dimca: Betti numbers of hypersurfaces and defects of linear systems II
Our approach is a generalization of Griffiths' results expressing the cohomology ofa smooth hypersurface V: f = 0 in a projective space P^n in terms of some graded pieces of the Jacobian algebra of f. We will start by recalling these classical results. Then we explain that when the hyp
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Duality In Higher Categories III by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Duality in Algebraic Geometry by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Duality In Higher Categories II by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Kirsten Wickelgren - Integrability Result for 𝔸^1-Euler Numbers
Notes: https://nextcloud.ihes.fr/index.php/s/q5f4YriEPGq6dBJ -- 𝔸^1-Euler numbers can be constructed with Hochschild homology, self-duality of Koszul complexes, pushforwards in 𝑆𝐿_𝑐 oriented cohomology theories, and sums of local degrees. We show an integrality result for 𝔸^1-Euler number
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Ben Webster: Gelfand-Tsetlin theory and Coulomb branches
Abstract: The algebra U(gln) contains a famous and beautiful commutative subalgebra, called the Gelfand-Tsetlin subalgebra. One problem which has attracted great attention over the recent decades is to classify the simple modules on which this subalgebra acts locally finitely (the Gelfand-
From playlist Algebra
On the Mod p Cohomology for GL_2 (II) by Yongquan Hu
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
From Cohomology to Derived Functors by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Jens Eberhardt: Motivic Springer Theory
27 September 2021 Abstract: Algebras and their representations can often be constructed geometrically in terms of convolution of cycles. For example, the Springer correspondence describes how irreducible representations of a Weyl group can be realised in terms of a convolution action on
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Verdier And Grothendieck Duality (Lecture 4) by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)