Directed graphs | Invariant theory | Representation theory
In mathematics, given a quiver Q with set of vertices Q0 and set of arrows Q1, a representation of Q assigns a vector space Vi to each vertex and a linear map V(α): V(s(α)) → V(t(α)) to each arrow α, where s(α), t(α) are, respectively, the starting and the ending vertices of α. Given an element d ∈ Q0, the set of representations of Q with dim Vi = d(i) for each i has a vector space structure. It is naturally endowed with an action of the algebraic group Πi∈Q0 GL(d(i)) by simultaneous base change. Such action induces one on the ring of functions. The ones which are invariants up to a character of the group are called semi-invariants. They form a ring whose structure reflects representation-theoretical properties of the quiver. (Wikipedia).
Pierre Descombes - Donaldson-Thomas Invariants of Toric Quivers
Donaldson-Thomas theory aims at counting sheaves on Calabi-Yau threefolds. The category of sheaves on a toric threefold is derived equivalent to the category of representation of a quiver with potential obtained from a tiling of the torus. On this class of example, the virtual Euler number
From playlist Workshop on Quantum Geometry
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 1/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 4/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 3/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Quiver moduli and applications, Markus Reineke (Bochum), Lecture 3
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Anna Seigal: "Principal Components along Quiver Representations"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Principal Components along Quiver Representations" Anna Seigal - University of Oxford, Mathematics Abstract: A quiver i
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum), Lecture 5
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 2/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum), Lecture 4
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Maxime Fairon - Integrable Systems on (Multiplicative) Quiver Varieties
Following the pioneering work of Wilson who realized the phase space of the (classical complex) Calogero-Moser system as a quiver variety, Chalykh and Silantyev observed in 2017 that various generalizations of this integrable system can be constructed on quiver varieties associated with cy
From playlist Workshop on Quantum Geometry
Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum), Lecture 2
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Victoria Hoskins: Group actions on quiver moduli spaces and applications
Abstract: We study two types of actions on King’s moduli spaces of quiver representations over a field k, and we decompose their fixed loci using group cohomology in order to give modular interpretations of the components. The first type of action arises by considering finite groups of qui
From playlist Algebraic and Complex Geometry
Emily Cliff: Hilbert Schemes Lecture 6
SMRI Seminar Series: 'Hilbert Schemes' Lecture 6 GIT stability, quiver representations, & Hilbert schemes Emily Cliff (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
From playlist SMRI Course: Hilbert Schemes
Singular moduli spaces and Nakajima quiver varieties - Giulia Saccà
Giulia Saccà Member, School of Mathematics October 28, 2014 The aim of this talk is to study a class of singularities of moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non generic polarization, with r
From playlist Mathematics
Robyn Brooks and Celia Hacker (6/24/20): Morse-based fibering of the rank invariant
Title: Morse-based fibering of the rank invariant Abstract: Given the success of single-parameter persistence in data analysis and the fact that some systems warrant analysis across multiple parameters, it is highly desirable to develop data analysis pipelines based on multi-parameter per
From playlist AATRN 2020