Algebraic Geometry

Skeleta for Monomial Quiver Relations

Speaker: 
Jesse Huang
Date: 
Wed, Dec 1, 2021
Location: 
PIMS, University of Alberta
Zoom
Online
Conference: 
Emergent Research: The PIMS Postdoctoral Fellow Seminar
Abstract: 

I will introduce a skeleton obtained directly from monomial relations in a finite quiver without cycles, and relate the construction to some classical examples in mirror symmetry. This is work in progress with David Favero.

Class: 

Differential Equations and Algebraic Geometry - 5

Speaker: 
Andreas Malmendier
Date: 
Mon, Nov 15, 2021
Location: 
PIMS, University of Alberta
Zoom
Online
Conference: 
PIMS Network Courses
Differential Equations and Algebraic Geometry
Abstract: 

This is a guest lecture in the PIMS Network Wide Graduate Course in Differential Equations in Algebraic Geometry.

Class: 

Differential Equations and Algebraic Geometry - 4

Speaker: 
Matt Kerr
Date: 
Fri, Nov 5, 2021
Location: 
PIMS, University of Alberta
Zoom
Online
Conference: 
PIMS Network Courses
Differential Equations and Algebraic Geometry
Abstract: 

This is a guest lecture in the PIMS Network Wide Graduate Course in Differential Equations in Algebraic Geometry.

Class: 

Differential Equations and Algebraic Geometry - 3

Speaker: 
Adrian Clingher
Date: 
Wed, Nov 3, 2021
Location: 
PIMS, University of Alberta
Zoom
Online
Conference: 
PIMS Network Courses
Differential Equations and Algebraic Geometry
Abstract: 

This is a guest lecture in the PIMS Network Wide Graduate Course in Differential Equations in Algebraic Geometry.

Class: 

Differential Equations and Algebraic Geometry - 2

Speaker: 
Hossein Movasati
Date: 
Sat, Oct 30, 2021
Location: 
PIMS, University of Alberta
Zoom
Conference: 
PIMS Network Courses
Differential Equations and Algebraic Geometry
Abstract: 

This is a guest lecture in the PIMS Network Wide Graduate Course in Differential Equations in Algebraic Geometry.

Class: 

Differential Equations and Algebraic Geometry - 1

Speaker: 
Hossein Movasati
Date: 
Wed, Oct 27, 2021
Location: 
PIMS, University of Alberta
Zoom
Conference: 
PIMS Network Courses
Differential Equations and Algebraic Geometry
Abstract: 

This is a guest lecture in the PIMS Network Wide Graduate Course in Differential Equations in Algebraic Geometry.

Class: 

Branes, Quivers, and BPS Algebras 4 of 4

Speaker: 
Miroslav Rapčák
Date: 
Thu, Aug 26, 2021
Location: 
PIMS, University of Saskatchewan
Online
Zoom
Conference: 
2nd PIMS Summer School on Algebraic Geometry in High Energy Physics
Abstract: 

This series of lectures covers a brief introduction into some algebro-geometric techniques used in the construction of BPS algebras. The starting point of our construction is a physical picture of D0-branes bound to D-branes of higher dimension. Using methods of the derived category of coherent sheaves, we are going to derive a framed quiver with potential describing supersymmetric quantum mechanics capturing the low-energy behavior of such D0-branes. For a large class of quivers, we are going to identify the space of BPS states with different melted-crystal configurations. Finally, by employing correspondences, we are going to construct an action of a BPS algebra known as the affine Yangian on the space of BPS states. The action of the affine Yangian factors through the action of various vertex operator algebras, Cherednik algebras, and more. This construction leads to an enormously rich interplay between physics, geometry and representation theory.

  1. Lecture 1
  2. Lecture 2
  3. Lecture 3
  4. Lecture 4
Class: 

Branes, Quivers, and BPS Algebras 3 of 4

Speaker: 
Miroslav Rapčák
Date: 
Wed, Aug 25, 2021
Location: 
PIMS, University of Saskatchewan
Online
Zoom
Conference: 
2nd PIMS Summer School on Algebraic Geometry in High Energy Physics
Abstract: 

This series of lectures covers a brief introduction into some algebro-geometric techniques used in the construction of BPS algebras. The starting point of our construction is a physical picture of D0-branes bound to D-branes of higher dimension. Using methods of the derived category of coherent sheaves, we are going to derive a framed quiver with potential describing supersymmetric quantum mechanics capturing the low-energy behavior of such D0-branes. For a large class of quivers, we are going to identify the space of BPS states with different melted-crystal configurations. Finally, by employing correspondences, we are going to construct an action of a BPS algebra known as the affine Yangian on the space of BPS states. The action of the affine Yangian factors through the action of various vertex operator algebras, Cherednik algebras, and more. This construction leads to an enormously rich interplay between physics, geometry and representation theory.

  1. Lecture 1
  2. Lecture 2
  3. Lecture 3
  4. Lecture 4
Class: 

Branes, Quivers, and BPS Algebras 2 of 4

Speaker: 
Miroslav Rapčák
Date: 
Tue, Aug 24, 2021
Location: 
PIMS, University of Saskatchewan
Online
Zoom
Conference: 
2nd PIMS Summer School on Algebraic Geometry in High Energy Physics
Abstract: 

This series of lectures covers a brief introduction into some algebro-geometric techniques used in the construction of BPS algebras. The starting point of our construction is a physical picture of D0-branes bound to D-branes of higher dimension. Using methods of the derived category of coherent sheaves, we are going to derive a framed quiver with potential describing supersymmetric quantum mechanics capturing the low-energy behavior of such D0-branes. For a large class of quivers, we are going to identify the space of BPS states with different melted-crystal configurations. Finally, by employing correspondences, we are going to construct an action of a BPS algebra known as the affine Yangian on the space of BPS states. The action of the affine Yangian factors through the action of various vertex operator algebras, Cherednik algebras, and more. This construction leads to an enormously rich interplay between physics, geometry and representation theory.

  1. Lecture 1
  2. Lecture 2
  3. Lecture 3
  4. Lecture 4
Class: 

Branes, Quivers, and BPS Algebras 1 of 4

Speaker: 
Miroslav Rapčák
Date: 
Mon, Aug 23, 2021
Location: 
PIMS, University of Saskatchewan
Online
Zoom
Conference: 
2nd PIMS Summer School on Algebraic Geometry in High Energy Physics
Abstract: 

This series of lectures covers a brief introduction into some algebro-geometric techniques used in the construction of BPS algebras. The starting point of our construction is a physical picture of D0-branes bound to D-branes of higher dimension. Using methods of the derived category of coherent sheaves, we are going to derive a framed quiver with potential describing supersymmetric quantum mechanics capturing the low-energy behavior of such D0-branes. For a large class of quivers, we are going to identify the space of BPS states with different melted-crystal configurations. Finally, by employing correspondences, we are going to construct an action of a BPS algebra known as the affine Yangian on the space of BPS states. The action of the affine Yangian factors through the action of various vertex operator algebras, Cherednik algebras, and more. This construction leads to an enormously rich interplay between physics, geometry and representation theory.

  1. Lecture 1
  2. Lecture 2
  3. Lecture 3
  4. Lecture 4
Class: 

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