Seminar on Algebra, Geometry and Physics
An introduction of Gromov-Witten theory and localization method - IV
Weiqiang He (Sun Yat-sen University) - 4:30pm-6:30pm, July 18, 2024 - UCA 208
Abstract: I will give four lectures on the Gromov-Witten theory and localization method. In the first two lectures I will talk about the motivation, the definition and some basic properties of Gromov-Witten theory. The second two lectures are a discussion in the Atiyah-Bott localization theorem and its application in the calculation of Gromov-Witten invariants.
An introduction of Gromov-Witten theory and localization method - III
Weiqiang He (Sun Yat-sen University) - 2:00pm-4:00pm, July 18, 2024 - UCA 208
Abstract: I will give four lectures on the Gromov-Witten theory and localization method. In the first two lectures I will talk about the motivation, the definition and some basic properties of Gromov-Witten theory. The second two lectures are a discussion in the Atiyah-Bott localization theorem and its application in the calculation of Gromov-Witten invariants.
An introduction of Gromov-Witten theory and localization method - II
Weiqiang He (Sun Yat-sen University) - 4:30pm-6:30pm, July 16, 2024 - UCA 208
Abstract: I will give four lectures on the Gromov-Witten theory and localization method. In the first two lectures I will talk about the motivation, the definition and some basic properties of Gromov-Witten theory. The second two lectures are a discussion in the Atiyah-Bott localization theorem and its application in the calculation of Gromov-Witten invariants.
An introduction of Gromov-Witten theory and localization method - I
Weiqiang He (Sun Yat-sen University) - 2:00pm-4:00pm, July 16, 2024 - UCA 208
Abstract: I will give four lectures on the Gromov-Witten theory and localization method. In the first two lectures I will talk about the motivation, the definition and some basic properties of Gromov-Witten theory. The second two lectures are a discussion in the Atiyah-Bott localization theorem and its application in the calculation of Gromov-Witten invariants.
From abelianization to stabilization - IV
Zhuyang Li - 10:00am-12:00am, June 6, 2024 - MATH 310
Abstract: Modules over a commutative ring can be regarded as abelian group objects in the over-category of commutative rings, and the same story also holds for associative algebras and their bimodules. This point of view was used by Quillen (in a derived way) to define cohomogy groups for objects in general model categories. The (derived) abelianization of the identity in a model category of objects over an object is referred to as the abstract cotangent complex of that object. Nowadays there is a refined version of abelianization, called stabilization, allowing this "abstract cotangent complex formalism" to hold in more general situations.
Dynamic polynomials and their irreducibility
Khudoyor Mamayusupov - 1:00PM-3:00pm, June 4, 2024 - MATH 209
In this talk we define dynamic polynomials of two complex variables that live in the parameter space of cubic polynomials and study their irreducibility.
From abelianization to stabilization - III
Zhuyang Li - 10:00am-12:00am, June 4, 2024 - MATH 209
Abstract: Modules over a commutative ring can be regarded as abelian group objects in the over-category of commutative rings, and the same story also holds for associative algebras and their bimodules. This point of view was used by Quillen (in a derived way) to define cohomogy groups for objects in general model categories. The (derived) abelianization of the identity in a model category of objects over an object is referred to as the abstract cotangent complex of that object. Nowadays there is a refined version of abelianization, called stabilization, allowing this "abstract cotangent complex formalism" to hold in more general situations.
From abelianization to stabilization - II
Zhuyang Li - 4:00pm-6:00pm, June 2, 2024 - MATH 109
Abstract: Modules over a commutative ring can be regarded as abelian group objects in the over-category of commutative rings, and the same story also holds for associative algebras and their bimodules. This point of view was used by Quillen (in a derived way) to define cohomogy groups for objects in general model categories. The (derived) abelianization of the identity in a model category of objects over an object is referred to as the abstract cotangent complex of that object. Nowadays there is a refined version of abelianization, called stabilization, allowing this "abstract cotangent complex formalism" to hold in more general situations.
From abelianization to stabilization - I
Zhuyang Li - 4:00pm-6:00pm, May 30, 2024 - MATH 210
Abstract: Modules over a commutative ring can be regarded as abelian group objects in the over-category of commutative rings, and the same story also holds for associative algebras and their bimodules. This point of view was used by Quillen (in a derived way) to define cohomogy groups for objects in general model categories. The (derived) abelianization of the identity in a model category of objects over an object is referred to as the abstract cotangent complex of that object. Nowadays there is a refined version of abelianization, called stabilization, allowing this "abstract cotangent complex formalism" to hold in more general situations.
Kleinian singularities and McKay correspondence - II
Meiliang Liu - 10:00am-12:00am, May 28, 2024 - MATH 209
Abstract: In this series of talks, I will introduce some basics of Kleinian singularities, espcially their constructions from geometric representation theory such as from Nakajima quiver varieties, Slowdowy slices and affine Grassmannians.
Diagrammatics for Coxeter groups and their braid groups - III
Xin Qin - 10:00am-12:00am, May 22, 2024 - MATH 308
I will give a monoidal presentation of Coxeter and braid 2-groups, in terms of decorated plannar graphs. This diagrammatic presentation extends the usual Coxeter presentation and gives a simple criterion for establishing a strict action of a Coxeter group and its braid group on a category.
Diagrammatics for Coxeter groups and their braid groups - II
Xin Qin - 10:00am-12:00am, May 21, 2024 - MATH 301
I will give a monoidal presentation of Coxeter and braid 2-groups, in terms of decorated plannar graphs. This diagrammatic presentation extends the usual Coxeter presentation and gives a simple criterion for establishing a strict action of a Coxeter group and its braid group on a category.
Diagrammatics for Coxeter groups and their braid groups - I
Xin Qin - 10:00am-12:00am, May 7, 2024 - MATH 201
I will give a monoidal presentation of Coxeter and braid 2-groups, in terms of decorated plannar graphs. This diagrammatic presentation extends the usual Coxeter presentation and gives a simple criterion for establishing a strict action of a Coxeter group and its braid group on a category.
Kleinian singularities and McKay correspondence - I
Meiliang Liu - 10:00am-12:00am, April 25, 2024 - MATH 109
Abstract: In this series of talks, I will introduce some basics of Kleinian singularities, espcially their constructions from geometric representation theory such as from Nakajima quiver varieties, Slowdowy slices and affine Grassmannians.
Introduction to Nakajima's Quiver Variety - III
Ruobing Chen - 10:00am-12:00am, April 23, 2024 - MATH 207
Abstract: In this series of talks, I will introduce Nakajima's quiver varieties, and discuss some of their basic properties. After that we will briefly discuss type A bow varieties and their 3d mirror symmetry. Examples of nilpotent cone/orbits will be given with some detail.
Introduction to Nakajima's Quiver Variety - II
Ruobing Chen - 10:00am-12:00am, April 17, 2024 - MATH 301
Abstract: In this series of talks, I will introduce Nakajima's quiver varieties, and discuss some of their basic properties. After that we will briefly discuss type A bow varieties and their 3d mirror symmetry. Examples of nilpotent cone/orbits will be given with some detail.
Introduction to Nakajima's Quiver Variety - I
Ruobing Chen - 10:00am-12:00am, April 16, 2024 - MATH 201
Abstract: In this series of talks, I will introduce Nakajima's quiver varieties, and discuss some of their basic properties. After that we will briefly discuss type A bow varieties and their 3d mirror symmetry. Examples of nilpotent cone/orbits will be given with some detail.