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

### 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

### 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.