Department of Mathematics
A working seminar on algebra, geometry and mathematical physics, run largely as short lecture series by visiting researchers rather than as single talks. Several of the series below ran over three or four consecutive meetings.
This seminar is not meeting at the moment. The talks given so far are listed below. If it resumes, announcements will appear here.
If you would like to help restart it, or to give a talk, write to math@newuu.uz. The department’s general Department Seminar is running in the meantime.
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.
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.
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.
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.
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.
In this talk we define dynamic polynomials of two complex variables that live in the parameter space of cubic polynomials and study their irreducibility.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.