| | Orateur(s) | Titre | Date | Début | Salle | Adresse |
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Dylan ALLEGRETTI
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Quiver representations, cluster varieties, and categorification of canonical bases |
22/02/2019 |
16:15 |
!1016 |
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| Associated to a compact oriented surface with marked points on its boundary is an interesting class of finite-dimensional algebras. These algebras are examples of gentle algebras, and their representation theory has been studied by many authors in connection with the theory of cluster algebras. An important fact about these algebras is that their indecomposable modules come in two types: string modules, which correspond to arcs connecting marked points on the surface, and band modules, which correspond to closed loops on the surface. Thanks to the work of many mathematicians, the string modules are known to categorify generators of a cluster algebra. In this talk, I will explain how, by including band modules in this story, one can define a family of graded vector spaces which categorify Fock and Goncharov's canonical basis for the algebra of functions on an associated cluster variety. These vector spaces are of interest in mathematical physics, where they are expected to provide a mathematical definition of the space of framed BPS states from the work of Gaiotto, Moore, and Neitzke. |
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Steffen OPPERMANN
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On higher Auslander-Reiten components |
04/05/2018 |
15:30 |
!salle 2015 |
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| This talk is based on joint work with \href{http://www2.math.uu.se/~martinh/}{Martin Herschend}.
In classical Auslander-Reiten theory, one first defines almost split sequence, and subsequently arranges them into AR components.
In higher dimensional Auslander-Reiten theory the notion of almost split sequences depends on the choice of a rigid (hence discrete) subcategory.
In this setup, we suggest an axiomatic definition of AR components, and explore examples and properties. |
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Gus SCHRADER
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Geometric construction of Yangians, after Maulik and Okounkov |
14/04/2016 |
16:00 |
!1002 |
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| I will present two expository lectures on the work of Maulik and Okounkov (\href{}{http://arxiv.org/abs/1211.1287}), focusing on the geometric R-matrix formalism which leads to the construction of a Hopf algebra $Y_Q$ acting on the equivariant cohomology of the Nakajima varieties associated to a quiver $Q$.
In the second lecture, we will see how many features of the Grassmannian example carry over to the more general setting of Nakajima quiver varieties. We will review the definition of these varieties, and present the definition of the Maulik-Okounkov Yangian $Y_Q$ associated to a quiver $Q$. Time permitting, we will outline some ideas on how to extend the Maulik-Okounkov construction to encompass Yangian coideal subalgebras, such as the reflection equation algebra. |
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Gus SCHRADER
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Geometric construction of Yangians, after Maulik and Okounkov |
11/04/2016 |
16:00 |
!1004 |
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| I will present two expository lectures on the work of Maulik and Okounkov (\href{}{http://arxiv.org/abs/1211.1287}), focusing on the geometric R-matrix formalism which leads to the construction of a Hopf algebra $Y_Q$ acting on the equivariant cohomology of the Nakajima varieties associated to a quiver $Q$.
In the first lecture, I will give an overview of the stable basis construction in the equivariant cohomology of an algebraic symplectic variety, which is the key technical tool used to construct the geometric R-matrices. I will then present an explicit example of the Maulik-Okounkov construction in the simple case of cotangent bundles to Grassmannians, which will yield a geometric construction of the Yangian of $gl_2$. |
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Ju-Lee KIM
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Quiver Hecke algebras, quantum affine algebras and monoidal categorification of cluster algebras |
21/03/2016 |
10:00 |
!1012 |
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Ju-Lee KIM
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Quiver Hecke algebras, quantum affine algebras and monoidal categorification of cluster algebras |
14/03/2016 |
10:00 |
!1012 |
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Ju-Lee KIM
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Quiver Hecke algebras, quantum affine algebras and monoidal categorification of cluster algebras |
22/02/2016 |
10:00 |
1012 |
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Ju-Lee KIM
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Quiver Hecke algebras, quantum affine algebras and monoidal categorification of cluster algebras |
15/02/2016 |
10:00 |
1012 |
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Ju-Lee KIM
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Quiver Hecke algebras, quantum affine algebras and monoidal categorification of cluster algebras |
25/01/2016 |
10:00 |
1012 |
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Ju-Lee KIM
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Quiver Hecke algebras, quantum affine algebras and monoidal categorification of cluster algebras |
18/01/2016 |
10:00 |
1012 |
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