Upcoming Talk
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Past and future talks
Date: 22 August, 2022, 14:00-15:30 (JST)
Place: Online
Speaker: Takashi Hara (Tsuda University)
Title: On algebraicity and integrality of critical values of the Rankin--Selberg L-functions for GL(n+1) × GL(n)
Abstract: Critical values of the Rankin--Selberg L-functions for GL(n+1) × GL(n) can be interpreted geometrically as the cup products of certain cohomology classes. Raghuram, Shahidi and others have used this fact to discuss algebraicity of the critical values. In this talk, after briefly introducing geometric interpretation of critical values of the Rankin--Selberg L-functions for GL(n+1) × GL(n), we will explain that one can deduce more detailed information on algebraicity and integrality of the critical values when the base field is totally imaginary, based upon precise analysis at archimedean places (more explicitly, by normalisation of generators of the (g,K)-cohomology groups). This is a joint work with Tadashi Miyazaki (Kitasato University) and Kenichi Namikawa (Tokyo Denki University).
Slide: Here
Video: Available. Email to Hayashi.
Date: 22 July, 2022, 17:30-19:00 (JST)
Place: Online
Speaker: Shunya Saito (Nagoya University)
Title: The spectrum of Grothendieck monoid: a new approach to classify Serre subcategories
Abstract: In his celebrated paper on abelian categories, Gabriel classified Serre subcategories of the category of coherent sheaves and reconstructed a noetherian scheme from the category of quasi-coherent sheaves on it.
In this talk, I will shed new light on these results via Grothendieck monoids. The Grothendieck monoid is a monoid version of the Grothendieck group, which is defined for each exact category. I will classify Serre subcategories of an exact category via its Grothendieck monoid and reconstruct the topology of a noetherian scheme from the Grothendieck monoid of the category of coherent sheaves. I will give examples of classifying Serre subcategories of exact categories related to a finite dimensional algebra and a smooth projective curve.
Slide: Here
Video: Available. Email to Asai.
Date: 20 June, 2022, 17:00-18:30 (JST)
Place: Online
Speaker: Fabian Januszewski (Paderborn University)
Title: Rational and integral structures on automorphic representations
Abstract: I will discuss known and expected relations between rational and integral structures on automorphic representations and special values of L-functions. This will touch upon joint work with Takuma Hayashi.
Slide: Here
Video: Available. Email to Hayashi.
Date: 30 May, 2022, 15:30-17:00 (JST)
Place: Online
Speaker: Mayu Tsukamoto (Yamaguchi University)
Title: Cotorsion pairs and silting subcategories in extriangulated categories
Abstract: Bondarko and Mendoza--Santiago--Saenz--Souto gave a bijection between bounded co-t-structures and silting subcategories in a triangulated category. In this talk, we generalize their result. Namely, we establish a bijection between bounded hereditary cotorsion pairs and silting subcategories in an extriangulated category. Moreover, we show that our result recovers a bijection between contravariantly finite resolving subcategories and basic tilting modules for a finite dimensional algebra with finite global dimension. This talk is based on a joint work with Takahide Adachi.
Slide: Here
Video: Available. Email to Asai.
Date: 25 January, 2022, 15:30-17:00 (JST)
Place: Online
Speaker: Shilin Yu (Xiamen University)
Title: Families of representations of Lie groups
Abstract: Beilinson and Bernstein generalized the Borel-Weil-Bott theorem and showed that representations of a (noncompact) reductive Lie group G can be realized as D-modules on flag variety. In this talk, I will show that such D-modules live naturally in families, which explains a mysterious analogy between representation theory of the group G and that of its Cartan motion group, due to Mackey, Higson and Afgoustidis.
Slide: Here
Video: Available. Email to Hayashi.
Date: 25 November, 2021, 15:30-17:00 (JST)
Place: Online
Speaker: Yasuaki Gyoda (Nagoya University)
Title: Generalization of Gabriel’s theorem in τ -tilting theory and its cluster algebraic approach
Abstract: Gabriel’s theorem, shown in 1972, is a theorem that classifies path algebras of finite representation type using Dynkin diagrams, and is a very important theorem that suggests a connection between Lie theory and the representation theory of algebras. In this talk, I will generalize Gabriel’s theorem by using cluster algebra theory, which has been rapidly developed recently and is closely related to both Lie theory and the representation theory of algebras.
Slide: Here
Video: Available. Email to Asai.
Date: 26 October, 2021, 15:30-17:00 (JST)
Place: Online
Speaker: Eyal Subag (Bar-Ilan University)
Title: The algebraic symmetry of the hydrogen atom
Abstract: The hydrogen atom system is a fundamental example of a quantum mechanical system. Symmetry plays the main role in our current understanding of the system. In this talk I will describe a new type of algebraic symmetry for the system. I will show that the collection of all regular solutions of the Schrödinger equation is an algebraic family of representations of different algebras. Such a family is known as an algebraic family of Harish-Chandra modules. The algebraic family has a canonical filtration from which the physically relevant solutions and the spectrum of the Schrödinger operator can be recovered.
If time permits I will relate the spectral theory of the Schrödinger operator to the algebraic family. No prior knowledge about quantum mechanics will be assumed.
Slide: Here
Video: Available. Email to Hayashi.
Date: 21 September, 2021, 15:30-17:00 (JST)
Place: Online
Speaker: Takahiro Honma (Tokyo University of Science)
Title: When is the silting-discreteness inherited?
Abstract: Silting objects play a central role in tilting theory. To classify silting objects, we observe the finiteness of silting objects of a triangulated category, say the silting discreteness. In this talk, we explain when the silting-discreteness is inherited from a given silting-discrete triangulated category. Moreover, we apply our results to Nakayama algebras; in fact, one obtains a surprising example of silting-indiscrete selfinjective Nakayama algebras.
Slide: Here
Video: Available. Email to Asai.
Date: 27 July, 2021, 15:30-17:00 (JST)
Place: Online
Speaker: Taiki Shibata (Okayama University of Science)
Title: Borel-Weil theorem for algebraic supergroups
Abstract: An algebraic supergroup defined over a field k is just the super-analogue of the notion of affine algebraic group schemes over k, that is, a representable group-valued functor on the category of commutative k-superalgebras (=Z_2-graded k-algebras with supersymmetry) represented by a finitely generated commutative k-superalgebra. Over the field of complex numbers, structures and representations of finite-dimensional simple Lie superalgebras have been well-studied. In contrast to this, the study of algebraic supergroups (especially, defined over a filed of positive characteristic) has just started.
In this talk, I will explain a framework of characteristic-free study of structures and representations of algebraic supergroups (more precisely, quasireductive supergroups which are the super-analogue of the notion of split reductive groups) via a Hopf-algebraic approach. First, we review some known results on algebraic supergroups by giving some examples. Then we construct all irreducible representations of an algebraic supergroup by the super-analogue of the Borel-Weil theorem.
Slide: Here
Video: Available. Email to Hayashi.
Date: 29 June, 2021, 15:30-17:00 (JST)
Place: Online
Speaker: Kota Murakami (Kyoto University)
Title: PBW parametrizations and generalized preprojective algebras
Abstract: There are many relationships between quiver representation theory and Lie theory after Gabriel’s theorem, which gives a bijection between the set of isoclasses of indecomposable representations of a Dynkin quiver and the set of positive roots. Recently, Geiss-Leclerc-Schröer has introduced certain classes of quivers with relations associated with symmetrizable Cartan matrices. They have developed representation theory of these algebras based on generalized preprojective algebras and their reflection functors. In this talk, we review GLS’s algebras and reflection functors. Then, we understand some combinatorial information about canonical basis of quantum groups through representation theory of generalized preprojective algebras.
Slide: Here
Video: Available. Email to Asai.
Organizing committee: Susumu Ariki, Yoshiki Oshima, Takuma Hayashi, Sota Asai, Toshitaka Aoki.
This seminar is supported by JSPS KAKENHI Grant Numbers 21J00023 (Hayashi) and 20J00088 (Asai).