Date

July 13, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Simon Lentner (OIST, Okinawa Institute for Science and Technology)

Title

Nichols algebras, braided tensor categories and conformal field theory

Abstract

　 To any object in a braided tensor category we can associate a Nichols algebra, either through braid group combinatorics or through a universal property. The main motivation for Nichols algebras is to systematically construct the quantum group from its Cartan part. This idea goes back to Lusztig, but I will present it in modern categorical language. Then I will sketch how Nichols algebras can be used to construct solutions of the Knishnik Zomolochikov differential equation from its respective abelian version, and to construct a conformal field theory associated to the (small) quantum group from a free field theory. This parallelism is a main ingredient in our recent proof of the logarithmic Kazhdan Lusztig correspondence, which is the nonsemisimple small-quantum-group-analog of the more familiar Kazhdan Lusztig correspondence, and our current work on the affine Lie algebra sl2 at admissible level.

Date

July 6, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Hsuan-Yi Liao (National Tsing Hua University)

Title

A dg manifold approach to derived differentiable geometry

Abstract

　 One of the primary motivations behind derived differential geometry is the systematic treatment of singularities arising from zero loci or intersections of submanifolds. Both situations can be formulated as fiber products of manifolds, which often fail to be smooth. To resolve this, we extend the category of differentiable manifolds to a larger category where "homotopy fiber products" are well-defined. In this talk, we will discuss such an extended category using dg manifolds. This talk is mainly based on joint work with Kai Behrend and Ping Xu.

Date

June 29, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Kai Behrend (University of British Columbia)

Title

Point counting on the non-commutative Fermat quintic

Abstract

　 Calabi-Yau threefolds provide a natural setting for the enumerative geometry of curves. A naive dimension count suggests that the number of curves should be finite; however, the actual geometry is far more intricate and has been the subject of intensive study over the past thirty years. In this talk, we investigate non-commutative analogues of this setting. We consider non-commutative projective varieties and construct moduli spaces of stable modules over them. In the three-dimensional Calabi-Yau case, this gives rise to non-commutative analogues of Donaldson-Thomas “sheaf counting” invariants. The simplest example is the Fermat quintic in quantum projective space, where the coordinates commute up to carefully chosen fifth roots of unity. We explore the moduli theory of finite length modules. This mixes features of the Hilbert scheme of commutative threefolds, with the representation theory of quivers. This is joint work with Yu-Hsiang Liu, with contributions by Atsushi Kanazawa.

Date

June 22, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Shuhei Yonehara (Yonago Collage)

Title

Godbillon-Vey classes of Lie subalgebroids

Abstract

　 The Godbillon-Vey class is a secondary characteristic class defined for regular foliations and has been studied extensively. On the other hand, extending the Godbillon-Vey class to the setting of singular foliations is a difficult problem. A Lie algebroid is a generalization of the tangent bundle and is known to induce a singular foliation. In this talk, we define relative Godbillon-Vey classes for Lie subalgebroids and study their properties. We also present several concrete examples.

Date

June 15, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Ping Xu (Pennsylvania State University)

Title

$BV_\infty$ quantization of (-1)-shifted derived Poisson manifolds

Abstract

　 In this talk, we will give an overview of (-1)-shifted derived Poisson manifolds in the $C^\infty$-context, and discuss the quantization problem. We describe the obstruction theory and prove that the linear (-1)-shifted derived Poisson manifold associated to any $L_\infty$-algebroid admits a canonical $BV_\infty$ quantization. This is a joint work with Kai Behrend and Matt Peddie.

Date

June 8, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Yuji Hirota (Azabu University)

Title

Infinitesimal symmetry of Lie algebroids and generalization of momentum maps

Abstract

　 The talk aims to introduce a generalization of momentum maps that is associated with Lie algebroids. In particular, (homotopy) momentum sections, a relation to quaternionic Kaehler momentum maps, and reduction theory will be briefly discussed. If time permits, prequantization via momentum sections will be presented. The talk is based on the joint work with Noriaki Ikeda.

Date

June 1, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Mathieu Stiénon (Pennsylvania State University)

Title

Atiyah class and formal exponential maps of differential graded manifolds

Abstract

　 Exponential maps arise naturally in the contexts of Lie theory and smooth manifolds. The infinite jets of these classical exponential maps are related to Poincaré–Birkhoff–Witt  isomorphisms and the complete symbols of differential operators. It turns out that these formal exponential maps can be extended to the context of graded manifolds.

For dg manifolds, the formal exponential maps need not be compatible with the homological vector field and the incompatibility is captured by a cohomology class reminiscent of the Atiyah class of holomorphic vector bundles.

Indeed, the space of vector fields on a dg manifold carries a natural $L_\infty$ algebra structure whose binary bracket is a cocycle representative of the Atiyah class of the dg manifold. This $L_\infty$ algebra is essentially a generalization of the one on the Dolbeault complex of a Kähler manifold discovered by Kapranov in his work on Rozansky-Witten invariants.

Date

May 25, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Wenda Fang (RIMS, Kyoto University)

Title

QP Structures, Poisson Vertex Algebras, and Applications to Integrable Systems

Abstract

　 In this talk, I will discuss classical (R)-matrices for Lie conformal algebras from the viewpoint of QP-geometry. I will explain how this perspective leads to a Maurer--Cartan description of such structures, and how it can be used to construct integrable systems via a generalized Adler--Kostant--Symes scheme. As an application, I will present an integrable system of Mumford--Beauville type. I will also briefly mention some ongoing directions related to joint work with Noriaki Ikeda.

Date

May 18, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Ryo Hayami (Nagano University)

Title

Lie group-rack triples and Lie-Leibniz triples -with a view towards an integration theory of embedding tensors-

Abstract

　 Embedding tensors are used in theoretical physics to describe higher gauge structures which are called tensor hierarchies. To understand geometric aspects of tensor hierarchies, we should find how to "integrate" embedding tensors.
A Lie-Leibniz triple is the mathematical formulation of an embedding tensor. In this talk, I will introduce an integrated object of a Lie-Leibniz triple, which we call a Lie group-rack triple. I will show that any real finite-dimensional Lie-Leibniz triple can be integrated to a local Lie group-rack triple. This integration procedure can be seen as a generalization of the Bordemann-Wagemann integration of an augmented Leibniz algebra into an augmented Lie rack.

Date

May 11, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Naoki Genra (Toyama University)

Title

BRST cohomology for linear quiver gauge theory and associated Poisson vertex algebras

Abstract

　 BRST cohomology is an analogous method with Hamiltonian reductions to obtain new vertex algebras from given ones. Using the construction of physicists, we give the BRST cohomology vertex algebras of 3d N=4 quiver gauge theory, and compute the associated graded Poisson vertex algebras. Then we show how to relate these Poisson vertex algebras to Higgs branches of linear quiver gauge theory.

Date

April 27, Monday, 10:30--11:30, 2026

Place

Room 206, RIMS

Speaker

Leonid Ryvkin (Claude Bernard University Lyon 1)

Title

Tepui fibrations and singular vector bundles

Abstract

　 As a differential-geometric object, a tepui fibration is a type of singular fiber bundle with smooth base space and smooth fibers, however the fiber dimension might jump when moving from one base point to another. Tepui fibrations naturally turn up in differential geometry, when one is quotienting by a smooth family of symmetries, which degenerates at certain points, e.g. in the context of singular foliations. In this talk I will give an introduction to tepui fibrations and show how they provide a natural way to extend the classical Serre-Swan theorem beyond the setting of projective modules.
Based on joint work with Alfonso Garmendia and David Miyamoto, https://arxiv.org/pdf/2510.20936.