Atsushi Takahshi: On the Frobenius structure for the Weierstrass ℘-function
Abstract: We will discuss the naturally normalized primitive form and the Frobenius structure associated to the Weierstrass $\wp$-function
We also plan to give the construction of the Frobenius structure via elliptic Weyl group invariants of type $A_1$, as well as the isomorphism between these two Frobenius structures via the period mappings. A relation to the space of stability conditions for a partially wrapped
Fukaya category will also be explained.
Sukjoo Lee: Irregular Hodge Number Duality for Clarke Mirror Pairs
Abstract: In the first part of the talk, I will introduce Clarke’s construction of mirror pairs of Landau–Ginzburg models, which can be regarded as a unifying framework for toric mirror constructions. I will focus in particular on how it recovers the Berglund–Hübsch–Krawitz (BHK) mirror symmetry. In the second part, I will discuss the irregular Hodge number duality for Clarke mirror pairs. This result recovers the orbifold Hodge number duality for BHK mirrors previously proven by Ebeling, Gusein-Zade, and Takahashi.
Keiho Matsumoto: K-theoretic Invariants of Non-commutative Spaces
Abstract: For an algebraic variety X, combining several cohomology theories—singular (Betti) cohomology H_B(X), de Rham cohomology H_{dR}(X), and ℓ-adic cohomology H_{l}(X)—yields fundamental motivic invariants such as L-functions, periods, and motivic height function.
In recent years, non-commutative spaces have emerged as broad generalizations of algebraic varieties. It is expected that, for these spaces as well, one can construct motivic invariants using various flavors of K-theory—such as topological K-theory, periodic cyclic homology, and K(1)-local K-theory. In this talk, I will survey these K-theoretic frameworks for non-commutative spaces and explain how they relate to each other.
Seokbong Seol: The Atiyah class of DG manifolds of positive amplitude
Abstract: Although the fibre product of smooth manifolds is not well-defined in the category of smooth manifolds, the notion of a homotopy fibre product is well-defined up to homotopy in the category of differential graded (DG) manifolds of positive amplitude. In a sense, the homotopy category of DG manifolds of positive amplitude captures aspects of derived geometry in the C-infinity setting.
The Atiyah class plays a central role in the study of DG manifolds. Originally introduced by Atiyah as an obstruction to the existence of a holomorphic connection, the Atiyah class of a DG manifold serves as an obstruction to the existence of a connection compatible with its DG structure. Moreover, it is a key ingredient in Duflo-Kontsevich-type theorem for DG manifolds.
In this talk, we will investigate the Atiyah class for DG manifolds of positive amplitude in two directions: its geometric interpretation in a simple case, and its invariance under homotopy