Date: 2026 July 4th (Sat) - 5th (Sun)
Venue: Tokyo Metropolitan University, Minami-Osawa Campus
Registration Form (TBA)
Dining Information (TBA)
::: Speakers :::
Kazuhiro Ito (Tohoku University)
Rikuto Ito (Nagoya University)
Masanobu Kaneko (Kyushu University)
Toshiki Matsusaka (Kyushu University)
Yuya Murakami (RIKEN iTHEMS)
Taro Sano (Kobe University)
Yuta Takada (University of Tokyo)
Hiro-o Tokunaga (Tokyo Metropolitan University)
Kenji Ueno (Yokkaichi University, Tokyo Metropolitan University)
Noriko Yui (Queen's University)
::: Program (tentative) :::
July 4th
10:00-10:45: Taro Sano
11:00-11:45: Yuta Takada
13:45-14:30: Kazuhiro Ito
14:45-15:30: Yuya Murakami
15:45-16:30: Hiro-o Tokunaga
discussion
July 5th
10:00-10:45: Masanobu Kaneko
11:00-11:45: Toshiki Matsusaka
13:45-14:30: Rikuto Ito
14:45-15:30: Kenji Ueno
15:45-16:30: Noriko Yui
discussion
::: Titles and Abstracts :::
::: Taro Sano ::: On Hodge structures of compact complex manifolds with semistable degeneration
Compact Kähler manifolds satisfy several nice cohomological properties such as Hodge symmetry and Hodge-Riemann bilinear relations. Friedman and Li recently showed that non-Kähler Calabi-Yau 3-folds which are obtained by conifold transitions of projective ones satisfy such properties. I will present examples of non-Kähler Calabi-Yau manifolds with such properties by smoothing normal crossing varieties and explain how we obtain such nice Hodge-theoretic properties.
::: Yuta Takada ::: Unboundedness of fixed point multiplicities on a K3 surface
One way to study dynamical systems is to focus on their fixed points. In this talk, I present automorphisms of a certain K3 surface in (P^1)^3 with an isolated fixed point at which the induced action on the stalk of the structure sheaf is arbitrarily close to the identity. This implies that the multiplicities of these automorphisms at the fixed point can be arbitrarily large. As another application, the intersection multiplicity of two isomorphic curves at a point can be arbitrarily large on this K3 surface. This is joint work with Kenji Hashimoto.
::: Kazuhiro Ito ::: Arithmetic monodromy of hyper-Kähler varieties over p-adic fields
For a hyper-Kähler variety X over a p-adic field, I will explain the relation between the Galois action on the étale cohomology groups of X and the Mumford-Tate group (associated with the total cohomology) of the complex analytification of X. As an application, I will prove the weight-monodromy conjecture for X when the second Betti number of X is at least 4. Although only four deformation types of hyper-Kähler varieties are currently known, the arguments presented in this talk do not rely on the specific geometry of these examples. Instead, I will explain a general approach based on Sen theory and the theory of Frobenius tori. If time permits, I will also discuss an arithmetic analogue of Nagai’s conjecture on nilpotency indices of monodromy operators. This talk is based on joint work with Tetsushi Ito, Teruhisa Koshikawa, Teppei Takamatsu, and Haitao Zou, as well as an ongoing joint project with Haitao Zou.
::: Yuya Murakami ::: Quantum Modularity for Topological Quantum Field Theory
Quantum modularity is a fascinating phenomenon that connects number theory and topology. Its study provides, on the topological side, clues for understanding the asymptotic behavior of quantum invariants of knots and 3-manifolds, while on the number-theoretic side, it reveals examples and properties of new arithmetic objects known as quantum modular forms.
In this talk, I will first give an overview of how quantum modularity connects number theory and topology. I will then introduce a new example of this connection: the quantum modularity of the “signatures of topological quantum field theories” and its relation to generalized Dedekind sums. This talk is based on arXiv:2602.16159.
::: Hiro-o Tokunaga ::: Six bitangent lines to a smooth plane quartic curve and a curve of genus 2 over ${\mathbb C}(t)$
It is well-known that there exist 28 bitangent lines for a smooth quartic $Q$. It is also known that if we choose six of them properly, there exists a cubic passing through 12 bitangent points. In this talk, we consider a curve $C$ of genus $2$ over $\CC(t)$ arising from these six lines and give an explicit method in producing such $Q$ via the jacobian of $C$. This is a joint work with S. Bannai.
::: Masanobu Kaneko ::: Quintic and Septic Elliptic Normal Curves and Related Modular Function Fields
We give explicit formulas for two torsion points on Bianchi’s quintic and Vélu’s septic elliptic curves. Using these descriptions, we determine generators and defining equations for several modular function fields of levels 10 and 14. This is joint work with Masato Kuwata.
::: Toshiki Matsusaka ::: On q-series identities from Lie superalgebras
In 1994, Kac and Wakimoto found the denominator identities for affine Lie superalgebras. As an application, they introduced an approach to derive power series identities for some powers of △(q), where △(q) is the generating function of triangular numbers. In this talk, we provide two different proofs of these identities. The first (and main) proof is analytic, relying on the modularity of q-series. In particular, the modularity is shown using the theory of indefinite theta functions developed by Roehrig and Zwegers. The second is algebraic, following the method of Kac and Wakimoto. This talk is based on joint work with Miyu Suzuki (Kyoto University).
::: Rikuto Ito ::: On simply connected non-rigid attractor threefolds
Attractor varieties are complex Calabi–Yau varieties discovered by the physicist Gregory Moore, and they are expected to be defined over number fields. Certain non-simply connected attractor threefolds, such as abelian threefolds, were characterized by Kanazawa and Fan. Moreover, rigid Calabi–Yau threefolds provide examples of simply connected attractor threefolds and are arithmetically well understood by the modularity theorem of Gouvêa and Yui. In this talk, I will introduce several examples of simply connected non-rigid attractor threefolds and discuss their arithmetic properties, e.g., modularity question. This is joint work with Noriko Yui.
::: Kenji Ueno ::: On the Connections of sl(2, C)-Conformal Field Theory over Curves of Genus 2
::: Noriko Yui ::: Examples of Siegel paramodular Calabi-Yau threefolds
::: Organizers :::
Noriko Yui (Queen's University)
Hiro-o Tokunaga (Tokyo Metropolitan University)
Yasuhiro Goto (Hokkaido University of Education)
Shinobu Hosono (Gakushuin University)
Yukiko Konishi (Tsuda University)
Atsushi Kanazawa (Waseda University)