1. Wolfram BAUER (Leibniz University Hannover)
   Title: The Laplacian on infinite cones in low dimensions
   Abstract: Let (N, g) be a closed Riemannian manifold. In this talk we consider the Laplacian ∆ on a metric cone C(N) = R_{+}×N over N equipped with a metric dr+r^{2}g. This manifold is incomplete and models conical singularities, which are among the simplest types of geometric singularities. Over the past several decades, more general singular spaces and their spectral theory have been widely studied, starting with the influential work of J. Cheeger. If dim N < 3, then ∆ is not selfadjoint on compactly supported smooth functions and admits many selfadjoint extensions. Based on the theory of Hankel functions and von Neumann’s theory of deficiency indices we recall a complete classification of these self-adjoint extensions. Then we discuss explicit constructions of the resolvent kernels and their dependence on the respective extension. An additional intriguing problem is the construction of the heat kernel associated with a specific self-adjoint extension of ∆.

This talk is based on joint work with K. Furutani and C. Iwasaki.

2. David EELBODE (University of Antwerp)
   Title: Spines and their potential in Geometric Algebra
   Abstract: The topic of this talk is to be situated in the setting of Geometric Algebra (GA), a term (re)introduced by David Hestenes in the 1960s. Better known in some circles as Clifford algebras, these GA are particularly suited for thinking about geometry (as the name suggests). The reason for this is the fact that both its generators and defining relations encode simple geometrical truths, and that geometric entities such as points, lines, planes and so on translate into (group) elements.
   Spinors are notoriously harder to explain intuitively, Sir Atiyah even called them ‘mysterious despite their algebraic properties being formally understood’. In an attempt to shed more light on this question, we started a project to look at spinors in a slightly different way using the concept of a spine (the generator of an isoclinic rotation). This led to a few interesting observations, with potential in both representation theory and particle physics.
   In this talk (which is joint work with Martin Roelfs and Steven De Keninck) we will define these spinors, and illustrate where the potential lies for questions such as the geometry of spinors.

3. Shouhei HONDA (本多 正平, University of Tokyo)
   Title: Poincaré inequality for one forms on four manifolds with bounded Ricci curvature
   Abstract: In this talk we provide a quantitative global Poincare inequality for one forms on a closed Riemannian four manifold with bounded Ricci curvature. This is a joint work with Andrea Mondino (University of Oxford).

4. Natsuki IMADA (今田 夏暉, Waseda University)
   Title: Killing spinors in higher spin geometry
   Abstract: Killing spinors are one of the important objects in spin geometry and general relativity. From a spin-geometric perspective, the existence of a Killing spinor imposes strong restrictions on the geometry of the underlying manifold, forcing it to be an Einstein manifold, for instance. In the context of general relativity, Killing spinors can be used to define conserved quantities. In this talk, we extend the concept of Killing spinors to the spin-j/2 bundle and discuss their properties. In particular, we will focus on spin-j/2 Killing spinors on 3-dimensional manifolds. This is joint work with Yasushi Homma and Soma Ohno.

5. Atsushi KATSUDA (勝田 篤, Kyushu University, Keio University)
   Title: Heat kernels and Nilpotent Floquet-Bloch theory
   Abstract: pdf-file
   The Floquet-Bloch theory is a widely used tool for investigating materials with　periodic structures. For instance, it can demonstrate that the spectrum of periodic Schrödinger operators exhibits band structures. Within the context of this talk, this theory has been applied to the following topics over several decades in the case of abelian extensions:
   A long time asymptotic expansion of the heat kernels on covering manifolds of compact Riemannian manifolds.
   In this talk, we will explain our version of the generalized Floquet-Bloch theory for discrete nilpotent groups and apply it to the above problems for nilpotent extension. This is based on arXiv:2509.16848.

6. Irina MARKINA (University of Bergen)
   Title: Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules
   Abstract: We investigate the geodesic orbit property of pseudo-Riemannian nilmanifolds, specifically those known in the literature as pseudo H-type Lie groups – i.e., 2-step nilpotent Lie groups of Heisenberg type equipped with a left invariant pseudo-Riemannian metric. The study of homogeneous geodesics on Riemannian H-type Lie groups was completed by C. Riehm in 1984. We extend these results to the pseudo-Riemannian H-type Lie groups and provide a complete characterization of the geodesic orbit property for the case where the underlying Lie algebras are constructed from the admissible Clifford modules of minimal dimension.

7. Masayoshi NAGASE (長瀬 正義, Saitama University)
   Title: Hermitian Tanno connection on contact Riemannian manifolds
   Abstract: In the study of contact Riemannian manifolds, it will be well-known that in the integrable case the Tanaka-Webster connection is a powerful tool and so is the Tanno connection in the general case including the non-integrable case. In the latte case, I introduced another connection called the hermitian Tanno connection. Unlike the Tanno connection, the new one desirably commutes with the almost complex structure the manifold has. Today I want to explain its usefulness by presenting some applications.

8. Shin NAYATANI (納谷 信, Nagoya University)
   Title: First-eigenvalue maximization and inflation of maps
   Abstract: Study of the maximization of the first Laplace eigenvalue began with the seminal work of Hersch (1970), who proved that for any Riemannian metric g on the 2-sphere, one has λ_{1}(g) ≤ 8π/Area(g). Then Berger (1973) posed the problem of whether the supremum of the scale-invariant quantity λ_{1}(g) · Vol(g)^{2/n} over all Riemannian metrics on a compact manifold is finite or not. There has been significant progress on this problem up to the present.
   In this talk, I will discuss the maximization of the first eigenvalue of the Bakry-Émery Laplacian on a manifold with a fixed volume element. The problem is formulated as the dual of a certain optimization problem concerning maps into a Hilbert space, which makes it possible to solve both problems in some cases, including the Berger spheres.

9. Soma OHNO (大野 走馬, Waseda University)
   Title: On the hypersurfaces of nearly Kähler statistical manifolds
   Abstract: Statistical structures can be regarded as a certain generalization of Riemannian structures. Statistical analogues of Kähler manifolds and almost Kähler manifolds have already been defined, and hypersurfaces of these manifolds have also been investigated.
   In this talk, I will present my recent results on hypersurfaces of nearly Kähler statistical manifolds, which may be seen as the statistical analogues of nearly Kähler manifolds.

10. Julie ROWLETT (Chalmers University of Technology)
    Title: Moduli spaces and isospectrality
    Abstract: Have you heard the question: can one hear the shape of a drum ? Do you know the answer ? Mathematically, this question is an inverse spectral problem, or equivalently, a question about isospectrality.
    In this talk, we will investigate isospectrality questions for moduli spaces of certain types of ‘drums.’

11. Mathai VARGHESE (University of Adelaide)
    Title: Index for projective families of elliptic operators
    Abstract: By a small bundle gerbe we mean a bundle gerbe consisting of a finite-dimensional, fibre bundle over a manifold. We construct such gerbes over (connected sums of) compact oriented aspherical 3-manifolds, as well as in higher dimensions, generalizing the construction of decomposable bundle gerbes in earlier work with I.M. Singer. We prove the Atiyah-Singer type theorem for projective families of elliptic operators in twisted K-theory. We also give an application via the index of projective families of Spinc Dirac operators, to show the existence of obstructions to metrics with large positive scalar curvature.
    This is joint work with R. B. Melrose.
    Updated: Oct 23, 2025