This site contains the schedule and past records of the online seminar "JA, surfaces and beyond". Seminars are held on Thursdays, about once every 3 or 4 weeks, with a 30-45 minutes presentation on cutting-edge research in the field of geometry of surfaces and related areas. ("JA" = "Japan/Austria")
September 11, 2025 ; 19:30 JST/12:30 CEST : Denis Polly (TU Wien)
Title: Spheres in isotropic geometries
Abstract: The classical notion of isotropic 3-space refers to a 3-dimensional real vector space with degenerate inner product. This space sits, on many occasions, between Euclidean and Minkowski geometry as a boundary case. In this talk, we will describe isotropic space as well as its spherical and hyperbolic analogue (the latter one also known as half-pipe geometry). In particular, we will show how sphere geometric methods can be used to describe extrinsic surface theory in these spaces. As an application, we will prove a Weierstrass-type representation for constant mean curvature surfaces in isotropic geometries. The talk covers the results of joint work with Joseph Cho.
October 9, 2025 ; 19:30 JST/12:30 CEST : Hirotaka Kiyohara (Osaka Kyoiku University) 清原 悠貴（大阪教育大学）
TBA
August 21, 2025 ; 19:30 JST/12:30 CEST : Jun Matsumoto (D3 at Science Tokyo) 松本 洵（東京科学大学 D3）
Title: A class of affine maximal surfaces with singularities and its relationship with minimal surface theory
Abstract: A surface in unimodular affine 3-space R^3 whose affine mean curvature vanishes everywhere is called an affine maximal surface. In this talk, I will explain the global theory of affine maximal surfaces with singularities, called affine maximal maps, which were defined by Aledo, Martínez, and Milán in 2009.
We define a new subclass of these surfaces, which we call affine maxfaces. By applying Euclidean minimal surface theory, we show that the ``complete'' affine maxfaces satisfy an Osserman-type inequality, and we provide examples of such surfaces that are related to Euclidean minimal surfaces.
July 17, 2025 ; 20:00 JST/13:00 CEST : Riku Kishida (D1 at Science Tokyo) 岸田 陸玖（東京科学大学 D1）
Title: The volume of marginally trapped submanifolds and flat surfaces in 3-dimensional light-cone
Abstract: A space-like submanifold of codimension 2 in a Lorentzian manifold is said to be marginally trapped if its mean curvature vector field is light-like. In this talk, I explain that a marginally trapped submanifold has a locally volume-maximizing property under specific conditions. As a typical example of marginally trapped surface in the 4-dimensional Minkowski spacetime, I also discuss flat surfaces in the 3-dimensional light-cone.
June 26, 2025 ; 20:00 JST/13:00 CEST : Philipp Käse (JSPS PD at Kobe University; TU Darmstadt)
Title: A new family of CMC surfaces in homogeneous spaces
Abstract: In 1841 Delaunay characterized surfaces of constant mean curvature H=1 in Euclidean 3-space invariant under rotation. This result was generalized by several authors to screw-motion invariant CMC surfaces in E(k,t), but it turns out that the classification is not complete. In fact, new (embedded) CMC surfaces arise in addition to the Delaunay family. In this talk I would like to talk about these new surfaces and present a complete classification of screw motion CMC surfaces in E(k,t).
June 12, 2025 ; 20:00 JST/13:00 CEST : Yuta Ogata (Kyoto Sangyo University) 緒方 勇太（京都産業大学）
Title: Darboux transformations for curves
Abstract: We introduce the Darboux transformations for smooth and discrete curves. This is related to the linearization of Riccati type equations and we study their monodromy problem. We will show some examples of periodic (closed) Darboux transformations for curves. This is based on the joint work with Joseph Cho and Katrin Leschke.
March 27, 2025 ; 20:00 JST/12:00 CEST : Udo Hertrich-Jeromin (TU Wien)
Title: Doubly cGc profiles
Abstract/Info: I plan to talk about a joint project on profile curves that generate two surfaces of revolution of constant Gauss curvature in different space forms. This is joint work with S Bentrifa, M Kokubu and D Polly.
Online Participation: Zoom link will be emailed to pre-registered participants.