News

14-18 Jun 2027, TU Wien

Conference on Geometry: Theory and Applications (CGTA 2027)

Abstract

The Conference on Geometry: Theory and Applications (CGTA 2027) is part of an (approximately) biannual conference series. It is an international forum for presenting new trends and results in theory, techniques, and applications of geometry.

More information at the conference web page

19 Oct 2026, 12:15 CEST: JA, surfaces and beyond

Kaoru Iino (Yokohama National University): Intrinsic invariants of (3,4)-cuspidal edges

Abstract

$(3,4)$-cuspidal edges are important singularities that arise naturally on parallel surfaces of regular surfaces, such as ellipsoids. For ordinary cuspidal edges, Saji-Umehara-Yamada introduced the singular curvature as an intrinsic invariant of cuspidal edges, and showed, in particular, that its sign describes the local convexity of cuspidal edges. On the other hand, for $(3,4)$-cuspidal edges, the sign of the singular curvature is not canonically well-defined, so different invariants are needed.

In this talk, we introduce two intrinsic invariants for $3$-type edges, a class of singularities that includes $(3,4)$- and $(3,5)$-cuspidal edges. We show that these invariants describe the local convexity of $(3,4)$-cuspidal edges. Moreover, using these invariants, we give a necessary and sufficient condition for the boundedness of the Gaussian curvature. We also obtain intrinsic criteria for generic $(3,4)$- and $(3,5)$-cuspidal edges.

09 Oct 2026: Geometry seminar

Ander Chocarro Salaberria (DTU): Mathematics of surface stackability

Abstract

Surface rationalization and segmentation is often unsatisfactory in architectural workflows, which can lead to practical shortcomings such as inefficient packing and material waste. We present a directional approach to the general problem of stackability, namely the segmentation of architectural elements into components that can be conveniently arranged into physical stacks. Moreover, especially relevant surface classes with desirable stackability properties are investigated.

22 Jul 2026, 12:00 CEST: JA, surfaces and beyond

Naoya Suda (Kobe University) Bäcklund transformations of K-surfaces via Darboux matrices in smooth and discrete settings

Abstract

Surfaces of constant negative Gaussian curvature in $3$-dimensional Euclidean space (hereafter abbreviated as $K$-surfaces) admit an integrable equation known as the sine-Gordon equation, and have been studied from the perspectives of both integrable systems and differential geometry. Furthermore, the existence of Bäcklund transformations, which construct a new $K$-surface from a given one, is an important property of $K$-surfaces, and the use of Darboux matrices is well known as one of the algebraic computation methods for these transformations. Meanwhile, Bobenko and Pinkall (1996) and Hoffmann and Sageman-Furnas (2016) each clarified the discretization of $K$-surfaces and their algebraic computation methods based on different coordinate systems. In this talk, we discuss the computation methods for Bäcklund transformations using Darboux matrices, comparing the smooth and discrete cases. Part of this presentation is based on joint work with Thomas Raujouan (University of Tours) and Wayne Rossman (Kobe University).

23 Jun 2026: Bachelor Seminar im Dissertantenzimmer (UF DG, in Deutsch)

09:15 V A Horak: Möbius-geometrische Symmetrien in einem euklidischen Dreieck
10:15 L Reisinger: Vom Parallelenproblem zur hyperbolischen Geometrie
11:15 B Szabo: Hopffaserung

Abstracts

Möbius-geometrische Symmetrien in einem euklidischen Dreieck: Gesucht werden Symmetrien zwischen den Eckpunkten eines Dreiecks und dessen In- und Ankreismittelpunkten. Tatsächlich lassen sich mithilfe der Möbius-Geometrie acht Abbildungen finden, die diese Punkte und den Punkt Unendlich aufeinander abbilden - obwohl Mittelpunkte Möbius-geometrisch nicht mit deren Kreisen zusammenhängen. Eine dieser Abbildungen, die Antipodenabbildung, wird im Detail vorgestellt und anhand von Visualisierungen veranschaulicht.

Vom Parallelenproblem zur hyperbolischen Geometrie: Über zweitausend Jahre lang wurde Euklids Parallelenpostulat, das nicht in die Reihe der anderen passte, immer wieder hinterfragt. Der Vortrag zeichnet nach, wie Janos Bolyai und Nikolai Lobatschewski im 19. Jahrhundert die Frage umdrehten. Sie behandelten die Negation des Postulats nicht länger als Fehler, sondern als Ausgangspunkt einer eigenständigen Geometrie. Im Zentrum stehen die mathematischen Ergebnisse ihrer Arbeit und die Frage, warum diese neue Geometrie erst spät Teil der wissenschaftlichen Debatte wurde.

Hopffaserung: Die Hopffaserung ordnet Punkten der $2$-Sphäre Kreise der $3$-Sphäre zu, wobei Quaternionen eingesetzt werden. Mithilfe der stereographischen Projektion werden Bilder der Fasern erzeugt. Auch die Bewegung entlang einer Hopffaser wird visualisiert, wobei die doppelte Überlagerung von $\mathrm{SO}(3)$ erkennbar wird.

18 Jun 2026: Geometry seminar

Eleni Pachyli (TU Wien): Lichnerowicz-Obata Theorem for the discrete spherical Laplacian, in dimension two

Abstract

The classical Lichnerowicz-Obata Theorem states that for an $n$-dimensional Riemannian manifold $(M,g)$ with $Ric \geq (n-1)g$, the first eigenvalue of the Laplacian is greater or equal than $n$. We prove a discrete analogue of this theorem in dimension 2, for a spherical cone metric with curvature $\kappa_i := 2\pi-\omega_i >0$ for the discrete spherical Laplacian defined by I. Izmestiev and W. Lam. Our proof draws on ideas from the theory of mixed volumes, in particular from Y. Shenfeld and R. van Handel's proof of the Alexandrov-Fenchel inequality. In the process, we also derive a discrete analogue for the Bochner method.

17 Jun 2026, 12:00 CEST: JA, surfaces and beyond

Keita Takahashi (Institute of Science Tokyo) Completeness conditions for globally hyperbolic spacetimes

Abstract

In this talk, we discuss several completeness conditions for globally hyperbolic spacetimes within the framework of low-regularity settings. These conditions, originally introduced by Busemann and Beem, serve as Lorentzian analogues to those found in the classical Hopf-Rinow theorem. As a related result, we explain an approximation theorem for the space of Cauchy hypersurfaces, a space whose properties have recently been investigated by Lange and Peteranderl.

11 Jun 2026: Geometry seminar

Ivan Izmestiev (TU Wien): Discrete Wirtinger inequality

Abstract

The classical Wirtinger inequality compares the $L_2$-norm of a periodic function with zero average with the $L_2$-norm of its derivative. It was used by Hurwitz to give a new proof of the isoperimetric inequality for smooth curves. A discrete version of the Wirtinger inequality is due to Fan, Taussky, and Todd. In this talk a generalization of the Fan-Taussky-Todd inequality will be stated and proved.

03 Jun 2026, 12:00 CEST: JA, surfaces and beyond

Shintaro Akamine (Nihon University): Constant mean curvature surfaces in the three-dimensional light cone

Abstract

Some classes of surfaces in spaces equipped with degenerate metrics often arise in correspondence with minimal surfaces in Euclidean space and maximal surfaces in Lorentz-Minkowski space. In this talk, we present local and global properties of spacelike constant mean curvature surfaces in the three-dimensional light cone. In particular, we explain Bernstein-type theorems for such surfaces. This talk is based on the joint work with Wonjoo Lee (Jeonbuk National University) and Seong-Deog Yang (Korea University).

28 May 2026: Geometry seminar

Darius Imre (TU Wien): Die Geometrie der Addition und Multiplikation

Abstract

In diesem Vortrag konstruieren wir, ausgehend von einer Menge von Punkten, Geraden und einer Inzidenzrelation, die zusammen eine projektive Ebene bilden, eine Addition und eine Multiplikation. Dazu untersuchen wir einige Eigenschaften von Homologien und Elationen und verwenden diese anschliessend zur Konstruktion eines Schiefkörpers. Dabei werden wir sehen, dass die Existenz der dafür benötigten Abbildungen nur in desarguesschen Ebenen garantiert ist. Abschliessend betrachten wir die erweiterte euklidische Ebene und zeigen, dass der dort entstehende Schiefkörper isomorph zu den reellen Zahlen ist.