Events

Conferences, Research Colloquia & Seminars, Defenses, and other events

Geometry Seminar

This is the research seminar of the group and focuses on recent research in (differential) geometry; during the semester the seminar is usually scheduled to take place on Thursday at 17:00 in the Zeichensaal 1. If you are interested in giving a talk, please contact the organizer: Ivan Izmestiev.

Seminar "JA, surfaces and beyond"

This is a joint online/hybrid research seminar with colleagues from Japan, focused on surface geometry; the seminar is currently scheduled on Thursday at 11:30 CET/19:30 JST (every 3-4 weeks) and can be followed either online or (at TUW) in the Dissertantenzimmer. If you are interested to participate, please contact (one of) the organizers: Gudrun Szewieczek, Atsufumi Honda, Udo Hertrich-Jeromin or Masatoshi Kokubu.

Student Seminars

These seminars are usually part of the assessment and are open to the public, in particular, to interested students; topics typically focus on geometry but cover a wider range of areas, depending on the students' and the advisor's interests. Presentations are often delivered in German.

Seminar talks

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05 Mar 2026 in Zeichensaal 3: Geometry seminar

Clara Oeverink (TU Wien): Classification of Pencils of Quadrics in the Real Projective Space

Abstract

In the complex projective space (of arbitrary dimension) the Segre symbol has long been known as a sufficient tool for classification of pencils of quadrics. However, it lacks information in the real case. This, the use of the index sequence, as introduced by Tu et al in 2006, can compensate for. Together, they determine the quadric pair canonical form (QPCF) of a pair of matrices representing quadrics in a nondegenerate pencil, as defined by Uhlig in 1976, thereby fixing the pencil itself.

Tu et al used index sequences, together with the related signature sequences, to construct a simple algebraic method of classifying pencils in projective 3-space and accordingly their intersection curves. This allows low-cost determination of basic topological properties of the curves for a more stable parametrisation.

The presentation aims to provide insight into the aforementioned tools via an examination on how Segre symbol, index sequence, signature sequence and QPCF are related. It illustrates how this enables the formal classification of pencils of quadrics in the real projective space. An emphasis is put on index sequences and their equivalence classes, leading to their implementation in a classification algorithm emulating Tu et al.

04 Mar 2026, 11:30 CET: JA, surfaces and beyond

Yoshiki Jikumaru (Toyo University): On the governing equations for membrane O surfaces

Abstract

It is known that a shell membrane in equilibrium where a constant purely normal load qn acts on the membrane, and where the principal curvature lines coincide with the principal stress lines, forms an integrable system called a membrane O surface. In this talk, we formulate the governing equations for membrane O surfaces of the 1st and 2nd kind, which are analogues to Guichard surfaces of the 1st and 2nd kind introduced by Calapso. Furthermore, under this formulation, we show that membrane O surfaces are a subclass of Demoulin's $\Omega$ surfaces, and that the Bäcklund transformation for membrane O surfaces preserves membrane O surfaces of the 1st and 2nd kind, respectively.

Seminar talks

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11 Feb 2026, 11:30 CET: JA, surfaces and beyond

Joseph Cho (Handong Global University): Geometry at infinity - from a Minkowski geometric viewpoint

Abstract

Many interesting surface classes in Minkowski 3-space including maximal surfaces and constant mean curvature surfaces are known to admit non-degenerate singularities. These singularities differ from the isolated singularities appearing on analogous surfaces in Euclidean 3-space. However, the case of constant mean curvature surfaces shows that some surfaces in Minkowski 3-space also appear with disconnected components, admitting blow-up points. In this talk, we propose Laguerre geometry to gain insight into the fundamental difference between Euclidean 3-space and Minkowski 3-space, and to obtain an intuitive understanding of why non-degenerate singularities and blow-up points appear on surfaces in Minkowski 3-space. This talk is based on joint work with Wonjoo Lee, Gudrun Szewieczek, and Seong-Deog Yang.

17 Dec 2025, 11:30 CET: JA, surfaces and beyond

Mason Pember (Univ of Bath): $\Omega_0$ surfaces

Abstract

An $\Omega_0$ surface is a surface for which one of the curvature sphere congruences is isothermic. To the speaker's knowledge, the only known examples of such surfaces are channel surfaces. In pursuit of finding non-channel examples, we discuss a method for creating examples by applying Lie-Darboux transformations to a particular class of channel surfaces. This leads to an explicit parametrisation of a non-channel $\Omega_0$ surface.

26 Nov 2025, 11:30 CET: JA, surfaces and beyond

Shun Kumagai (Hachinohe Institute of Technology): Self-affinity of planar curves: towards unified description of aesthetic curves

Abstract

Self-affinity is a symmetry of planar curves and is regarded as playing a crucial role in characterizing log-aesthetic curves (LACs), which have been studied as reference curves for designing aesthetic shapes in CAD systems. Inoguchi et al. showed a variational principle and an integrable deformation of LACs in similarity geometry, as well as its application to geometric shape generation. In this talk, we discuss LACs and their self-affinity, and their parallels in Klein geometries, where LACs meet with parabolas.

This talk is based on joint work with Kenji Kajiwara.

12 Nov 2025: Bachelor seminar

Enzo Kitt (TU Wien): Infinitesimal rigidity of surfaces under projective transformations

Abstract

I present a proof that infinitesimal rigidity of smooth surfaces is preserved under projective transformations. Following an argument of Sevennec, the deformation condition for an immersion p and its infinitesimal isometric deformation (IID) q is encoded by a map into a quadric Q. The maximal isotropic subspaces of this quadric correspond to graphs of orthogonal transformations and split into two families. This observation allows the construction of a map into these subspaces whose constancy characterizes infinitesimal rigidity. The result then follows since the entire construction is formulated in projectively invariant terms. Given an IID q, I also establish a formula that explicitly produces an IID of the projective image, which in particular provides a simple way to construct IIDs of the quadrics in three-space.

05 Nov 2025, 11:30 CET: JA, surfaces and beyond

Masaya Hara (NIT, Anan College; Kobe University): Darboux transformations between zero mean curvature surfaces

Abstract

Darboux transformations are transformations that preserve the isothermicity of surfaces and have been studied not only in classical differential geometry but also actively in modern differential geometry.

In this talk, we impose an additional condition on Darboux transformations and study such transformations between zero mean curvature surfaces in the Euclidean, Minkowski, and isotropic three-spaces. In comparing these spaces, we analyze and contrast their geometric behaviors, including singularities and ends.

This talk is based on joint work with J Cho, A Honda, T Raujouan, and W Rossman.

29 Oct 2025: Geometry seminar

Ruzica Mijic-Rasoulzadeh (TU Wien): Sphericity and geometric properties of ratios in Möbius and Laguerre geometry

Abstract

In recent years, several applications ($S$-nets, $S^\ast$-nets, circular nets, conical nets, etc.) have renewed the interest in incidence conditions involving circles and spheres. This talk develops a systematic comparison of incidence theorems in Möbius and Laguerre geometry, in terms of algebraic ratios. As a starting point, we recall a well-known Möbius theorem, stating that four points in the plane lie on a circle if and only if their cross-ratio is real. We dualize this statement for the Laguerre case, and look at four further incidence theorems, increasing the dimension and the number of objects involved, respectively (for example five planes touching a common sphere). In particular, we use the cross-ratio as long as the number of objects remains four, whereas for five objects we need the novel diagonal-ratio. With the appropriate algebraic structures chosen for each configuration, the resulting incidence theorems take strikingly parallel forms, highlighting the close relationship between Möbius and Laguerre geometry.

22 Oct 2025: Geometry seminar

Hans-Peter Schröcker (University of Innsbruck): Recent results on rational PH curves

Abstract

A polynomial or rational parametric curve $r(t)$ is said have a "Pythagorean Hodo-graph" if $\langle r'(t),r'(t)\rangle$ is a square in the ring of polynomials $R[t]$ or in the field of rational functions $R(t)$, respectively. Curves with this property are called PH curves. They offer some advantages over conventional polynomial or rational curves in typical CAGD constructions or in the control of objects moving along PH trajectories. While polynomial PH curves are well-studied and understood, less is known for rational PH curves - probably due to the lack of convenient construction methods. This has changed recently. We present a simple construction for rational PH curves and then continue with three further topics:

Rational curves with a rational arc-length function. Rational curves with a (piecewise) rational arc-length function are necessarily PH but only few rational PH curves enjoy this property (while the arc length function of polynomial PH curves is always at least piecewise polynomial). They have an interpretation as curves of constant slope in 4D and the ensuing constraints can be conveniently incorporated into the construction of general rational PH curves.

Bounded and regular rational PH curves. In contrast to polynomial curves - which are always infinite - rational curves may be bounded. Of particular interest are bounded rational PH curves as they give rise to closed rational framing motions that can be used, for example, as camera trajectories. While previous approaches rely on piecewise constructions with limited smoothness, we design bounded rational PH curves with closed framing motions. The challenge is to ensure curve regularity. We present a simple necessary criterion to ensure this and sketch the proof for its sufficiency.

Minimal surfaces as complex PH curves. Finally, we talk about a recently dis- covered relations between PH curves and minimal surfaces. A result from quaternionic function theory ensures that any polynomial or rational minimal surface in isothermal parametrization can be obtained by a complex extension of our construction method. The parameter lines of these surface parametrizations are necessarily PH curves.

This is joint work, mostly with Zbynek Sir (Charles University in Prague), but also with Amedeo Altavilla (Universita degli Studi di Bari Aldo Moro) and Jan Vrsek (University of West Bohemia).

09 Oct 2025, 12:30 CEST: JA, surfaces and beyond

Hirotaka Kiyohara (Osaka Kyoiku University): Singularities on timelike minimal surfaces in the three-dimensional Heisenberg group

Abstract

Most timelike minimal surfaces in the $3$-dimensional Heisenberg group can be represented via Lorentzian harmonic maps into the de Sitter $2$-sphere. These surfaces naturally admit singularities, and we provide a characterization of several types of them. This talk is based on joint work with Shintaro Akamine.

42. Österreichisches und Süddeutsches Kolloquium zur Differentialgeometrie

Organizers: Mohammad N. Ivaki, Ivan Izmestiev
Location: Freihaus Hörsaal 8 (Nöbauer)

Mon 07 Jul 2025

Programme ...

Programme (Monday)

08:55

Welcome Address

09:00

Julian Scheuer (Goethe Univ Frankfurt): Mean curvature flow in null hypersurfaces

10:00

Anna Dall'Acqua (Ulm Univ): On the free boundary elastic flow

11:00

Coffee break

11:30

Denis Polly (TU Wien): Surfaces in isotropic geometries

12:30

Lunch

14:00

Philipp Reiter (TU Chemnitz): Modeling self-repulsion of geometric objects

15:00

Elias Döhrer (TU Chemnitz): Incorporating Self-Repulsion into Riemannian metrics

16:00

Coffee break

16:30

Clemens Sämann (Univ of Vienna): Non-smooth spacetime geometry via metric (measure) geometry

19:00

Conference dinner at Restaurant Waldviertlerhof, Schönbrunnerstr. 20, 1050 Wien

Tue 08 Jul 2025

Programme ...

Programme (Tuesday)

09:00

Esther Cabezas-Rivas (Univ of Valencia): The ROF model for image denoising (beyond flatland)

10:00

Gudrun Szewieczek (Univ of Innsbruck): Isothermic annuli and snapping mechanisms from elastic curves

11:00

Coffee break

11:30

Thomas Koerber (Univ of Vienna): The Penrose inequality in extrinsic geometry

12:30

Lunch

14:00

Roman Prosanov (TU Wien): Projective background of $(2+1)$-spacetimes of constant curvature

15:00

Volker Branding (Univ of Vienna): On biharmonic and conformal biharmonic maps to spheres

16:00

Coffee break/Farewell

Seminar talks

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11 Sep 2025, 12:30 CEST: JA, surfaces and beyond

Denis Polly (TU Wien): 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.

21 Aug 2025, 12:30 CEST: JA, surfaces and beyond

Jun Matsumoto (Inst of Science Tokyo): A class of affine maximal surfaces with singularities and its relationship with minimal surface theory

Abstract

A surface in unimodular affine $3$-space $\mathbb{R}^3$ 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, Martinez, and Milan 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.

17 Jul 2025, 13:00 CEST: JA, surfaces and beyond

Riku Kishida (Inst of Science Tokyo): 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.

26 Jun 2025, 13:00 CEST: JA, surfaces and beyond

Philipp Käse (Kobe University, TU Darmstadt): 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 $E(k,t)$.

20 Jun 2025: Bachelor Seminar im Dissertantenzimmer (UF DG, in Deutsch)

10:15 I Demir: Villarceau-Kreise am Torus
11:15 S Amsz: Villarceau Kreise auf Dupinschen Zykliden

Abstracts

Villarceau-Kreise am Torus: Der Vortrag behandelt eine spezielle Familie von Kreispaaren am Torus, die Villarceau-Kreise. Nachdem die Kreise vorgestellt werden, widmet sich die restliche Präsentation der Konstruktion eines Torus als Sliceform mithilfe von Villarceau-Segmenten.

Villarceau Kreise auf Dupinschen Zykliden: In der Präsentation wird ein 100-minütiger Unterrichtsentwurf vorgestellt, zum Thema "Villarceau Kreise auf Dupinschen Zykliden". Der Entwurf überführt die theoretischen Konzepte in eine anschauliche und strukturierte Lernsituation.

12 Jun 2025, 13:00 CEST: JA, surfaces and beyond

Yuta Ogata (Kyoto Sangyo Univ): 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.

14 May 2025: Geometry seminar

Niklas Affolter (TU Wien): Discrete Koenigs nets and inscribed quadrics

Abstract

In this talk we consider discrete Koenigs nets with parameter lines contained in d-dimensional spaces. For these Koenigs nets we show that there is a unique quadric, such that the parameter spaces are tangent to the quadric. This allows us to establish a bijection between discrete Koenigs nets and discrete autoconjugate curves contained in the quadric. I will also explain some of the technique we used to derive these results, including lifts to "maximal" dimensions and the relation to touching inscribed conics. Joint work with Alexander Fairley (TU Berlin).

07 May 2025: Geometry seminar

Jan Techter (TU Berlin): Discrete parametrized surfaces via binets

Abstract

In several classical examples discrete surfaces naturally arise as pairs consisting of combinatorially dual nets describing the "same" surface. These examples include Koebe polyhedra, discrete minimal surfaces, discrete CMC surfaces, discrete confocal quadrics, and pairs of circular and conical nets. Motivated by this observation we introduce a discretization of parametrized surfaces via binets, which are maps from the vertices and faces of the square lattice into space. We look at discretizations of various types of parametrizations using binets. This includes conjugate binets, orthogonal binets, Gauss-orthogonal binets, principal binets, Königs binets, and isothermic binets. Those discretizations are subject to the transformation group principle, which means that the different types of binets satisfy the corresponding projective, Möbius, Laguerre, or Lie invariance respectively, in analogy to the smooth theory. We discuss how the different types of binets generalize well established notions of classical discretizations. This is based on joint work with Niklas Affolter and Felix Dellinger.

30 Apr 2025: Geometry seminar

Emil Pobinger (TU Wien): The 27 lines on a cubic surface

Abstract

The fact that cubic surfaces (in the appropriate space) contain exactly 27 lines is one of the first major results one encounters when studying algebraic geometry. There are many ways to prove this statement; in this seminar paper, we will work through a proof on an intermediate level - originally due to Reid - and fill out its details. Additionally, we also provide visual examples not originally provided by Reid.

02 Apr 2025: Geometry seminar

Marcin Lis (TU Wien): Zeros of planar Ising models via flat SU(2) connections

Abstract

Livine and Bonzom recently proposed a geometric formula for a certain set of complex zeros of the partition function of the Ising model defined on planar graphs. Remarkably, the zeros depend locally on the geometry of an immersion of the graph in the three dimensional Euclidean space (different immersions give rise to different zeros). When restricted to the flat case, the weights become the critical weights on circle patterns. I will rigorously prove the formula by geometrically constructing a null eigenvector of the Kac-Ward matrix whose determinant is the squared partition function. The main ingredient of the proof is the realisation that the associated Kac-Ward transition matrix gives rise to an SU(2) connection on the graph, creating a direct link with rotations in three dimensions. The existence of a null eigenvector turns out to be equivalent to this connection being flat.

27 Mar 2025, 12:00 CEST: JA, surfaces and beyond

Udo Hertrich-Jeromin (TU Wien): Doubly cGc profiles

Abstract

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.