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.

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

(hover/tap name or title to view more information)

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.

Talks in the geometry seminar

(hover/tap name or title to view more information)

08 Jan 2025: Geometry seminar

Martin Winter (TU Berln): Rigidity and Reconstruction of Convex Polytopes via Wachspress Geometry

Abstract

In how far is a convex polytope determined by partial combinatorial and geometric data, such as its edge graph, edge lengths and dihedral angles; up to combinatorial type, affine equivalence or isometry? Questions of this nature have a long history and are intimately linked to rigidity theory, convexity and real algebraic geometry. After a short overview of the state of the art I will focus on one particular reconstruction problem: is a polytope uniquely determined by its edge graph, edge lengths and the distance of each vertex from some interior point? If yes, this would generalize and unify a number of known results, such as Cauchy's rigidity theorem, the Kirszbraun theorem and matroid reconstruction. I will explain how this conjecture was resolved in three relevant special cases using tools from Wachspress Geometry and why a full resolution of the conjecture is likely to come from an understanding of the so-called Wachspress variety. If there is time, I will elaborate on a fascinating new conjecture that emerged in this context - the stress-flex conjecture.

13 Nov 2024: Geometry seminar

Morteza Saghafian (ISTA): The MST-Ratio: A New Measure of Mixedness for Colored Point Sets

Abstract

Recently, motivated by applications in spatial biology, we explored the interactions between color classes in a colored point set from a topological perspective. We introduced the concept of the MST-ratio as a measure for quantifying the mingling of points with different colors. Investigating this measure raises intriguing questions in discrete geometry, which is the primary focus of this talk.

In this talk, I will introduce the concept of the MST-ratio, present the best-known bounds and key complexity results for computing its maximum, and share new findings on its behavior in both random and arbitrary point sets. Finally, I will highlight several open questions in discrete and stochastic geometry that arise from this work.

16 Oct 2024: Geometry seminar Seminarraum DB gelb 07

Ivan Izmestiev (TU Wien): Ivory's lemma and theorem revisited

Abstract

Newton has investigated the gravitational field of a solid homogeneous ball and has shown that the field inside a homogeneous spherical shell vanishes ("no gravity in the cavity"). Later, Laplace and Ivory have studied the gravitational field created by ellipsoids. It is during this work that Ivory has proved his famous lemma about the diagonals in a curvilinear quadrilateral formed by four confocal conics. We revisit these classical theorems and state their non-Euclidean analogs. The talk is based on a joint work with Serge Tabachnikov.

Project presentations "Themen der höheren Geometrie" (in German)

30 Jan 2025 at 14:00 (Dissertantenzimmer)

E Tabakovic: Rotationsflächen konstanter Gaußkrümmung - Klassifikation nach Tjaden

Abstract

Die Untersuchung der Krümmung von Flächen ist ein zentrales Thema der Differentialgeometrie. Wir wiederholen die Grundlagen zu Rotationsflächen und zur Gaußschen Krümmung. Nach der Einführung der wichtigsten Begriffe und Sätze wird die Klassifikation nach Tjaden vorgestellt, die zeigt, dass Rotationsflächen konstanter Gaußkrümmung $K=\pm 1$ von speziellen Profilkurven dargestellt werden können.

30 Jan 2025 at 14:45

13 Mar 2025 at 13:15 (Dissertantenzimmer)

J Reisinger: Elliptische Funktionen

Abstract

Elliptische Funktionen stellen eine Verallgemeinerung trigonometrischer und exponentieller Funktionen dar und spielen eine wichtige Rolle in der modernen Mathematik, unter anderem auch in der Differentialgeometrie. Dieser Vortrag soll eine Einführung in die elliptischen Funktionen, ihre Definition und ihre Nutzung liefern, wobei ein besonderer Fokus hierbei auf ihrem Bezug zur Arbeit von Tjaden liegt. In diesem Zusammenhang wird besonders auf die drei grundlegenden Jacobischen Funktionen eingegangen. Abschließend soll auf eine Implementierung dieser elliptischen Funktionen in Mathematica eingegangen werden.

30 Jan 2025 at

15:30

14:45 (Dissertantenzimmer)

L Rupf: Chebyshev-Netze auf Rotationsflächen mit konstanter negativer Gaußkrümmung

Abstract

In diesem Vortrag werden ergänzend zu den beiden vorangegangenen Vorträgen sogenannte Chebyshev-Netze auf den Rotationsflächen mit konstanter Gaußkrümmung untersucht. Nach einer allgemeinen Einführung zu Chebyshev-Netzen und einem einfachen Beispiel, wird explizit für die Pseudosphäre ein derartiges Netz bestimmt. Weiters wird auf die lokale Existenz dieser Netze auf Flächen mit konstanter negativer Krümmung eingegangen und Visualisierungen werden vorgestellt.