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

November 2024
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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 Wednesday at 16:00 in the
Seminarraum DB yellow 07.
If you are interested in giving a talk, please contact
the organizers:
Ivan Izmestiev.
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.

This semester's schedule 
Talks in the geometry seminar
(hover/tap name or title to view more information)
 08 Jan 2025: Geometry seminar
 Martin Winter (TU Berln): TBA
Abstract
 13 Nov 2024: Geometry seminar
 Morteza Saghafian (ISTA): The MSTRatio: 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 MSTratio 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 MSTratio,
present the bestknown 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
nonEuclidean analogs. The talk is based on a joint work with
Serge Tabachnikov.

Summer term 2024 
Talks in the geometry seminar
(hover/tap name or title to view more information)
 27 Jun 2024: Geometry seminar
 Ilya Kossovskiy (Masaryk University in Brno and TU Wien):
Sphericity and analyticity of a strictly pseudoconvex hypersurface in
low regularity
Abstract
It is well known that the sphericity of a strictly pseudoconvex
CRhypersurface amounts to the vanishing of its ChernMoser
tensor. The latter is computed pointwise in terms of the 6jet
of the hypersurface at a point, and thus requires regularity of
the hypersurface of class at least C^6.
In our joint work with Zaitsev, we apply our recent theorem on
the analytic regularizability of a strictly pseudoconvex
hypersurface to find a necessary and sufficient condition for
the sphericity of a strictly pseudoconvex hypersurfaces of
arbitrary regularity starting with C^2. Further, we obtain a
simple condition for the analytic regularizability of
hypersurfaces of the respective classes. Surprisingly, despite
of the seemingly analytic nature of the problem, our technique
is geometric and is based on the Reflection Principle in SCV.
 20 Jun 2024: Geometry seminar
 Denis Polly (TU Wien):
Linear Weingarten surfaces in isotropic spaces
Abstract
According to a result by Burstall, HertrichJeromin and Rossman,
linear Weingarten surfaces in Riemannian and Lorentian space
forms are the envelopes of isothermic sphere congruences with
constant curvature. This description is derived via the use of
Lie sphere geometry (LSG) and symmetry breaking to obtain
results about metric subgeometries of LSG. While this method
recovers all linear Weingarten surfaces in Riemannian and
Lorentzian space forms, surfaces in isotropic space, as
described by Strubecker, do not appear. Our goal is to close
this gap.
To this end, we introduce a way of breaking symmetry that has
not recieved much attention. This leads us to the study of
isotropic space forms and the linear Weingarten surfaces
therein. As an application we describe Weierstrasstype
representations for certain linear Weingarten surfaces in these
space forms.
 13 Jun 2024: Geometry seminar
 Fabian Achammer (TU Wien):
Formula equations and the affine solution problem
Abstract
Formula equations are certain kinds of equations whose solutions
are logical formulas.
They serve as a common framework for many different problems in
computational logic, ranging from software verification to
inductive theorem proving.
We start with a short introduction to mathematical logic and
computational problems, then introduce formula equations and
give a glimpse of their wide applicability.
In the main part of the talk we explore the solution of a
particular problem in the area of formula equations  the affine
solution problem  which translates into a problem about affine
spaces.
Finally, we discuss some results surrounding a generalization of
the affine solution problem, which is still open, namely the
convex solution problem which is a computational problem about
convex polytopes.
 06 Jun 2024: Geometry seminar
 Kiumars Sharifmoghaddam (TU Wien):
Rigidfoldable Quad Meshes with Control Polylines: Interactive Design and Motion Simulation
Abstract
Generic discrete surfaces composed of quadrilateral plates connected by
rotational joints in the combinatorics of a square grid are rigid, but
there also exist special ones with 1parametric flexibility. This
dissertation focuses on two particular classes of socalled Thedra
(trapezoidal quad surfaces) and Vhedra (discrete Voss surfaces).
Thedra can be thought of as a generalization of discrete surfaces of
revolution in such a way that the axis of rotation is not fixed at one
point but rather sweeping a polyline path on the base plane. Moreover,
the action does not need to be a pure rotation but can be combined with
an axial dilatation. After applying these transformations to the
breakpoints of a certain discrete profile curve, a flexible quadsurface
with planar trapezoidal faces is obtained. Therefore, the design space
of Thedra also includes as subclasses discretized translational
surfaces and moulding surfaces beside the already mentioned rotation
surfaces. Vhedra are the discrete counterpart of Voss surfaces which
carry conjugate nets of geodesics. In discrete case the opposite
interior angles of a vertex star are equal. From a Vhedral vertex one
can always generate an antiVhedral vertex with the same kinematics, in
which the sum of corresponding opposite angles equal to pi and therefore
is a known case of valence four flatfoldable and developable origami
vertex. The author developed Rhino/Grasshopper plugins, implemented with
Csharp, which make the design space of Thedra, Vhedra and
antiVhedra accessible for designers and engineers. The main components
enable the user to design these quad surfaces interactively and
visualize their deformation in real time based on a recursive
parametrization of the quadmesh vertices under the associated isometric
deformation. Furthermore, this research investigates semidiscrete
Thedral surfaces and other topologies, such as tubular structures
composed of Thedra.
 23 May 2024: Geometry seminar (14:30 Dekanatsraum 9th floor)
 Georg Nawratil (TU Wien):
A global approach for the redefinition of higherorder flexibility and rigidity
Abstract
The famous example of the doubleWatt mechanism given by Connelly and Servatius [Higherorder rigidity  What is the proper definition? Discrete & Computational Geometry 11:193200, 1994] raises some problems concerning the classical definitions of higherorder flexibility and rigidity, as they attest the cusp configuration of the mechanism a thirdorder rigidity, which conflicts with its continuous flexion. Some attempts were done to resolve the dilemma but they could not settle the problem. According to Müller [Higherorder analysis of kinematic singularities of lower pair linkages and serial manipulators. Journal of Mechanisms and Robotics 10:011008, 2018] cusp mechanisms demonstrate the basic shortcoming of any local mobility analysis using higherorder constraints. Therefore we present a global approach inspired by Sabitov's finite algorithm for testing the bendability of a polyhedron given in [Local Theory of Bendings of Surfaces. Geometry III, pp. 179250, Springer, 1992], which allows us (a) to compute iteratively configurations with a higherorder flexion (e.g. all configurations of a given 3RPR manipulator with 3rdorder flexion) and (b) to come up with a proper redefinition of higherorder flexibility and rigidity.
 16 May 2024: Geometry seminar
 Martina Iannella (TU Wien):
Classification of noncompact $3$manifolds
Abstract
A classification problem consists of an equivalence relation on
some set of mathematical objects; a solution to such a problem
is an assignment of complete invariants. In this talk we
consider the problem of classifying noncompact 3manifolds up
to homeomorphism from the perspective of descriptive set theory.
We first look at the parametrization of 3manifolds as objects
of a Borel subset of a Polish space. We then discuss the
framework of Borel reducibility, a standard tool for comparing
the complexity of different classification problems, and present
our recent result which determines the exact complexity of the
classification of noncompact 3manifolds up to homeomorphism.
This is joint work with Vadim Weinstein.
 02 May 2024: Geometry seminar
 Niklas Affolter (TU Wien):
Discrete maximal Lorentz surfaces and incircular nets
Abstract
Incircular nets (sembeddings) were introduced by Chelkak as a
generalization of Smirnov's approach to study the conformal
invariance of the Ising model in the continuous limit. We build
upon the work of Chelkak, Laslier and Russkikh to present a
class of incircular nets that corresponds to discrete isothermic
surfaces in Lorentz space. As a special case, we identify
discrete maximal surfaces, which are discrete surfaces with
vanishing discrete mean curvature. In this way, we introduce a
result on the discrete level that was obtained by CLR in the
limit. We also introduce an associated family of discrete
maximal surfaces and the corresponding family of incircular
nets. Joint work with Dellinger, Müller, Polly, Smeenk and
Techter.
 25 Apr 2024: Geometry seminar
 Alessandro Andretta (University of Turin):
The BanachTarski paradox
Abstract
One of the most surprising results of modern mathematics is the
following result proved by Hausdorff, Banach and Tarski:
the unit ball of the euclidean space can be partitioned in a
finite number of pieces so that these can be rearranged, using
rigid motions so to form two balls identical to the original.
The proof is nonconstructive, relying on the Axiom of Choice,
and the pieces of the decomposition are inconceivably sharp and
edgy!
Geometry plays a substantial role, as the core of the proof is
based on the existence of a free subgroup of the group of
rotations.
(A similar result cannot be proved for the plane, i.e. it is not
possible to duplicate a disk.)
In this talk I will sketch the proof of the BanachTarski
paradox, and survey many related results that have been proved
in the following years.
18 Apr 2024: Geometry seminar
 Ivan Izmestiev (TU Wien): CayleyBacharach theorem and sums of squares
Abstract
The CayleyBacharach theorem (first proved by Chasles) says that
if two cubics meet at nine points, then any other cubic passing
through eight of these nine points also passes through the
ninth. This theorem includes as special cases the Pappus and the
Pascal theorems.
The sums of squares problem was posed by Hilbert: can every
positive definite homogeneous polynomial of degree $2d$ in n
variables be represented as a sum of squares of polynomials of
degree $d$? While the answer is positive for $d=1$ and n arbitrary
as well as for d arbitrary and $n=2$, Hilbert has proved the
negative for $d=3$ and $n=3$. And a crucial point in his proof was
the CayleyBacharach theorem.
This talks is based on the articles by EisenbudGreenHarris and
Blekherman.
 21 Mar 2024: Geometry seminar
 Gudrun Szewieczek (TU Munich):
Discrete isothermic nets with a family of spherical parameter lines from holomorphic maps
Abstract
Smooth surfaces with a family of planar or spherical curvature
lines are an active area of research, driven by both purely
differential geometric aspects and practical applications such
as architectural design. In integrable geometry it is a natural
question to ask which of these surfaces admit a conformal
curvature line parametrization and are therefore isothermic
surfaces.
It is an open problem to explicitly describe all those smooth
isothermic surfaces. However, over time, prominent examples were
found in this rich integrable surface class: above all Wente's
torus. More recently, further specific examples have led to the
discovery of compact Bonnet pairs and to free boundary solutions
for minimal and CMCsurfaces.
This talk covers a discrete version of the problem: we shall
generate all discrete isothermic nets with a family of spherical
curvature lines from special discrete holomorphic maps via the
concept of "liftedfolding".
In particular, we point out how this novel approach leads to
quasiperiodic solutions and to topological tori with
symmetries.
This is joint work with Tim Hoffmann.
 14 Mar 2024: Geometry seminar (Sem.R. DB gelb 03)
 David Sykes (TU Wien):
CR Hypersurface Geometry, an Introduction
Abstract
CR geometry concerns structures on real submanifolds in complex
spaces that are preserved under biholomorphisms. This talk will
present a light introduction to CR geometry of real
hypersurfaces. We will survey some of the area's major
classical results, namely solutions to local equivalence
problems of E Cartan, Tanaka, and ChernMoser and their
applications. And we will preview some of the area's currentday
research trends related to Levi degenerate structures.

Winter term 2023/24 
Talks in the geometry seminar
(hover/tap name or title to view more information)
 29 Nov 2023: Geometry seminar 16:15
 Martin Kilian (TU Wien): Meshes with Spherical Faces
Abstract
A truly MÃ¶bius invariant discrete surface theory must consider
meshes where the transformation group acts on all of its
elements, including edges and faces. We therefore systematically
describe so called sphere meshes with spherical faces and
circular arcs as edges. Driven by aspects important for
manufacturing, we provide the means to cluster spherical panels
by their radii. We investigate the generation of sphere meshes
which allow for a geometric support structure and characterize
all such meshes with triangular combinatorics in terms of
nonEuclidean geometries. We generate sphere meshes with
hexagonal combinatorics by intersecting tangential spheres of a
reference surface and let them evolve  guided by the surface
curvature  to visually convex hexagons, even in negatively
curved areas. Furthermore, we extend meshes with circular faces
of all combinatorics to sphere meshes by filling its circles
with suitable spherical caps and provide a remeshing scheme to
obtain quadrilateral sphere meshes with support structure from
given sphere congruences. By broadening polyhedral meshes to
sphere meshes we exploit the additional degrees of freedom to
minimize intersection angles of neighboring spheres enabling the
use of spherical panels that provide a softer perception of the
overall surface.
 22 Nov 2023: Geometry seminar
 Felix Dellinger (TU Wien): Orthogonal structures
Abstract
In this talk we introduce a definition for orthogonal
quadrilateral
nets based on equal diagonal length in every quad. This
definition can
be motivated through Ivory's Theorem and rhombic binets. We
find that
nontrivial orthogonal multinets exist, i.e., nets where the
orthogonality condition holds for every combinatorial rectangle
and
present a method to construct them.
The orthogonality condition is well suited for numerical
optimization.
Since the definition does not depend on planar quadrilaterals it
can
be paired with common discretizations of conjugate nets,
asymptotic
nets, geodesic nets, Chebyshev nets or principal symmetric nets.
This
gives a way to numerically compute prinicipal nets, minimal
surfaces,
developable surfaces and cmcsurfaces.
 11 Oct 2023: Geometry seminar
 Sadashige Ishida (IST Austria): Area formula for spherical polygons via prequantization
Abstract
I derive a formula for the signed area of a spherical polygon
via the
socalled prequantization. In contrast to the traditional
formula based on
the GaussBonnet theorem that requires measuring angles, the
new formula
mimics Green's theorem and is applicable to a wider range of
degenerate
spherical curves and polygons. I also explain that the classical
formula can
be recovered from a specific choice of prequantum bundle and
lift.

Summer term 2023 
Talks in the geometry seminar
(hover/tap name or title to view more information)
 31 May 2023: Geometry seminar
 Gunter Weiss (TU Wien & TU Dresden):
Der Satz von Miquel und seine Brüder
Abstract
Der elementargeometrische Satz von Miquel geht von einem Dreieck
$ABC$ und Punkten $R, S, T$ auf dessen Seiten aus und behauptet,
dass die drei Kreise $\bigcirc ART$, $\bigcirc BRS$, $\bigcirc CST$ einen Punkt, den
"MiquelPunkt" $M$, gemeinsam haben. Für $M$ hat man die
Dreiecksebene, also eine zweiparametrige Menge, von
Möglichkeiten, sodass es zu jedem $M$ eine einparametrige Menge
von Tripeln $R, S, T$ geben muss. Wählt man $R, S, T$ speziell
und/oder voneinander abhängig, so ergeben sich das
"BierdeckelTheorem", die Sätze von Brocard und
SimsonWallace als Spezialfälle des Satzes von Miquel. Dabei
ergeben sich auch überraschende "merkwürdige Inzidenzen"
und Zusammenhänge mit anderen elementargeometrischen Sätzen.
Der Satz von Miquel erlaubt auch eine direkte
3DVerallgemeinerung, während etwa die Satzgruppe von Brocard
nur mit Modifikationen ins Dreidimensionale übertragbar ist.
 03 May 2023: Geometry seminar
 Mohammad Ivaki (TU Wien):
Firey's worn stones are round
Abstract
I will talk about the Gauss curvature flow, which in $R^3$ was
proposed by Firey as a model for the changing shape of smooth,
strictly convex stones as they tumble on a beach. I'll give a
summary of the results on this flow from its inception to its
complete resolution.

Winter term 2022/23
Hans Havlicek with participants, 9 Dec 2022
photograph © Gunter Weiß
Hellmuth Stachel, 18 Nov 2022
photograph © Georg Glaeser

Festkolloquia
 09 Dez 2022, Zeichensaal 3: Festkolloquium
 zum 70. Geburtstag von Hans Havlicek
Programm
 13:30  14:30
 Silvia Pianta (Universita Cattolica del Sacre Cuore, Brescia):
1984, and beyond ... through joint Hanswers around parallelisms
 14:30  15:30
 Markus Stroppel (Universität Stuttgart):
Projective geometry in an algebraist's toolbox
 15:30  16:00
 Kaffeepause
 16:00  17:00
 Mark Pankov (University Warmia and Mazury, Olsztyn):
One result of Hans and a nonbijective version of Wigner theorem
 17:00  18:00
 Corrado Zanella (Universita di Padova):
Incidence properties of algebraic varieties
 18 Nov 2022, Zeichensaal 3: Festkolloquium
 zum 80. Geburtstag von Hellmuth Stachel
Programm
 13:15  14:00
 Eröffnung und Laudatio von Otto Röschel
 14:00  15:00
 Johannes Wallner (TU Graz):
Flexible nets and discrete differential geometry
 15:00  16:00
 Georg Glaeser (Universität für angewandte Kunst Wien):
Forty years between descriptive and computational geometry:
the universe of spatial imagination
 16:00  16:30
 Kaffeepause
 16:30  17:30
 HansPeter Schröcker (Universität Innsbruck):
Devil in paradise II  recent results in motion factorization
 17:30  18:30
 Giorgio Figliolini (Universität Cassino):
Kinematics of mechanisms with higherpairs:
fundamentals and applications
 19:00
 Abendessen im Restaurant Waldviertlerhof,
Schönbrunnerstr. 20, 1050 Wien
Talks in the geometry seminar
(hover/tap name or title to view more information)
 21 Feb 2023: Geometry seminar 15:00, ZS1
 Alex Fairley (TU Berlin): Circular nets with spherical parameter lines
Abstract
In the context of discrete differential geometry, circular nets
provide a discretisation of curvature line parametrisations. In
this talk, we will present incidence theorems to construct
circular nets with spherical parameter lines. And we will
present geometric properties of circular nets with spherical
parameter lines. We will compare them with the classical
properties of surfaces with spherical curvature lines. These are
classical surfaces that were intensely studied in the 19th
century.
 23 Jan 2023: Geometry seminar
 Sergey Agafonov (Sao Paulo State University):
Confocal conics and 4webs of maximal rank
Abstract
Confocal conics form an orthogonal net. Supplementing this net
with one of the following: 1) the net of Cartesian coordinate
lines aligned along the principal axes of conics, 2) the net of
Apollonian pencils of circles whose foci coincide with the foci
of conics, 3) the net of tangents to a conic of the confocal
family, we get a planar 4web. We show that each of these 4webs
is of maximal rank and characterize confocal conics from the web
theory viewpoint.
12 Dec 2022
16 Jan 2023: Geometry seminar
 Christian Müller (TU Wien):
The Geometry of Discrete AGAGWebs in Isotropic 3Space
Abstract
We investigate webs from the perspective of the geometry of webs
on surfaces in three dimensional space. Our study of AGAGwebs
is motivated by architectural applications of gridshell
structures where four families of manufactured curves on a
curved surface are realizations of asymptotic lines and geodesic
lines. We describe all discrete AGAGwebs in isotropic space and
propose a method to construct them. Furthermore, we prove that
some subnets of an AGAGweb are timelike minimal surfaces in
Minkowski space and can be embedded into a oneparameter family
of discrete isotropic Voss nets. This is a joint work with
Helmut Pottman.
 09 Jan 2023: Geometry seminar
 Jan Gregorovic (TU Wien):
Invariants of curves in conformal manifolds
Abstract
I will talk about invariants that can be assigned to curves in
conformal manifolds of dimension greater than 2. An invariant is
a quantity depending only on the curve and the conformal class
of metrics and in particular, is invariant under all conformal
transformation. The construction of these invariants uses the
description of conformal manifolds via tractor bundles, which I
describe in detail. Using tractor fields instead of vector
fields along the curve allows to construct an analogy of the
Frenet frame and use it to define invariants.
 28 Nov 2022: Geometry seminar
 Günter Rote (FU Berlin):
Grid peeling and the affine curveshortening flow
Abstract
Grid Peeling is the process of taking the integer grid points
inside a convex region and repeatedly removing the convex hull
vertices.
It has been observed by Eppstein, HarPeled, and Nivasch,
that, as the grid is refined, this process converges to
the Affine CurveShortening Flow (ACSF), which is defined
as a deformation of a smooth curve.
As part of the M.Ed. thesis of Moritz Rüber, we
have investigated the grid peeling process for special
parabolas, and we could observe some striking phenomena.
This has lead to a conjecture for the value of the constant
that relates the two processes.
 14 Nov 2022: Geometry seminar
 Karoly Bezdek (University of Calgary):
Ball polyhedra  old and new
Abstract
We survey a number of metric properties of intersections of
finitely many congruent balls called ball polyhedra in Euclidean
spaces. In particular, our talk is centered around the status of
the shortest billiard conjecture, the global rigidity
conjecture, Hadwiger???s covering conjecture, and the
GromovKleeWagon volumetric conjecture for ball polyhedra.
 17 Oct 2022: Geometry seminar
 Group meeting


Events in former years
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