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

February 2023
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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 Wednesdays at 15:30 in the
Dissertantenzimmer
(or, during times of a pandemic, online).
If you are interested in giving a talk, please contact
the organizers:
Ivan Izmestiev
and
Gudrun Szewieczek
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.

Summer term 2021 
Talks in the geometry seminar
(hover/tap name or title to view more information)
 18 Jun 2021 (Fri!): Geometry seminar
 Graham Andrew Smith (Federal University of Rio de Janeiro):
On the Weyl problem in Minkowski space
Abstract
We show how the work of Trapani & Valli may be
applied to solve the Weyl problem in Minkowski space.
This work is available on arXiv at
https://arxiv.org/abs/2005.01137.
 02 Jun 2021: Geometry seminar
 Sergey Tabachnikov (Penn State University):
Variations on the TaitKneser theorem
Abstract
The TaitKneser theorem, first demonstrated by Peter
G. Tait in 1896, states that the osculating circles along
a plane curve with monotone nonvanishing curvature
are pairwise disjoint and nested.
I shall present Tait's proof and discuss variations on
this result.
For example, the osculating circles can be replaced by the
osculating Hooke and Kepler conics along a plane curve;
the proof uses the Lorentzian geometry of the space
of these conics.
I shall also present a version of this theorem for
the graphs of Taylor polynomials of even degrees
of a smooth function.
 12 May 2021: Geometry seminar
 Hana Kourimska (IST Austria):
Uniformization with a new discrete Gaussian curvature
Abstract
The angle defect  $2\pi$ minus the cone angle at
a vertex  is the commonly used discretization of
the Gaussian curvature for piecewise flat surfaces.
However, it does not possess one of the principal features
of its smooth counterpart  upon scaling the surface by
a factor $r$, the smooth Gaussian curvature is scaled by
the factor of ${1\over r^2}$, whereas the angle defect is
invariant under global scaling.
In my talk, I will introduce a new discretization of
the Gaussian curvature, that preserves the properties of
the angle defect and, in addition, reflects the scaling
behavior of the smooth Gaussian curvature.
I will also answer the accompanying Uniformization question:
Does every discrete conformal class of a piecewise flat
surface contain a metric with constant discrete
Gaussian curvature?
And if so, is this metric unique?
The results I will present in this talk constitute
a part of my PhD research, which was supervised
by Prof. Boris Springborn.
 05 May 2021: Geometry seminar
 Matteo Raffaelli (TU Wien):
Nonrigidity of flat ribbons
Abstract
Developable, or flat, surfaces are classical objects in
differential geometry, with lots of realworld applications
within fields such as architecture or industrial design.
In this talk I will discuss the problem of constructing
a developable surface that contains a given space curve.
The natural question here is the following.
Given a curve, how many locally distinct developables
can be defined along it?
It turns out that, for any suitable choice of ruling angle
(function measuring the angle between the ruling line and
the curve's tangent vector), there exists a full circle
of flat ribbons.
In the second part of the talk we will examine the set
of flat ribbons along a fixed curve in terms of energy.
In particular, we will see that the classical rectifying
developable of a curve maximizes the bending energy
among all infinitely narrow flat ribbons having
the same ruling angle.
I will conclude by presenting some important open
questions.
 28 Apr 2021: Geometry seminar
 Gudrun Szewieczek (TU Wien):
Smooth and discrete cyclic circle congruences
Abstract
A 2dimensional congruence of circles in 3space
is called cyclic if it admits a 1parameter family
of smooth orthogonal surfaces. By imposing further
(geometric) conditions on such circle congruences,
those can be employed to construct families of surfaces
of various special types, as for example, pseudospherical
surfaces, Guichard surfaces and flat fronts in hyperbolic
space.
In this talk we shall give an integrable discretization
of cyclic circle congruences and characterize them
by the existence of a flat connection comprised of
"reflections" of the underlying ambient geometry.
These explicit flat connections will then provide an
efficient way to construct the orthogonal discrete
surfaces and could be used to reveal geometric
properties of them. As an application of the
developed theory, we will construct parallel
families of discrete flat fronts in hyperbolic space.
Furthermore, we will discuss how the concept of those
discrete flat connections can be carried over to the
smooth case.
 24 Mar 2021: Geometry seminar
 Felix Dellinger (TU Wien):
A checkerboard pattern approach to discrete differential
geometry
Abstract
Given a quad mesh of regular combinatorics one can
obtain a checkerboard pattern by performing a midpoint
subdivision, i.e., by connecting all midpoints of
neighbouring edges. Such a checkerboard pattern has
the property hat every second face is a parallelogram,
compare Figure.
It turns out, that this checkerboard pattern is very well
suited numerically as well as theoretically to define
discrete differential geometric properties.
In particular, discrete versions of the shape operator,
conjugate nets, principal nets, Koenigs nets and isothermic
nets can be consistently defined via this checkerboard
pattern approach. Some nice results from the smooth
theory also hold for their discrete counter parts:
 Trace and determinant of the shape operator
fit a discrete version of the Steiner formula for
offset surfaces.
 The parameter lines of a principal mesh follow the
eigenvectors of the shape operator.
 Conjugate meshes/Koenigs meshes are mapped to
conjugate meshes/Koenigs meshes under projective
transformations.
 Isothermic meshes and in general Koenigs meshes are
dualizable.
 Isothermic meshes/principal meshes are mapped to
isothermic meshes/principal meshes under Moebius
transformations.
 10 Mar 2021: Geometry seminar
 Efilena Baseta (TU Wien): TBA

Winter term 2020/2021 
Talks in the geometry seminar
 Wed 20/01/2021, Raman Sanyal (GoetheUniversität Frankfurt)
Inscribable polytopes, routed trajectories, and reflection arrangements
 Wed 9/12/2020, Hellmuth Stachel (TU Wien)
The motion of billiards in ellipses
(slides)
 Wed 2/12/2020, Joseph Cho (TU Wien)
Darboux transformations and discrete mKdV equations
 Wed 25/11/2020, Daniil Rudenko (University of Chicago)
Trigonometry of tetrahedra and rational elliptic surfaces
 Wed 18/11/2020, Michael Jimenez (TU Wien)
Navigating a Family of Particular Linear Weingarten Surfaces
 Wed 11/11/2020, Christian Müller (TU Wien)
On a Möbius invariant subdivision algorithm
 Wed 4/11/2020, Kurt Leimer (TU Wien)
ReducedOrder Simulation of Flexible MetaMaterials
 Wed 28/10/2020, Mohammad Ghomi (Georgia Inst of Technology)
Total curvature and the isoperimetric inequality
(slides)
 Wed 21/10/2020, Stefan Pillwein (TU Wien)
On Elastic Geodesic Grids and Their Planar to Spatial
Deployment
 Wed 14/10/2020, Silviana Amethyst (Univ of Wisconsin Eau Claire)
Using Numerical Algebraic Geometry to Solve Polynomial Systems
(slides)


Events in former years
External Links
