Colloquia in the current semester
[colloque] Tue 20.2.2018, Phys 2.52 at 17h15 | more |
Prof. Alexandre Stauffer (University of Bath): Spatial growth processes: dendritic formation and competition
This talk focuses on a classical growing process, called multi-particle diffusion-limited aggregation (MDLA), where growth is governed by the aggregation of moving particles.
This model was introduced in the physics literature in 1980 with the goal of providing an example of “a simple and tractable” mathematical model of dendritic growth, which (similar to what has been observed in nature) produces a delicate, fractal-like geometry. Almost four decades later we still encounter tremendous mathematical challenges studying its geometric and dynamic properties, and understanding the driving mechanism lying behind the formation of fractal-like structures. In this talk, I will survey the developments in this field, giving emphasis to a new process, based on the competition of two growing systems, which we introduce and use to better understand MDLA. This is based on joint works with Elisabetta Candellero and Vladas Sidoravicius.
[colloque] Tue 6.3.2018, Phys 2.52 at 17h15 | more |
Prof. Jan Maas (IST Austria): Gradient flows and optimal transport in discrete and quantum systems
At the end of the 1990s it was discovered by Jordan/Kinderlehrer/Otto that the diffusion equation can be formulated as a gradient flow in the space of probability measures, where the driving functional is the Boltzmann-Shannon entropy, and the dissipation mechanism is given by an optimal transport metric. This result has been the starting point for striking developments at the interface of analysis, probability theory, and geometry.
In this talk I will review work from recent years, in which we introduced new optimal transport metrics that yield gradient flow descriptions for discrete stochastic dynamics and dissipative quantum systems. This allows us to develop a discrete notion of Ricci curvature, and to obtain sharp rates of convergence to equilibrium in several examples. The talk is based on joint works with Matthias Erbar and with Eric Carlen.
[colloque] Tue 13.3.2018, Phys 2.52 at 17h15 | more |
Prof. Florian Bertrand (American University of Beirut): Invariant metrics in complex analysis
The unit disc in C endowed with the Poincaré metric is an example of complete hyperbolic space. In higher dimension, the Poincaré metric admits different generalizations such as the Bergman metric or the Kobayashi metric. In this talk, we will explain how the study of such metrics and related objects is particularly adapted to understand the geometry of complex manifolds.
[colloque] Tue 20.3.2018, Phys 2.52 at 17h15 | more |
Prof. Jean-Marc Schlenker (Luxembourg): Polyhedra inscribed in quadrics
Steiner asked in 1832 what are the combinatorial types of convex polyhedra with
their vertices on a quadric in 3-dimensional projective space.
We will describe two recent advances on this problem.
One result (joint with Jeff Danciger and Sara Maloni)
describes the combinatorial types of polyhedra inscribed in a one-sheeted
hyperboloid or cylinder, while the other (joint with Hao Chen) deals
with polyhedra
having their vertices on a sphere in projective space which are not
contained in the ball.
The first result is based on anti-de Sitter geometry, while the second uses
a natural extension of the hyperbolic space by the de Sitter space.
[colloque] Tue 10.4.2018, Phys 2.52 at 17h15 | more |
Prof. Pierre Pansu (Université Paris-Sud Orsay): Large scale conformal geometry
Benjamini and Schramm's work on incidence graphs of sphere packings suggests a notion of conformal map between metric spaces which is natural under coarse embeddings. We show that such maps cannot exist between nilpotent or hyperbolic groups unless certain numerical inequalities hold.
[colloque] Tue 8.5.2018, Phys 2.52 at 17h15 | more |
Prof. Luis Guijarro (Universidad Autónoma de Madrid): The transverse Jacobi equation for geodesics
The classical Jacobi equation is a linearization of the geodesic equation, and its solutions give topological and geometrical information about the manifold. A few years ago, Burkhard Wilking found a far reaching generalization of it, the transverse Jacobi equation, whose geometric significance is still far from understood. In this talk, aimed for the general public, we will show how to do some comparison geometry using it, and will try to give an idea of why the right context for the new comparison theorems is the notion of intermediate Ricci curvature.
[colloque] Tue 15.5.2018, Phys 2.52 at 17h15
| more |
Prof. Andrea Mondino (Warwick): Smooth and non-smooth aspects of Ricci curvature lower bounds
After recalling the basic notions coming from differential geometry, the colloquium will be focused on spaces satisfying Ricci curvature lower bounds.
The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the ‘80s and was pushed by Cheeger and Colding in the ‘90s who investigated the fine structure of possibly non-smooth limit spaces.
A completely new approach via optimal transportation was proposed by Lott-Villani and Sturm almost ten years ago. Via such an approach one can give a precise definition of what means for a non-smooth space to have Ricci curvature bounded below. Such an approach has been refined in the last years giving new insights to the theory and yielding applications which seems to be new even for smooth Riemannian manifolds.
[colloque] Tue 22.5.2018, Phys 2.52 at 17h15 | more |
Prof. Stéphane Loisel (ISFA Lyon): Reevaluation of the capital charge in insurance after a large shock: empirical and theoretical views
Motivated by the recent introduction of regulatory stress tests in the Solvency II framework, we
study the impact of the re-estimation of the tail risk and of loss absorbing capacities on poststress
solvency ratios. Our contribution is threefold. First, we build the first stylized model
for re-estimated solvency ratio in insurance. Second, this leads us to solve a new theoretical
problem in statistics: what is the asymptotic impact of a record on the re-estimation of tail
quantiles and tail probabilities for classical extreme value estimators? Third, we quantify the
impact of the re-estimation of tail quantiles and of loss absorbing capacities on real-world
solvency ratios thanks to regulator data from EIOPA. Our analysis sheds a first light on the
role of the loss absorbing capacity and its paramount importance in the Solvency II capital
charge computations. We conclude with a number of policy recommendations for insurance
regulators.
[colloque] Tue 29.5.2018, Phys 2.52 at 17h15 | more |
Prof. Aleksandr Kolpakov (Uni Neuchâtel): Super-exponential families of hyperbolic manifolds
A classical theorem of Wang says that for every positive real number $v$ the number $N(v)$ of distinct (up to an isometry) hyperbolic $n$-manifolds with volume bounded by $v$, provided $n\geq 4$, is finite. The recent results by Burger-Gelander-Lubotzky-Mozes, Belolipetsky-Gelander-Lubotzky-Shalev, Gelander-Levit show that there are super-exponentially many non-isometric hyperbolic manifolds with respect to volume as a "complexity measure", i.e. $a_1 v^{b_1 v} \leq N(v) \leq a_2 v^{b_2}v$ (if $v$ is large enough), and an analogous statement holds for the number of arithmetic hyperbolic $n$-manifolds, and even the number of their commensurability classes.
We shall continue in this direction and investigate some particular families of $4$-dimensional hyperbolic manifolds with more specific properties (still not entirely accessible in arbitrary dimensions), such as having a given number of cusps, a given symmetry group, and other natural geometric or topological restrictions. We shall show that in all cases the number of such manifolds grows super-exponentially with respect to volume.
This talk is based on the joint papers and work in progress with Bruno Martelli (University of Pisa), Leone Slavich (University of Pisa), Steven Tschantz (Vanderbilt University), Alan Reid (Rice University) and Stefano Riolo (University of Neuchâtel).
Other talks and events in the current semester
[oberseminar] Oberseminar Geometrie, Tue 13.02.2018, Math II (Lonza) at 10h20 | more |
Arielle Leitner (Technion): Generalized cusps on convex projective manifolds
Convex projective manifolds are a generalization of hyperbolic manifolds. They are more flexible, and some occur as deformations of hyperbolic manifolds. Generalized cusps occur naturally as ends of properly convex projective manifolds. We classify generalized cusps, discuss their geometry, and ways they can deform. Joint work with Sam Ballas and Daryl Cooper.
[oberseminar] Oberseminar Geometrie, Wed 21.02.2018, Math II (Lonza) at 10h20 | more |
Corina Ciobotaru (Fribourg): Applications of hyperbolic geometry to Kuramoto model of synchronization
The Kuramoto model of synchronization is a mathematical model describing the phenomenon of self-synchronization in large systems of interacting oscillatory elements. Examples include synchronization of cardiac pacemaker cells, firefly populations, electro-chemical oscillations, synchronization of people walking, etc… Those phenomena are modelled via a system of ordinary differential equations (the Kuramoto model) and the solution to this o.d.e ‘converges’ with time to an equilibrium point, the synchronisation of the system. Amazingly, the equilibrium point is linked to the hyperbolic geometry on the Poincaré disc model and the Moebius transformations.
By employing the four different models for the hyperbolic plane, in the recent joint work with Hoessly—Mazza—Richard, we unify and clarify various aspects of the Kuramoto model previously existed in the literature.
[oberseminar] Informal Analysis Seminar, Tue 27.02.2018, Seminar room 0.102, at 10:15 | more |
Kevin Wildrick: The theory of Newton-Sobolev mappings
[oberseminar] Oberseminar Geometrie, Wed 28.02.2018, Math II (Lonza) at 10h20 | more |
Cesar Ceballos (University of Vienna): Combinatorics and Geometry of v-Tamari lattices
In this talk I will present some recent developments on geometric and combinatorial aspects of v-Tamari lattices. On the geometric side, we answer an open question of F. Bergeron regarding their realizability in terms of polytopal subdivisions of associahedra in the Fuss-Catalan case, present some connections with tropical geometry, and a potential extension to Coxeter groups of type B. On the combinatorial side, we show that they can be obtained as the duals of well chosen subword complexes, and provide a simple proof of the lattice property using certain bracket vectors of v-trees. Our approach also gives conjectural insight on the geometry of more general objects in terms of polytopal subdivisions of multiassociahedra. This talk is based on joint work with Arnau Padrol and Camilo Sarmiento.
[oberseminar] Geometric Analysis Seminar, Fri 02.03.2018, Science de la Terre 1.309, at 14:15 | more |
Changyu Guo (Fribourg): Theory of p-harmonic mappings: progress and open problems
[oberseminar] Combinatorics Seminar, Wed 7.3.2018, Math II (Lonza) at 14h00 | more |
Enrico Cecini (Genoa): Matroid structures in Graph Signal Processing
I will start by reviewing a setting of rising relevance in some applications, namely the so called Graph Signal Processing, that is the study of spaces of functions defined on the vertexes of a graph, whose properties are induced by the eigensystem of a combinatorial laplacian operator. Within this setting I will show how certain natural notions of independent interest, such as admissible sampling subsets, Poisson-like summation formulae and translation operators, can be interpreted in terms of bases and circuits of a certain class of matroids. Next I will derive the defining properties of such matroids, striving to place them within the theory of Coxeter matroids. (This seminar is a report of an ongoing PhD project.)
[oberseminar] Oberseminar Geometrie, Wed 07.03.2018, Math II (Lonza) at 10h20 | more |
Thibaut Dumont (Jyväskylä): Growth of the volume cocycle in Euclidean buildings
Euclidean buildings are the analogue of symmetric spaces for p-adic Lie groups. For example, the (p+1)-regular tree is the rank one buildings attached to SL_2 over the field of p-adic number. These buildings are CAT(0) spaces and come with a natural boundary at infinity and horospherical coordinates. B. Klingler used the latter to introduce a notion of volume. It is an open problem to determine the growth of this volume cocycle related to the cohomology of p-adic Lie groups. The detailed case of a regular tree has been solved and will be given in parallel.
[oberseminar] Oberseminar Topologie, Mon 12.03.2018, Math II (Lonza) at 16h00 | more |
Uwe Semmelmann (Stuttgart): The kernel of the Rarita-Schwinger operator on Riemannian spin manifolds
The Rarita-Schwinger operator is a twisted Dirac operator. It has several
interesting applications in physics and differential geometry. In my talk
I will introduce this operator, give some of its properties and then
concentrate on its kernel. In contrast to the classical Dirac operator
the Rarita-Schwinger operator can have a non-trivial kernel on compact
manifolds with positive scalar curvature. I will discuss several examples
for this. In particular I will explain how one can identify the
kernel of the Rarita-Schwinger operator with subspaces of harmonic
forms on manifolds with special holonomy. My talk is based on a
project with Yasushi Homma (Waseda University, Tokyo).
[oberseminar] Oberseminar Topologie, Monday 19.03.2018, Math II (Lonza) at 16h00 | more |
Jan-Bernhard Kordass (Karlsruhe): Spaces of Riemannian Metrics satisfying Surgery Stable Curvature
Conditions
In an effort to extend a well-known result by V. Chernysh and
M. Walsh, we explore the notion of a surgery stable curvature condition
as suggested by the work of S. Hoelzel. We will sketch the construction
of a deformation map, which allows to continuously alter a riemannian
metric to a certain prescribed one in a small neighbourhood of an
embedded submanifold, while curvature conditions are controlled.
Moreover, we will comment on disconnectedness properties for spaces of
metrics satisfying several curvature conditions and explain an
application to highly-connected manifolds.
[oberseminar] Combinatorics Seminar, Wed 21.3.2018, Math II (Lonza) at 14h00 | more |
Viola Siconolfi (Roma): Wonderful models for generalized Dowling lattices
Given a subspace arrangement, De Concini and Procesi in the
'90s described the construction of a variety associated to it, namely its won-
derful model. An important feature of these model is that some of its geo-
metric aspects are linked to some combinatorical properties of the subspace
arrangement, in particular the description of its boundary and its Betti num-
bers. Some examples of computation of Betti numbers have been studied,
among others, by Gaiffi, Henderson and Yuzwinsky. During the talk I will
consider the subspace arrangement associated to a generalized Dowling lat-
tice, a combinatorial object introduced by Hanlon. Our aim is to study the
wonderful model associated to it and to give a description of its boundary.
To deal with this I will use a bijection between the set of boundary compo-
nents of the wonderful model and a family of graphs. The results presented
have been obtained in collaboration with G. Gaiffi.
[oberseminar] Oberseminar Geometrie, Wed 21.03.2018, Math II (Lonza) at 10:20 | more |
Roman Prosanov (Fribourg): From cusped hyperbolic surfaces to convex ideal Fuchsian polyhedra
The Alexandrov theorem states that every flat metric on the 2-sphere with conical singularities of positive curvature can be uniquely (up to isometry) realized as the induced metric on the boundary of a 3-dimensional convex polytope. Various authors generalized this result to the case of hyperbolic metrics on surfaces. We are interested especially in hyperbolic cusp-metrics. Igor Rivin proved that every cusp-metric on the 2-sphere can be uniquely realized as the induced metric on the boundary of a convex ideal polytope in $\mathbb{H}^3$. To generalize this statement to higher genus surfaces $S_g$, one needs to find an appropriate analogue of the notion of ideal polytope. It is possible to consider polytopes not only in $\mathbb{H}^3$, but also in non-compact three-dimensional hyperbolic manifolds called \emph{Fuchsian manifolds}. The boundary of such a polytope (called \emph{Fuchsian polytope}) is homeomorphic to two copies of $S_g$ with punctures. Jean-Marc Schlenker proved that every hyperbolic cusp-metric on $S_g$ with $g>1$ can be uniquely realized as the induced metric on both components of the boundary of a Fuchsian polytope.
In our talk we will discuss a new proof of this result.
[oberseminar] Oberseminar Topologie, Monday 26.03.2018, Math II (Lonza) at 16h00 | more |
Raphael Zentner (Regensburg/FIM): Irreducible SL(2,C)-representations of integer homology 3-sphere
We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. This uses instanton gauge theory, and in particular a non-vanishing result of Kronheimer-Mrowka and some new results that we establish for holonomy perturbations of the ASD equation. Using a result of Boileau, Rubinstein and Wang (which builds on the geometrization theorem of 3-manifolds), it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C).
[oberseminar] Oberseminar Geometrie, Wed 28.03.2018, Math II (Lonza) at 10:20 | more |
Kurt Falk (Kiel): Dimension gaps for limit sets of Kleinian groups
In this talk I shall give a brief survey of results on dimension gaps for limit sets of geometrically infinite Kleinian groups. We will concentrate on an important notion from geometric group theory, amenability, as a criterion for the existence of such gaps.
[oberseminar] Oberseminar Geometrie, Wed 11.04.2018, Math II (Lonza) | more |
Olivier Mila (Bern): Nonarithmetic hyperbolic manifolds and trace rings
We will recall the definition of arithmetic manifolds and explain the construction
of Belolipetsky-Thomson yielding hyperbolic manifolds with short systole. A simple
condition on the hyperplanes used in the construction will be given to ensure
nonarithmeticity. Finally we will introduce the (adjoint) trace ring and explain
how it can be used in this case to get pairwise non-commensurable manifolds.
[oberseminar] Oberseminar Geometrie, Wed 18.04.2018, Math II (Lonza) | more |
Stefano Riolo (Neuchatel): Growth of geometrically bounding hyperbolic 3-manifolds
A complete hyperbolic manifold of finite volume is said to bound geometrically if it is isometric to the boundary of a complete finite-volume hyperbolic manifold with totally geodesic boundary.
We show that the number of geometrically bounding hyperbolic 3-manifolds with bounded volume grows asymptotically at least super-exponentially with the bound on the volume, both in the arithmetic and non-arithmetic case.
This is part of a work in progress joint with Alexander Kolpakov.
[oberseminar] Oberseminar Geometrie, Wed 02.05.2018, Math II (Lonza) at 10h20 | more |
Ivan Izmestiev (Fribourg): Flexible Kokotsakis polyhedra
A Kokotsakis polyhedron is made of nine faces:
a central quadrilateral surrounded by four quadrilaterals and four triangles so that at every interior vertex four faces meet.
A generic Kokotsakis polyhedron is rigid, but there are several classes of flexible polyhedra.
One of them is the famous Miura-ori used to fold solar panels in a Japanese spacecraft in 1996.
In this talk I will describe an approach to the classification of all flexible Kokotsakis polyhedra. It uses a parametrization of the configuration space of a four-bar linkage by means of trigonometric or elliptic functions.
[oberseminar] Oberseminar Topologie, Thursday 03.05.2018, Math II (Lonza) at 15h00 | more |
Wilderich Tuschmann (Karlsruhe, KIT): Nikolaev manifolds and Alexandrov metrics
I will discuss smoothability questions for
and the existence of Alexandrov metrics
on closed topological manifolds.
[oberseminar] Geometric Analysis Seminar, Fri 04.05.2018, Sciences de la Terre, room 1.309, at 14:15 | more |
Thomas Mettler (Goethe-Universitaet Frankfurt): The Beltrami differential revisited
The Beltrami differential is a fundamental object in the study of
quasiconformal mappings. It is a relative object in the sense that it describes
a complex structure relative to a given one. One might wonder whether there
exists a notion of an “absolute” Beltrami differential which does not require
the presence of an initial complex structure. In my talk I will explain that
this is indeed the case and discuss a resulting non-linear cousin to the Bel-
trami equation and its significance in 2D projective geometry.
Joint with G.Paternain
Goethe-Universitaet Frankfurt
[oberseminar] Oberseminar Topologie, Monday 07.05.2018, Math II (Lonza) at 16h00 | more |
Mauricio Bustamante (Augsburg): Bundles with fiberwise negatively curved metrics
A smooth M-bundle is said to be negatively curved if its fibers are
equipped with Riemannian metrics of negative sectional curvature,
varying continuously from fiber to fiber. The difference between
negatively curved M-bundles and smooth M-bundles is measured by the
space of all negatively curved metrics on M. In this talk I will show
that the latter space has non-trivial rational homotopy groups, provided
certain dimension constraints are satisfied. Hence the two bundle
theories generally differ. The results extend to other spaces of
metrics, e.g. spaces of Riemannian metrics with geodesic flow of Anosov
type. This is joint work with F.T. Farrell and Y. Jiang.
[oberseminar] Geometric Analysis Seminar, Tue 08.05.2018, Physics 2.52, at 10:15 | more |
Hubert Sidler (University of Fribourg): Harmonic quasi-isometric maps into Gromov hyperbolic CAT(0)-spaces
The Schoen-Li-Wang conjecture asserts that for every quasi-isometric
map between rank-one symmetric spaces there is a unique energy minimizing
harmonic map within bounded distance. Several breakthroughs by Markovic,
Lemm-Markovic and Benoist-Hulin finally led to an affirmative answer to this
conjecture. Later Benoist-Hulin generalized the existing results to the case of
Hadamard manifolds with negatively pinched curvature.
In this talk, I will first briefly recall the above results, and the notion of
Korevaar-Schoen energy. Then, I will discuss a generalization of the existence
results of Benoist-Hulin where the target is a Gromov hyperbolic, locally-
compact, CAT(0)-space. This is a joint work with Stefan Wenger.
[oberseminar] Oberseminar Geometrie, Wed 09.05.2018, Math II (Lonza) at 10h20 | more |
Christoforos Neofytidis (Geneva): Aspherical circle bundles and a problem of Hopf
A long-standing question of Hopf asks whether every self-map of absolute degree one of a closed oriented manifold is a homotopy equivalence. This question gave rise to several other problems, most notably whether the fundamental groups of aspherical manifolds are Hopfian, i.e. any surjective endomorphism is an isomorphism. Recall that the Borel conjecture states that any homotopy equivalence between two closed aspherical manifolds is homotopic to a homeomorphism.
In this talk, we verify a strong version of Hopf's problem for certain aspherical manifolds. Namely, we show that every self-map of non-zero degree of a circle bundle over a closed oriented aspherical manifold with hyperbolic fundamental group (e.g. negatively curved manifold) is either homotopic to a homeomorphism or homotopic to a non-trivial covering and the bundle is trivial. Our main result is that a non-trivial circle bundle over a closed oriented aspherical manifold with hyperbolic fundamental group does not admit self-maps of absolute degree greater than one. This extends in all dimensions the case of circle bundles over closed hyperbolic surfaces (which was shown by Brooks and Goldman) and provides the first examples (beyond dimension three) of non-vanishing semi-norms on the fundamental classes of circle bundles over aspherical manifolds with hyperbolic fundamental groups.
[oberseminar] Geometric Analysis Seminar, Tue 15.05.2018, Physics 2.52, at 10:15 | more |
Andrea Mondino (Warwick): Geometric and functional inequalities via a 1-dimensional localisation method
In the talk I will review the localization method from its roots in
the 50’ies by Payne-Weinberger, to the L1 approach in smooth Riemannian
manifolds by Klartag, to the work in collaboration with Cavalletti in metric
measure spaces. The second part of the talk will be devoted to the proof of
the Levy-Gromov inequality in metric measure spaces with Ricci curvature
bounded below obtained via such a technique in a joint work with Cavalletti.
[oberseminar] Oberseminar Geometrie, Wed 16.05.2018, Math II (Lonza) at 10h20 | more |
Edoardo Dotti (Fribourg): Classification of Hyperbolic Coxeter Groups
We will start by introducing the theory of hyperbolic Coxeter groups and discuss known results about their existence and their classification. After that, we will focus on the classification in commensurability classes, especially considering arithmetic Coxeter groups of finite volume.
[oberseminar] Geometric Analysis Seminar, Fri 18.05.2018, Science de la Terre 1.309, at 14:15 | more |
Tomasz Adamowicz (Warsaw): Mean-value harmonic functions
In the talk we introduce and study strongly and weakly harmonic
functions on metric measure spaces defined via the mean value property hold-
ing for all and, respectively, for some radii of balls at every point of the underly-
ing domain. We explain the historical background, relations of the harmonicity
to stochastic games and discuss some of the properties of strongly and weakly
harmonic functions including Harnack estimates, maximum and comparison
principles, the H ̈older and the Lipshitz estimates and some differentiability
properties. Moreover, we will discuss the mean value-harmonic functions in
the setting of the Carnot–Carath ́eodory groups, focusing on regularity and
relations of such functions to the sub-Laplace equation.
The talk is based on joint works with Gaczkowski, Gorka and Warhurst.
IMPAN Warsaw
[oberseminar] Geometric Analysis Seminar, Fri 25.05.2018, place TBA, at 14:15 | more |
Roger Züst (University of Bern): TBA
[oberseminar] Oberseminar Geometrie, Tue 29.05.2018, Math II (Lonza) at 13h15 | more |
Matthieu Jacquemet (HES-SO Valais (Sion) and University of Fribourg): Computational aspects of the classification of hyperbolic Coxeter polyhedra
Hyperbolic Coxeter polyhedra are quite easy to describe, and yet they are of central interest in various quite deep contexts, such as small volume hyperbolic orbifolds, growth rate of groups, and sphere packings.
A hard question in this setting is the classification question. This is somehow surprizing: the spherical and Euclidean Coxeter polyhedra exist in all dimensions, and we have a complete (and very short) classification for them. This is no longer the case in the hyperbolic space, where there is a dimensional bound for the existence of such objects, as well as a totally different situation as for the combinatorial types which are realizable.
In this talk, we will focus on combinatorial tools which can be used in order to (try to) exhibit new classes of hyperbolic Coxeter polyhedra, or even just one new example enjoying certain properties. The fact that these polyhedra have a very simple combinatorial description suggests that an algorithmic approach could be promising, but we are going to see what kind of difficulties can arise, and give a couple of ideas on how to address them.