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 1.5.2018, Phys 2.52 at 17h15 | more |
Prof. Bernard Ries (Uni Fribourg): tba
[colloque] Tue 8.5.2018, Phys 2.52 at 17h15 | more |
Prof. Luis Guijarro (Universidad Autónoma de Madrid): tba
[colloque] Tue 15.5.2018, Phys 2.52 at 17h15
| more |
Prof. Andrea Mondino (Warwick): tba
[colloque] Tue 22.5.2018, Phys 2.52 at 17h15 | more |
Prof. Stéphane Loisel (ISFA Lyon): tba
[colloque] Tue 29.5.2018, Phys 2.52 at 17h15 | more |
Prof. Aleksandr Kolpakov (Uni Neuchâtel): tba
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 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 15.05.2018, Physics 2.52, at 10:15 | more |
Andrea Mondino (Warwick): tba
[oberseminar] Geometric Analysis Seminar, Fri 18.05.2018, Science de la Terre 1.309, at 14:15 | more |
Tomasz Adamowicz (Warsaw): tba