# Oberseminar Analysis, Geometrie und Stochastik

Die Oberseminare Analysis & Geometrie (A&G) sowie Dynamische Systeme & Mathematische Physik (DS&MP) werden gemeinsam von den Arbeitsgruppen von Prof. Hasler, Prof. Lenz, Prof. Matveev, Prof. Oertel-Jäger und Prof. Wannerer veranstaltet.

• Zeit: Donnerstag 14.30-16.00 Uhr (A&G) und 16.00-17.30 Uhr (DS&MP)
• Ort: Ernst-Abbe-Platz 2, SR 3517 (siehe auch OpenStreetMap)

Frühere Semester

## Seminarplan WS 2015/16

Eine Liste der Vorträge im Wintersemester 2015/2016 findet sich hier.

## Seminarplan SS 2015

15. Juli
Mikhail  Hlushchanka (Jacobs Universität Bremen)
"From self-similar groups to self-similar sets: the iterated monodromy group perspective"

08. Juli
Dušan Pokorný ( Karlsuniversität Prag)
"Curvatures of sets defined by differences of convex functions"

A real function is called delta-convex if it can be expressed as a difference of two convex functions. A subset of a Euclidean space is called WDC if it is a sublevel set of a delta-convex function at a weakly regular value. The sets of positive reach, for instance, form a strict subclass of WDC sets. In the talk, the existence and properties of Federer's curvature measures, namely the validity of kinematic formulas, for the class of WDC sets will be discussed. The presented results are a joint work with Jan Rataj and Joseph Fu.

01. Juli
Michel L. Lapidus (University of California, Riverside)
"Fractal Zeta Functions and Complex Dimensions of Fractals"

We will give some sample results from the new higher-dimensional theory of complex fractal dimensions developed jointly with Goran Radunovic and Darko Zubrinic in the forthcoming 530-page research monograph (joint with these same co-authors), "Fractal Zeta Functions and Fractal Drums: Higher Dimensional Theory of Complex Dimensions" (Springer, 2016). We will also explain its connections with the earlier one-dimensional theory of complex dimensions developed, in particular, in the research monograph (by M. L. Lapidus and M. van Frankenhuijsen) entitled "Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings" (Springer Research Monographs, Springer, New York, 2013; 2nd rev. and enl. edn. of the 2006 edn.).

In particular, to an arbitrary compact subset A of the N-dimensional Euclidean space (or, more generally, to any relative fractal drum), we will associate new distance and tube zeta functions, as well as discuss their basic properties, including their holomorphic and meromorphic extensions, and the nature and distribution of their poles (or 'complex dimensions'). We will also show that the abscissa of convergence of each of these fractal zeta functions coincides with the upper box (or Minkowski) dimension of the underlying compact set A, and that the associated residues are intimately related to the (possibly suitably averaged) Minkowski content of A. Example of classical fractals and their complex dimensions will be provided. Finally, if time permits, we will discuss and extend to any dimension the general definition of fractality proposed by the authors (and M-vF) in their earlier work, as the presence of nonreal complex dimensions. We will also provide examples of "hyperfractals", for which the 'critical line' {Re(s)=D}, where D is the Minkowski dimension, is not only a natural boundary for the associated fractal zeta functions, but also consist entirely of singularities of those zeta functions.

These results are used, in particular, to show the sharpness of an estimate obtained for the abscissa of meromorphic convergence of the spectral zeta functions of fractal drums.

Furthermore, we will also briefly discuss recent joint results in which we obtain general fractal tube formulas in this context (that is, for compact subsets of Euclidean space or for relative fractal drums), expressed in terms of the underlying complex dimensions.

We may close with a brief discussion of a few of the many open problems stated at the end of the aforementioned forthcoming book (and in the accompanying series of seven papers, joint with the same authors).

24. Juni
Uta Freiberg (Universität Stuttgart)
"Differential operators and generalized trigonometric functions on fractal subsets of the real line"

17. Juni
Tobias Graf (Jenoptik)
"Inverse Problems in Free-Form Reflector and Lens Design"

The design problem of finding one or more reflecting or refracting surfaces to redistribute the light emitted from a source into a prescribed illumination pattern can be stated as an inverse problem. For various design tasks, it has been shown that solutions can be constructed as envelopes of elementary building blocks such as paraboloids, ellipsoids or hyperboloids. Moreover, the methods employed in the analysis can often be motivated in analogy to methods from convex analysis and optimal transport theory. I will present an inverse problem arising in the design of a free-form reflector surface for a collimated source. Aside from a geometric proof of existence and uniqueness, I plan to outline an interesting variational approach. The latter is closely linked to optimal transport theory and its previous applications to lens and reflector design problems.

3. Juni
Claudia Grabs (Universität Potsdam)
"Geometrische Elastizitätstheorie"

So wie Seifenhäute natürliche Minimalflächen formen, formen auch elastische Membranen geometrisch interessante Flächen. Hier wird aber im Allgemeinen nicht die Oberfläche, sondern die Spannungsenergie minimiert und die Form ist von der Wahl des Materialgesetzes abhängig.

Im Vortrag wird die nötige Theorie zur Berechnung solcher Gleichgewichtskonfigurationen vorgestellt und damit die sich ergebenden PDEs hergeleitet.

27. Mai
Daniel Lenz (Friedrich-Schiller-Universität Jena)
"Schreier Graphen der Grigorchuk Gruppe und aperiodische Ordnung"

Die Grigorchuk Gruppe ist die erste Gruppe mit mittlerem Wachstum. Sie kann als eine Untergruppe der Automorphismen des binaeren Baumes gesehen werden. Wir untersuchen Schreier Graphen der Grigorchuk Gruppe.  Dabei handelt es sich um gewichtete 'eindimensionale' Graphen.

Es zeigt sich, dass diese Graphen durch einen Subshift über einem endlichen Alphabet beschrieben werden können. Das ermöglicht es, Schrödinger-Operatoren mit aperiodischer Ordnung zu nutzen, um die Spektraltheorie der Laplace-Operatoren auf den Schreier-Graphen zu untersuchen. Als Ergebnis erhält man Cantor-Spektrum vom Lebesgue-Maß Null.

(Gemeinsame Arbeit mit Tatiana Nagnibeda-Smirnova und Rostislav Grigorchuk)

06. Mai
Ulrich Menne (Albert-Einstein-Institut MPG und Universität Potsdam)
"Regularity results for 'singular submanifolds' modelled by integral varifolds - an introductory overview"

Variational problems involving the m dimensional area integrand in n dimensional Euclidean space lead naturally to various classes of m dimensional surfaces with singularities; all of which give rise to integral varifolds. The subsequent regularity theory is strongly tied to elliptic partial differential equations. Based on this connection, the talk will systematically explore a series of results - both positive and negative - investigating which of the familiar a priori estimates and regularity results of elliptic PDE have analogous formulations for integral varifolds. Some of these results are joint work with Sławomir Kolasiński.

22. April Hörsaal 308 (Carl-Zeiß-Str. 3)
Matthias Keller (FSU Jena)

14:00 Habilitationsverteidigung "Analysis und Geometrie auf Graphen"
16.00 Uhr Lehrprobe "Der Fünf-Farben-Satz"

Ebenso findet um 17:30 Uhr im üblichen Seminarraum folgender Vortrag statt:

Alexey Bolsinov (Loughborough)
"Argument shift method and sectional operators: applications in differential geometry"

15. April
Sebastian Egger (Royal Holloway University of London)
"Semiclassics of quantized torus Hamiltonians"

## Seminarplan WS 2014/15

28. Januar
Sebastian Ohm (Ubimax GmbH Bremen)
"Computergestützte Bestimmung geometrischer Parameter von Umgebungen kompakter Mengen "

Abstrakt: Der Vortrag beschäftigt sich mit der algorithmischen Bestimmung von geometrischen Parametern für die epsilon-Umgebungen allgemeiner kompakter Mengen Y im 2- und 3-dimensionalen Raum, wobei epsilon ein regulärer Abstand ist. Diese Mengen werden durch endliche Punktmengen P approximiert, die im klassischen polykonvexen Fall aus einer großen Zahl von unabhängigen gleichverteilten Punkten aus Y bestehen. Das Grundziel ist es, für diese Art von Mengen ein Verfahren zu entwickeln, das solche Parameter mit Hilfe der verallgemeinerten Steiner-Formel berechnet. Im planaren Fall sind das Fläche, Umfang und Euler-Charakteristik, im Raum Volumen, Oberfläche, totale mittlere Krümmung und Euler-Charakteristik, also auch totale Gauß-Krümmung. Als theoretischer Ausgangspunkt dient die Definition der zugehörigen geometrischen Maße über das Komplement der regulären epsilon-Umgebungen von Y, welche durch die von P approximiert werden.

21. Januar
Andras Telcs (University Pannonia)
"Diffusion on the Penrose tiling"

14. Januar
One Day Workshop 2015

3. Dezember
Michael Hinz (University Bielefeld)
"An introduction to the analysis on fractals and some recent results"

Abstract: The talk deals with analysis and stochastic processes on fully singular spaces (i.e. singular at every or almost every point). In the first part we give a brief introduction to the subject which was started in the late eighties and early nineties by Goldstein, Kusuoka, Barlow, Bass, Kigami and others and is now referred to as 'Analysis on fractals'. Markov processes and their energy functionals (Dirichlet forms) play a key role. In the second part we explain items of a related vector calculus and point out some recent results and applications.

19. November
Maxim Pavlov (Lebedev Physical Institute of Russian Academy of Sciences, Moscow)
"The Vlasov kinetic equation"

Abstract:

1. Mathematical definition of Vlasov kinetic equation;
2. Hamiltonian formulation;
3. Moments. Benney hydrodynamic chain;
4. Conservation laws. Hamiltonian structure. Higher commuting flows;
5. Simplest hydrodynamic reductions;
6. Hamiltonian systems with one-and-a-half degree of freedom. Liouville integrability.

12. November
Felix Voigtländer (University Aachen)
"Embeddings between decompostion spaces"
An abstract can be found here.

5. November
Satoshi Ishiwata (University Yamagata)
"A central limit theorem for non-symmetric random walks on crystal lattices"

Abstract: A covering graph of a finite graph whose covering transformation group is abelian is called crystal lattice. Around 2000, Kotani, Shirai and Sunada have studied long time behavior of symmetric random walks on crystal lattices. In this talk, we discuss about the non-symmetric random walks on crystal lattices. This talk is based on a joint work with Hiroshi Kawabi(Okayama) and Motoko Kotani(Tohoku).

29. Oktober
Heike Gimperlein (University Edinburgh)
"Nonclassical Weyl laws for commutators."

Abstract: Weyl's law describes the asymptotic growth of the eigenvalues of the Laplacian on a closed manifold or a smooth bounded domain. We consider such laws for commutators $[P,f]$ and related Hankel operators for a pseudodifferential operator $P$ and a function $f$, in cases where the singularities of $f$ govern the growth of the eigenvalues. Their study is based on an interplay of techniques from spectral theory, harmonic analysis on $\mathbb{R}^n$ and the Heisenberg group, and noncommutative geometry.
In this talk we illustrate the rich spectral asymptotics of $[P,f]$, when $P$ is the Szegö projection on $S^1$, the truncation to positive Fourier modes. Higher-dimensional variants, and the general theory, lead to applications in complex analysis and noncommutative sub-Riemannian geometry. (joint work with Magnus Goffeng)

## Seminarplan SS 2014

3. September (Sondertermin 16:00-17:00, Raum 3517 EAP)
Jan Rataj (Charles University Prague)
Kinematic formulas for curvature measures of delta-convex Domains

9. Juli (Two talks 16.00-18.00)
Shiping Liu (Durham University)
Cheeger constant, spectral clustering and eigenvalue ratios of Laplacian
Norbert Peyerimhoff
(Durham University)

Trivalent Expanders and Delta-Y-Transformations

2. Juli
Vsevolod Shevchishin (Universität Hamburg)
Superintegrable metrics on surfaces admitting linear and quartic integrals

1. Juli (Sondertermin 16:15-17:45, SR 307, Carl-Zeiß-Str. 3)
Gerhard Bräunlich (Universität Tübingen)
The Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit

25. Juni
Naotaka Kajino (University of Kobe, z. Z. Bonn)
Spectral volume and surface measures via the Dixmier trace for local Dirichlet spaces with Weyl type eigenvalue asymptotics
Abstract

18. Juni (Two talks 16.00-18.00)
Radoslaw Wojciechowski (City University of New York)
The Feller Property for Graphs
Abstract:  The Feller property concerns the behavior at infinity of solutions of the heat equation.  In this talk, we will follow recent work of Pigola and Setti who use a maximum principle approach to derive certain criteria for the Feller property on Riemannian manifolds.  In particular, we will discuss this in the spherically symmetric case.
Ivan Veselic (TU Chemnitz)
Uncertainty and unique continuation principles for the observation of eigenfunctions

10. Juni (Sondertermin 16:15-17:45, SR 5, Helmholtzweg 4)
Andrea Posilicano (University of Insubria)
Self-adjoint, globally defined Hamiltonian operators for systems with boundaries
Abstract

28. Mai
Martin Tautenhahn (TU Chemnitz)
Carleman estimates and quantitative unique continuation principles

21. Mai
Sergei Matveev (Chelyabinsk State University)
The Diamond Lemma and prime decompositions
We describe a far generalization of the famous Diamond Lemma, which had been  published  by  Newman in 1942  and turned to be very useful in algebra and functional analysis. We replace his confluence condition by so-called mediator condition, which has a clear topological meaning. Using this new Diamond Lemma,  we get several  interesting results:
1.  The Kneser-Milnor prime decomposition theorem  (new proof).
2. The Swarup theorem for  boundary connected sums for orientable 3-manifolds (new proof and generalization two non-orientable case).
3. A spherical splitting theorem for knotted graphs in 3-manifolds.
4.  Counterexamples to the prime  decomposition   theorem for 3-orbifolds. During a long time the uniqueness of prime decompositions of 3-orbifolds had been accepted by mathematical community as a folklore theorem.  So the existence of counterexamples is quite unexpected.
5.  A new theorem on annular splitting  of 3-manifolds, which is independent of the JSJ-decomposition theorem.
6. Prime decomposition theorem for virtual knots (new result).

14. Mai
Low conjecture, Linking and causality in globally hyperbolic Lorentz spacetimes
Low conjecture and the Legendrian Low conjecture formulated by Natário and Tod say that for many spacetimes X two events x,y in X are causally related if and only if the link of spheres S_x, S_y whose points are light rays passing through x and y is non-trivial in the contact manifold N of all light rays in X.
We prove the Low and the Legendrian Low conjectures and show that similar statements are in fact true in almost all 4-dimensional globally hyperbolic spacetimes.
We also show that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard R^4.

23. April
Tatjana Eisner (Universität Leipzig)
A generalisation of the Wiener-Wintner theorem

1. April (Sondertermin 16:00-17:00, Ernst-Abbe-Platz 2, SR 3517)
Kumiko Hattori (Tokyo Metropolitan University)
Loop-erased random walk on fractals -- a random fractal approach

## Seminarplan WS 2013/14

Eine Liste der Vorträge im Wintersemester 2013/2014 findet sich hier.

## Seminarplan SS 2013

Eine Liste der Vorträge im Sommersemester 2013 findet sich hier.

## Wintersemester 2012/13

Eine Liste der Vorträge im Wintersemester 2012/13 findet sich hier.

## Seminarplan SS 2012

21. August (Sondertermin 10:00-11:00, SR 3517 EAP)
Bobo Hua (MPI Leipzig)
"Discrete harmonic functions on graphs"

20. August (Sondertermin 14:00-15:00, SR 3517 EAP)
Frank Bauer (MPI Leipzig)
"The dual Cheeger constant und the essential spectrum of a graph"

16. August (Sondertermin 14:00-17:00, SR 3517 EAP)
Michael Hinz (University of Conneticut)  (14:00-15:00)
"Vector analysis on fractals and applications"
Abstract: The talk is concerned with some recent progress in the analysis on fractals. We discuss the construction of a vector analysis that is solely based on the notion of (Dirichlet) energy. It is related to differential geometry (L²-differential forms) as well as to stochastic analysis (additive functionals of Markov processes) and can be used to study scalar and vector equations on fractals, for example magnetic Schrödinger equations or Navier-Stokes type models.
Radoslaw Wojciechowski (York College New York)  (15:00-16:00)
"Uniqueness of self-adjoint extensions of graph Laplacians"
Xueping Huang (Bielefeld University)
(16:00-17:00)
"An analytic approach to stochastic completeness of weighted graphs"

19. Juli (Sondertermin 16:15-18:00, CZ 3 SR 131)
Maria Korotiaeva (Boardeaux)
"Accoustic wave propagation in periodic media"
"Common dynamics of the tribonacci substitutions" (oder (auf deutsch) "Tribonacci substitutionen und die Raender ihrer Rauzy-Fraktale")

18. Juli
Christoph Bandt und Rüdiger Zeller (Greifswald)
"Verzweigte dynamische Systeme und Schnitte durch Fraktale"

17. Juli (Sondertermin, 11:00 SR 3319 Ernst-Abbe-Platz 2)
Christoph Schumacher (Chemnitz)
"Klassische Bewegung in zufälligen Potentialen"

13. Juli (Sondertermin 14:15-16:00 SR 3319 Ernst-Abbe-Platz 2)
Eman Hamza (Cairo)
"Quantum spin systems, Lieb-Robinson bounds and disorder"
Jun Masamune (Penn State)
"Non-explosion and recurrence of jump-diffusions on a metric measure space"

12. Juli (Sondertermin, 16:15 SR 3319 Ernst-Abbe-Platz 2)
Joe Chen (Cornell)
"Gaussian free fields on self-similar fractals"

11. Juli
Klaus Mecke
(Erlangen)
"Tensor valuations: linking physics to  spatial structures"

Abstract: Spatially structured matter such as foams, gels or biomaterials are of increasing technological importance due to their shape-dependent material properties. But the shape of disordered structures is a remarkably incoherent concept and cannot be captured by correlation functions alone. Integral geometry furnishes a suitable family of morphological descriptors, so-called tensorial Minkowski functionals, which are related to curvature integrals and do not only characterize shape but also anisotropy and even topology of disordered structures. These measures can be used to derive structure-property relations for complex materials.

4. Juli
Jun Morita (Tsukuba)

"Symmetry, Lie algebras and aperiodic orders"
Abstract: A common key word between Lie theory and aperiodic theory is symmetry. We review several recent topics in both areas including Moody conjecture and Kac conjecture as well as a new invariant of words and automata. Then, we create a new approach combining Lie structures and aperiodic structures.

28. Juni
Konstantin Pankrashkin (Paris) (HS5, Abbeanum, Beginn: 16:15)
"Self-adjoint extensions and Herglotz functions: applications to unitary equivalence between differential and finite-difference operators II"

26. Juni
Konstantin Pankrashkin (Paris)
(SR 121, CZ 3, Beginn: 16:15)
"Self-adjoint extensions and Herglotz functions: applications to unitary equivalence between differential and finite-difference operators I"

20. Juni
Sabrina Kombrink (Bremen)
"Fraktale Krümmungsmaße für selbst-konforme Mengen"

31.Mai (Seminar Analysis 16:30 Uhr im SR 3319),
Nicolae Strungaru (Edmonton)
"Meyer sets and their diffraction"

24.Mai (Sondertermin, 10:30, Raum 3319, EAP)
Steffen Winter (KIT Karlsruhe)
"Über eine Lokalisierung des Minkowski-Inhalts für beliebige Minkowski-messbare Mengen"

11. Mai (Seminar Analysis 11:15-12.15 - Treffpunkt 11:00 am Zimmer 3537A),
Ivan Veselic (Chemnitz)
"Anwendungen des Satzes von Glivenko-Cantelli"

9. Mai
Friedrich Liese (Rostock)
"Homogene Verteilungen - Struktur und statistische Anwendungen"

2.Mai
Jan Rataj (Prague)
"Normal cycles and curvature measures for sets with d.c. boundary"
Abstract: A real function (defined on an open convex subset of $R^d$) is called d.c. if it can be written as a difference of two convex functions. Let $A$ be a $d$-dimensional d.c. submanifold in $R^d$, i.e., each point of $A$ has a neighbourhood which can be represented as a subgraph of a d.c. function. We show that $A$ admits a normal cycle and, hence, its curvature measures can be defined so that the Gauss-Bonnet formula holds.

26. April (Seminar Analyis und Stochastik14:00 Uhr, SR 308, CZP3.)
Amos Koeller (Tübingen)
"Rektifizierbarkeit für nicht-ganzzahlige Dimensionen"
Abstract: Wir betrachten ein Vergleichsprinzip für die Dimension verschiedener Mengen. Wir benutzen dann dieses Prinzip, um eine Definition der Rektifizierbarkeit von Mengen mit nicht-ganzzahligen Dimensionen zu entwickeln. Wichtig ist, dass diese Definition nicht davon abhängig ist, eine spezifische fraktale Menge als kanonische Vergleichsbasis zu benutzen. Falls es Ihnen lieber ist, schicke ich auch eine englische Version. Title: Non-integer rectifiability arising from a dimension comparison principle. Abstract: We discuss a comparison principle for the dimensions of sets. We go on to, based on this principle, develope a definition of rectifiability for non-integer dimensions that is not dependent on any specific fractal being used as a canonical basic comparison set.

25. April
Batu Güneysu (HU Berlin)
"Hydrogen type stability problems on manifolds"
Abstract: In this talk, I will explain how classical results on the stability of Hydrogen type atoms can be extended to certain abstract Riemannian 3-manifolds. This clarifies which geometric and topological properties of the Euclidean space are actually needed to formulate and prove such stability results. If time admits, I will also explain some path integral techniques for the underlying Schrödinger semigroups.

19. April (10:15-11:45, SR 207 CZ)
Naotaka Kajino (Bielefeld)
"Weyl's Laplacian eigenvalue asymptotics for the measurable Riemannian structure on the Sierpinski gasket"
Abstract: On the Sierpinski gasket, Kigami [Math. Ann. 340 (2008), 781--804] has introduced the notion of the measurable Riemannian structure, with which the "gradient vector fields" of functions, the "Riemannian volume measure" and the "geodesic metric" are naturally associated. Kigami has also proved in the same paper the two-sided Gaussian bound for the corresponding heat kernel, and I have further shown several detailed heat kernel asymptotics, such as Varadhan's asymptotic relation, in a recent paper [Potential Anal. 36 (2012), 67--115]. In the talk, Weyl's Laplacian eigenvalue asymptotics is presented for this case. The correct scaling order for the asymptotics of the eigenvalues is given by the Hausdorff dimension d of the gasket with respect to the "geodesic metric", and in the limit of the eigenvalue asymptotics we obtain a constant multiple of the d-dimensional Hausdorff measure. Moreover, we will also see that this Hausdorff measure is Ahlfors regular with respect to the "geodesic metric" but that it is singular to the "Riemannian volume measure".

18. April Doppelsitzung
Giuseppe de Nittis (Cergy-Pontoise) (16:15-17:15)
"Magnetic symmetries: applications and prospects"

Naotaka Kajino (Bielefeld) (17:15-18:15)
"On-diagonal oscillation of the heat kernels on self-similar fractals"
Abstract: For the canonical heat kernel $p_{t}(x,y)$ associated with a self-similar Dirichlet form on a self-similar fractal, the following recent results of the speaker will be presented: under certain mild assumptions on the fractal or on $p_{t}(x,y)$, for a "generic" (in particular, almost every) point $x$ of the fractal, $p_{(\cdot)}(x,x)$ NEITHER varies regularly at $0$ (and hence $t^{a}p_{t}(x,x)$ does NOT converge for the appropriate scaling order $a$) NOR admits a log-periodic oscillation as $t\downarrow 0$. Furthermore the non-existence of the limit of $t^{a}p_{t}(x,x)$ is proved for ANY point $x$ of the fractal in the particular cases of the $d$-dimensional standard Sierpinski gasket with $d\geq 2$ and of the $N$-polygasket with $N\geq 3$ odd, e.g. the pentagasket ($N=5$) and the heptagasket ($N=7$).

29. März 10 Uhr c.t. im SR 3517
Marco Schreiber (Tübingen)
"Topologische Wiener-Wintner Theoreme"
Abstract: "In dem Vortrag untersuchen wir das asymptotische Verhalten von Wiener-Wintner Ergodenmitteln im Raum der stetigen Funktionen. Resultate von Robinson, Assani, Lenz und Walters werden in vereinheitlichter Weise dargestellt und für Halbgruppen von Markovoperatoren verallgemeinert."

## Seminarplan WS 2011/12

27. Februar 14:15 (Seminar Analysis - Ernst-Abbe-Platz 2, SR 3519)
Robin Nittka (MPI Leipzig)
"Pointwise convergence of Markov semigroups"

15. Februar 16:15 (Seminar Analysis - Ernst-Abbe-Platz 2, SR 3519)
Mark Lawson (Edingburgh)
"From partial symmetries to non-commutative Stone duality"

Abstract： Shechtman's work on quasi-crystals, for which he received the 2011 Nobel prize for chemistry, inspired both mathematicians and physicists to investigate more deeply the specific theory of aperiodic tilings, but it also raised more general questions about the nature of symmetry and how it can be formalized mathematically. In this talk, I shall describe one way, inverse semigroups, in which the classical notion of group has been extended to deal with more exotic notions of symmetry. I shall explain how this theory had its origins in the the classical work of Lie, was then developed in the mid 1950's only to be rather marginalized, and then experienced a renaissance in the 1990's with the discovery of unexpected connections with aperiodic tilings and C*-algebras. My main goal in this talk is to explain one way of generalizing Marshall Stone's famous duality between Boolean algebra and Boolean spaces that uses inverse semigroups --- and why this might be interesting. The work I shall describe evolved, and continues to develop, in collaboration with Jonathon Funk (West Indies), Johannes Kellendonk (Lyon), Ganna Kudryavtseva (Ljublyana), Daniel Lenz (Jena), Stuart Margolis (Bar Ilan), and Ben Steinberg (CUNY).

02. Februar 10:15 (Seminar Analysis - Ernst-Abbe-Platz 2, SR 3319)
Vasso Anagnostopoulou (TU Dresden)
"Sturmian measures and stochastic dominance in ergodic optimization"

01. Februar 16:15
Jiaxin Hu (Tsinghua University Bejing)
"Heat kernel estimates for non-local Dirichlet forms on metric spaces"
Abstract：I will present new heat kernel upper bounds for a certain class of non-local regular Dirichlet forms on metric measure spaces, including fractal spaces. As an application, we obtain two-sided estimates of heat kernels for non-local regular Dirichlet forms with finite effective resistance, including settings with the walk dimension greater than 2. The talk is based on a joint work with Alexander Grigor'yan and Ka-Sing Lau.

11. Januar 16:45
Tobias Jäger (TU Dresden)
"Dimensions of attractors in pinched skew products"

14. Dezember,
Karl-Theodor Sturm, (Uni Bonn)

"Optimal Transport in Geometry, Analysis and Probability
"

7. Dezember
Peter Stollmann (TU Chemnitz)
"The complex Laplacian and its heat semigroup"
The $\bar{\partial}$ Neumann operator is an important operator from several complex variables. In joint work with J. Perez we study its heat semigroup in noncompact situations. In the talk we give an overview over these results.

30. November,
Ivan Veselic, (Technische Universität Chemnitz
)
TBA

23. November
Holger R. Dullin (University of Sydney)
"A Lie-Poisson structure and integrator for the reduced N-body problem"
The general N-body problem is invariant under the symmetry group of translations, rotations, and Galilein boosts. The Hilber-Weyl invariants of this symmetry group can be represented by symmetric block-Laplacian matrices and we show that they satisfy a Lie-Poisson structure. Using this Lie-Poisson structure we construct a splitting integrator for the symmetry reduced N-body problem. For small N=3,4 this gives an efficient computational method, which is illustrated by computing the figure-8 choreography orbit in 3 steps.

18. November (Seminar Analysis - Ernst-Abbe-Platz 2, SR 3319)
Christian Seifert (TU Chemnitz)
"Ein Satz von Gordon für maßgestörte eindimensionale Schrödinger-Operatoren"

16.November
Shiping Liu (MPI Leipzig
)
"Ollivier-Ricci curvature on neighborhood graphs"
Abstract: In this talk, I will firstly give two kinds of understanding of Ollivier-Ricci curvature on graphs. One is the relation with local clustering, or number of triangles and self-loops. The other one is the relation with the expectation distance between two random walks. Based on those two aspects, I will discuss the combination of this curvature and the so-called neighborhood graph method which is developed by Bauer-Jost in order to explore the eigenvalue estimates of normalized graph Laplace operator.

9. November, (HS 1 im Abbeanum)
Michael Marcus, (City University New York
)
"Gaussian processes, permanental processes and local times
"

2. November,
Yury Burago, (Institute of Mathematics of the Russian Academy of Sciences, St.Petersburg
)
"$BV$-functions on irregular sets: trace and inequalities"

7. September,
Yehuda Pinchover (Technion Haifa
)
"Some aspects of large time behaviour of the heat kernel
"

2. September,
Kazuhiro Kuwae (
Kumamoto University)
"Large deviations for generalized Feynman-Kac semigroup and L^p-independence of its spectral radius"

## Seminarplan SS 2011

12. April,
J. A. Prieto (UDC Santiago / TU Dresden)
Tower systems for linearly repetitive Delone sets

19. April,
G. Kiss (ELU Budapest)
On the decomposition of balls into finitely many pieces

03. Mai,
M. Hinz (Jena)
Differential 1-forms on harmonic spaces

24. Mai,
S. Agafonov (UF Paraiba)
Local classification of singular hexagonal 3-webs with holomorphic Chern connection and infinitesimal symmetries

07. Juni,
A. Mimica (Bielefeld)
Continuity properties of harmonic functions for jump processes

21. Juni, Doppelseminar,
A. Teplyaev (Connecticut) / J. Masamune (Penn State)
Derivations and Dirichlet forms on fractals / Stochastic completeness, parabolicity and the uniqueness of Laplacians

27. Juni, ausserplanmässiges Doppelseminar, EAP 2, Raum 3319, Beginn 13.00 Uhr
S. Winter (KIT Karlsruhe) / R. Cowan (Sydney)
Characterization of Minkowski measurability in terms of surface area / On some open problems for random tesselations

28. Juni,
G. Stolz (UAB)
tbd.

## Seminarplan WS 2010/2011

18. Oktober,
J. Hutchinson (ANU Canberra)
V-variable fractals: A new approach and their spectral theory

25. Oktober,
M. Barnsley (ANU Canberra)
Theory and applications of fractal transformations

01. November,
V. Matveev (Jena)
Pseudo-Riemannian metrics on closed surfaces

08. November,
M. Keller (Jena)
Curvature and Spectrum of planar graphs

15. November,
F. Leitner (Stuttgart)

22. November,
W. Woess (Graz)
Brownian motion and harmonic functions on treebolic spaces

29. November,
F. Halasan (Jena)
The Anderson model and its absolutely continuous spectrum

6. Dezember,
M. Zähle (Jena)
Dynamische Systeme und fraktale Krümmungen

10. Dezember, ausserplanmässiges Seminar im Rahmen der Geometrie-Tage, Ort: CZ 3 HS 8, Beginn: 10.15 Uhr
R. Schneider (Freiburg)
Ungleichungen für Zonoide und Anwendungen auf Schnittdichten

20. Dezember, ausserplanmässiges Seminar, Ort: CZ 3 SR 308, Beginn: 16.15 Uhr
R. Milson (Halifax)
The IC bound for four-dimensional Lorentzian geometry

10. Januar,
M. Zähle (Jena)
Dynamische Systeme und fraktale Krümmungen II

17. Januar, Doppelseminar, Beginn der Vorträge: 16.00 Uhr und 17.00 Uhr
J. Kellendonk (Lyon) / P. Ghanaat (Fribourg)
Spectral triples and aperiodic order / Nilpotente Gruppen in der Riemannschen Geometrie

24. Januar,
M. Tautenhahn (Chemnitz)
Fractional moment bounds and localization for Anderson models with sign-changing single-site potential

31. Januar,
O. Baues (Karlsruhe)
Riemannsche Mannigfaltigkeiten mit grosser Symmetrie

## Seminarplan SS 2010

13. April,
A. Fedorova / S. Rosemann (Jena)
h-projective Kählerian metrics on compact complex manifolds

27. April,
V. Matveev (Jena)
Superintegrable metrics with one linear and one cubic integral

04. Mai,
M. Koch / Ch. Redies (Jena)
Universelle Bildstatistiken visueller Kunst als Grundlage für die ästhetische Wahrnehmung

11. Mai,
M. Keller (Jena)
Discrete spectrum for Schrödinger operators on graphs

18. Mai,
M. Zähle (Jena)
Curvature densities and dynamical systems for self-similar fractals

25. Mai,
H. Krüger (ESI Wien)
Schrödinger operators with skew-shift potential

08. Juni,
C. Richter (Jena)
Entropy numbers and lattice arrangements in l∞(Γ)

15. Juni, Doppelseminar, Raum- und Zeitänderung: Beginn jeweils 14.00 Uhr und 15.30, Raum 3517
D. Damanik (Rice Univ.) / A. Teplyaev (Univ. of Connecticut)
Schrödinger operators with limit-periodic potentials / Spectral analysis on infinite Sierpinski fractafolds

22. Juni,
K. Pakrashkin (Paris)
Spektrum, Streuung und Levinson-Sätze für die Aharonov-Bohm-Operatoren

06. Juli,
V. Knopova (Kiev)
Asymptotic behaviour of the transition densities of some Lévy functionals

## Seminarplan WS 2009/10

27. Oktober,
C. Richter (Jena)
Selbstaffine konvexe Scheiben

03. November,
M. Zähle (Jena)
Thermodynamischer Formalismus, V-variable Fraktale und Krümmungen

17. November,
J. Rataj (Prag)
On the regularity of distance spheres in Euclidean and Riemannian spaces

24. November,
W. Spitzer (Erlangen)
Neuigkeiten vom Heisenberg-Modell

01. Dezember,
A. Tetonov (Novosibirsk)
Topological definition of self-similar sets

08. Dezember,
M. Hinz (Jena)
Form Laplacians on fractals

15. Dezember,
H. Vogt (TU Dresden)
Kato class and Gaussian bounds for the heat equation on the half-space

05. Januar, Zusätzliches Seminar der Gruppe Fraktale Geometrie: Beginn 14.15 Uhr, Carl-Zeiss-Strasse 3 SR 308
N. Son (Greifswald)
Neighbourhoods in self-similar sets

05. Januar,
A. Wust (Jena)
Krümmungen, Masse, Fraktale und Graphen

12. Januar,
J. Brasche (TU Clausthal)
Konvergenz von Dirichlet-Formen

19. Januar,
F. Sobieczky (Jena)
Comparison theorems for random subgraphs of bounded geometry

29. Januar, Ausserplanmässiges Seminar: Beginn 12.15 Uhr, Abbeanum HS 1
A. Grigor'yan (Bielefeld)
On heat kernel estimates on metric measure spaces

09. Februar,
L. Gontarz (Warschau)
On the intrinsic invariance of the volumes of ε-hulls of manifolds with boundary in Euclidean spaces

25. Februar, Ausserplanmässiges Seminar: Beginn 16.30 Uhr, Raum 3517
S. Winter (Karlsruhe)

Der s-Inhalt und die Weyl-Berry-Vermutung

## Seminarplan SS 2009

07. April, Zusätzliches Seminar: Beginn 16.00 Uhr, Abbeanum HS 5
G. Hall (Aberdeen)
Curvature and Weyl tensor structure on 4-dimensional Lorentz manifolds

14. April,
V. Matveev (Jena)
Geodesically equivalent metrics: At the intersection of differential geometry, integrable systems and mathematical physics

05. Mai,
D. Lenz (Jena)
Spektraltheorie spezieller Schrödingeroperatoren

07. Mai, Zusätzliches Seminar, SR 224 CZ3, Beginn 16.15
S. Winter (Karlsruhe)
On the surface area of parallel sets

12. Mai,
D. Hardin (Vanderbilt Univ.)
Discrete minimum energy problems on fractal sets

26. Mai,
V. Matveev (Jena)
Beweis der konformen Finsler-Lichnerowicz-Obata Vermutung

09. Juni,
M. Zähle (Jena)
Lipschitz-Killing Krümmungen für Zellkomplexe und Fraktale

16. Juni,
J. Chaika (Rice University)
Interval exchange transformations

23. Juni,
D. Wingert (TU Chemnitz)
Non-local symmetric Dirichlet forms - Intrinsic metrics and Schnol'-type

30. Juni,
J. Giesen (Jena)
The medial axis transform

07. Juli,
P. Dittrich (Jena)
Chemical organization theory

14. Juli, gemeinsam mit den Arbeitsgruppen von Prof. Engelbert, Prof. Zähle und Prof. Matveev, 14.15 Uhr, SR 113 TO
A. Teplyaev (Connecticut)
Kigami's resistance forms on fractals and the energy measures

14. Juli,
M. Kassmann (Bielefeld)
Punktweise Abschätzungen für Lösungen von Integro-Differentialgleichungen

## 30. September, Zusätzliches Seminar: Beginn 14.00 Uhr, Raum 3517 Ernst-Abbe-Platz 2

J. Hu (Tsinghua Univ.)
Heat kernels for local and non-local Dirichlet forms

04. November,
Martina Zähle (Jena)
A survey on current research topics

11. November,  gemeinsames Seminar mit der Arbeitsgruppe von Prof. Matveev
Vsevolod Shevchishin (Jena)
On Lagrangian embeddings of the Klein bottle

18. November,
Uta Freiberg
(Jena)
Crossing times through self-similar nested graphs

24. November,
Peter Stollmann (TU Chemnitz),
Konzentrationsungleichungen und die Wegner-Abschätzung

09. Dezember
Fabian Schwarzenberger (TU Chemnitz)
Asymptotik der integrierten Zustandsdichte des Adjazenzoperators eines Cayley Graphen

16. Dezember,
Christian Richter (Jena)
Disjoint tilings of convex sets

06. Januar,
Christoph Thäle (Univ. Fribourg)
Segmentlängenverteilungen in stationären ebenen STIT-Mosaiken

13. Januar,
Franz Lehner (TU Graz /Univ. Bielefeld)
On the Eigenfunctions of Lamplighter Random Walks and Percolation Clusters

19. Januar,
Jan Rataj (Karlsuniv. Prag)
Properties of distance functions on convex surfaces and Alexandrov spaces

03. Februar,
Marc Troyanov (Lausanne)
L_qp cohomology: A survey.

10. Februar,