The research seminars Analysis & Geometry (A&G) and Dynamical Systems & Mathematical Physics (DS&MP) are organised by the research groups of Prof. David Hasler, Prof. Daniel Lenz, Prof. Vladimir Matveev, Prof. Tobias Oertel-Jäger, Prof. Anke Pohl and Prof. Thomas Wannerer.

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**When**: Thursdays @ 14:30-16:00 (A&G) and 16:00-17:30 (DS&MP)

**Where**: Ernst-Abbe-Platz 2, seminar room 3517 (OpenStreetMap)

# Winter term 2016/17

## 18. August 2016

*14:15, seminar room 3517***Michael Baake** (Universität Bielefeld)

**Renormalisation theory for primitive substitutions**

## 20. October 2016

*14:30 (A&G)***Jakub Konieczny** (University of Oxford, United Kingdom)

**Automatic sequences, generalised polynomials and nilmanifolds**

*16:00 (DS&MP)*

**Tanja Eisner** (Universität Leipzig)

**Weighted Ergodic Theorems**

## 27. October 2016

*14:00 (A&G)***Aapo Kauranen** (Jyväskylä/Prague)

**Sobolev spaces and Lusin's condition (N) on hyperplanes**

## 03. November 2016

*14:30 (A&G)***Alexander Teplyaev** (University of Connecticut, USA)

**Existence, uniqueness and vector analysis on fractals**

The talk will describe how the heat kernel estimates, which are mainly due to Grigor'yan and Telcs, and related functional spaces and potential theory, imply the existence and uniqueness of self-similar Dirichlet forms (and hence Laplacians and diffusion processes) on generalized Sierpinski carpets. This is a joint result with Barlow, Bass and Kumagai. The second part of my talk will review recent results on vector analysis on such spaces, such as quasilinear PDEs, Dirac and magnetic Schrödinger operators, spectral triples, Hodge theory, Navier-Stokes equations, and some unusual properties of the classical curl operator. This includes joint results with J.P. Chen, M. Hinz, D. Kelleher, M. Röckner. The motivation for this vector analysis come from physics, such as studying magnetic properties of fractal structures.

## 10. November 2016

*14:30 (A&G)***Franz Schuster** (Technische Universität Wien, Austria)

**Affine vs. Euclidean isoperimetric inequalities**

In this talk we explain how every even, zonal measure on the Euclidean unit sphere gives rise to an isoperimetric inequality for sets of finite perimeter which directly implies the classical Euclidean isoperimetric inequality. The strongest member of this large family of inequalities is shown to be the only affine invariant one among them - the Petty projection inequality. As an application, a family of sharp Sobolev inequalities for functions of bounded variation is obtained, each of which is stronger than the classical Sobolev inequality. This is joint work with Christoph Haberl.

## 24. November 2016

*14:30 (A&G)***Marc Rauch** (Universität Jena)

**The inverse variational principle**

*16:00 (DS&MP)***Dan Rust** (Universität Bielefeld)

**TBA**

## 01. December 2016

*14:30 (A&G)***Matthias Reitzner** (Universität Osnabrück)

**Random polytopes: limit theorems**

Let η be the set of random points of a Poisson point process in R^{d}, and let K be a convex set of volume 1. Denote by s the mean number of random points in K, and by K_{s} the convex hull of these points. We are interested in properties of K_{s} as s tends to infinity: expectations, variances, limit theorems and large deviations for functionals of K_{s}.

*16:00 (DS&MP)*

**Alexey Bolsinov** (Loughborough University, United Kingdom)https://redproxy.rz.uni-jena.de/admin.php?site=oag&site=oag

**TBA**

## 08. December 2016

*14:30 (A&G)***Nina Lebedeva** (Steklov Institute of Mathematics at St.Petersburg, Russia)

**TBA**

*16:00 (DS&MP)***Peter Stollmann** (TU Chemnitz)

**TBA**

## 05. January 2017

*14:30 (A&G)***Felix Dorrek** (Technische Universität Wien, Austria)

**TBA**

## 02. February 2017

*14:30 (A&G)* or 16:00 (DS&MP)**Andreas Knauf** (Universität Erlangen-Nürnberg)

**TBA**