## Reinhold-Baer-Kolloquium im Winter 2018/2019

Am **Samstag, 19. Januar 2019,** findet das Reinhold-Baer-Kolloquium in Magdeburg statt. Alle Interessierten sind herzlich eingeladen. Eine Anmeldung ist nicht erforderlich.

Veranstaltungsraum ist **Raum 214 in Gebäude 3** der** Otto-von-Guericke-Universität Magdeburg**. (Lageplan des Campus).

Markus Stroppel (Stuttgart) pflegt eine sehenswerte Übersicht über (fast) alle vergangenen Reinhold-Baer-Kolloquien.

### Programm

10.00 - 11.00 Uhr | Christian Lehn (Chemnitz): Limit theorems in topological data analysis (Abstract) |

11.30 - 12.30 Uhr | Petra Schwer (Magdeburg):Kostant Convexity in the affine flag variety and affine grassmannian (Abstract) |

Mittagspause mit Gelegenheit zum gemeinsamen Essen | |

14.00 - 15.00 Uhr | Christian Günther (Paderborn):Flat polynomials, low autocorrelation sequences, and difference sets (Abstract) |

15.15 - 16.15 Uhr | Milena Wrobel (Leipzig): A combinatorial tool for Fano varieties (Abstract) |

### Abstracts

#### Christian Lehn (Chemnitz): *Limit theorems in topological data analysis*

In a joint work with V. Limic and S. Kalisnik Verosek we generalize the notion of barcodes in topological data analysis in order to prove limit theorems for point clouds sampled from an unknown distribution as the number of points goes to infinity. We also investigate questions of applicability of general probability theory in Banach spaces in order to deduce a law of large numbers and a central limit theorem for barcode valued random variables.

#### Petra Schwer (Magdeburg): *Kostant Convexity in the affine flag variety and affine grassmannian*

In this talk I will explain the classical Kostant convexity theorem and will show how one can obtain natural analogs for the affine flag variety and affine grassmannian using combinatorial and geometric methods.

#### Christian Günther (Paderborn): *Flat polynomials, low autocorrelation sequences, and difference sets*

The problem of constructing binary sequences with large merit factor arises naturally in complex analysis, condensed matter physics, and digital communications engineering. Equivalent formulations involve the minimisation of the mean-squared aperiodic autocorrelations of binary sequences or the minimisation of the *L ^{4} * norm on the complex unit circle of polynomials with all coefficients in {-1,1}.

Most known constructions arise (sometimes in a subtle way) from classical difference sets, namely Paley and Singer difference sets. After a review of known constructions, I will present more recent results involving cyclotomy and other difference sets, in particular Gordon-Mills-Welch and Hall difference sets. These constructions provide the first essentially new examples since 1991, answer questions posed by Jensen, Jensen, and Høholdt; and prove conjectures due to Jedwab, Katz, and Schmidt.

This talk is based on joint work with Kai-Uwe Schmidt.

#### Milena Wrobel (Leipzig): *A combinatorial tool for Fano varieties*

Looking at toric Fano varieties, their classification with respect to their singularity type turns out to be a purely combinatorial task: they can be described by certain lattice polytopes, the so called Fano polytopes. The anticanonical complex has been introduced as a natural generalisation of the toric Fano polytope and so far has been successfully used for the study of varieties with a torus action of complexity one, i.e. the general torus orbit is of codimension one. In this talk I will present a sufficient criterion on a Fano T-variety of

arbitrary complexity that allows the construction of an anticanonical complex describing their singularities in full analogy to the complexity one case. Moreover, we show that the possibility to construct the anticanonical complex for these varieties is connected to certain properties of their quotients.