#### Block Course Lecturers

- Omer Bobrowski (Technion)

- Matthew Kahle (Ohio State, TU Berlin)

- J. Andrew Newman (TU Berlin)

- Yuval Peled (NYU Courant Institute)

- Érika Roldán (Ohio State)

#### Parent Program

Thematic Einstein Semester Summer 2020 Geometric and Topological Structure of Materials.

Coronovirus Update

[March 9, 2020] TU Berlin is closely monitoring the developments related to the outbreak
of the coronavirus disease (COVID-19).

For now, the university is not impacted by the outbreak and remains open.

[March 11, 2020] !!! TU Berlin ordered all events to be cancelled !!!

#### Topics

- Probabilistic and topological preliminaries

- Random geometric complexes and percolation theory

- Phase transitions for homology and cohomology

- Random fundamental groups and geometric group theory

- Laplacians of graphs and simplicial complexes and applications to topology

- Morse theory, especially in random settings

#### Suggested prerequisites

- Chapters 1–4 of N. Alon & J. Spencer. The Probabilistic Method. Fourth Edition. Wiley Series in Discrete Mathematics and Optimization. John Wiley & Sons, Inc., Hoboken, NJ, 2016. xiv+375 pp. ISBN: 978-1-119-06195-3 .

- Sections 9 & 10 of A. Björner. Topological methods. Handbook of combinatorics, Vol. 1, 2, 1819–1872, Elsevier Sci. B. V., Amsterdam, 1995.

- R. Forman. A user's guide to discrete Morse theory. Sém. Lothar. Combin. 48 (2002).

#### Venue

The block course will be held in the lecture hall MA 005
of the Mathematics Building
of TU Berlin, Straße des 17. Juni, 10623 Berlin.

#### Participation

free

#### Registration

Deadline for registration: at earliest convenience.

#### Collegiality

MATH+ Collegiality Statement#### Schedule

Monday | Tuesday | Wednesday | Thursday | Friday | |
---|---|---|---|---|---|

09:15 - 10:00 | Kahle | Bobrowski | Newman | Roldán | Peled |

10:15 - 11:00 | Kahle | Kahle | Bobrowski | Bobrowski | Kahle |

11:00 - 11:30 | Coffee Break | ||||

11:30 - 12:15 | Bobrowski | Newman | Kahle | Newman | Roldán |

12:15 - 14:00 | Lunch Break | ||||

14:00 - 14:45 | Bobrowski | Peled | Problem Solving & Recitation | Peled | |

15:00 - 15:45 | Problem Solving & Recitation | Problem Solving & Recitation | Problem Solving & Recitation | Problem Solving & Recitation | |

16:00 - 16:45 | Problem Solving & Recitation | Problem Solving & Recitation | Problem Solving & Recitation | ||