Network Games, Tropical Geometry, and
These advanced courses are part of the Thematic Einstein Semester of the newly installed MATH+ excellence cluster on application-oriented mathematics within the Berlin research landscape. All three advanced courses follow the same format. In the first half of the semester, there will be lectures aiming to provide the theoretical basis for following and understanding the talks at the international conference from June 3-7, 2019. All students are expected to take part in the conference. In the second half of the semester, the students will work on small research topics. Students of the three Berlin universities can earn credits (10 ECTS for two courses) by participating in the courses and the subsequent research project. Credits will be given based on a portfolio exam at the end of the semester.
Network games and mechanism designLecturer: Max Klimm
Time: every Thursday 16:00 - 17:30 (takes place April 18 - July 4, 2019)
Place: Room 125, School of Business and Economics, HU Berlin, Spandauer Str. 1, 10178 Berlin
Description: Algorithmic game theory has emerged as a new and interdisciplinary research area at the intersection of mathematics, computer science, and economics, and is used to study the behavior of large systems with features that are governed by the selfish decisions of independent users such as telecommunication networks and online marketplaces. We will visit fundamental models of the field and discuss main problems such as the existence, computation, and efficiency of equilibria.
Quantum communication and quantum networksLecturer: Jens Eisert
Description: Quantum communication offers new modes of communication that is provably secure against unwanted eavesdropping, based on the laws of quantum physics. While this field of research is receiving significant attention due to recent technological developments, important mathematical questions are still open. This course offers an overview over notions of quantum communication, including notions of channel capacities and security. A particular emphasis will be put onto discussing questions of multi-partite quantum networks, addressing issues of computational complexity.
Optimization and tropical geometryLecturer: Michael Joswig
Time: every Monday 10:00 - 12:00 (takes place April 15 - May 27, 2019)
Place: Room MA041, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623 Berlin
Description: Tropical geometry is a field of mathematics on the border between algebraic geometry and geometric combinatorics. This reveals interesting connections between classical algebraic concepts and known algorithms from combinatorial optimization. Here network methods play a crucial role. For instance, computing a tropical determinant is the same as solving a maximum bipartite matching problem. More recently, this approach revealed deep connections to notoriously open questions in computational complexity, e.g., NP intersected with co-NP vs. P and Smale's 9th problem. This course addresses topics both in geometry and optimization, but the focus is on the intersection. For further information check out the course website.