After successful completion of the course, students are able to work by themselves with original literature in the field of probabiliy theory and to present the results and discuss them with a group of peers.
How long is the longest increasing subsequence in a uniformly random permutation? The solution to this easy-to-formulate probabilistic problem is highly non-trivial and will take us on a fascinating journey through some of the most interesting mathematics of the last decades. Thanks to the rich interdisciplinary nature of this topic, along the way we will also learn ideas and techniques from combinatorics (integer partitions and Robinson-Schensted algorithm), operator theory (Fredholm determinants), and random matrices (Tracy-Widom distribution), among others. The seminar course will be based on the book “The Surprising Mathematics of Longest Increasing Subsequences” by Dan Romik.
The lecturer will introduce the topic. The students will give the subsequent presentations after reading parts of the book.
The schedule of the module is intended for the first week. After that, a more convenient schedule might be agreed directly with the students.
Students will be assessed based on their presentations and participation to the discussion.
Not necessary
The course will be accessible to any student with a basic knowledge of probability theory, analysis and linear algebra. Some previous knowledge in combinatorics will be also helpful but not necessary.
