This page contains content from the 2025 Columbia Math Undergraduate Summer Research Program. During the first two weeks, we held lectures to prepare for the research project. Students interested in my research will benefit from reading the notes below and working on the exercises.
Faculty lead: Evan Sorensen
Graduate TA: Xinyi (Sara) Zhang
Our project resulted in preprint on arXiv that has been submitted to a peer-reviewed journal. It is available here
First two week lecture notes and exercises
Tuesday, May 27 (Last-passage percolation) (Evan)
Wednesday, May 28 (RSK) (Sara)
Thursday, May 29 (Directed polymers) (Evan)
Friday, May 30 (Geometric RSK) (Sara)
Monday, June 2 (Invariance of polymer partition functions under Geometric RSK Lecture 1) (Sara)
Tuesday, June 3 (Periodic Pitman transform) (Evan)
Wednesday, June 4 (Invariance under geometric RSK lecture 2) (Sara)
Thursday, June 5 (Periodic polymers) (Evan)
Friday, June 5. The lecture will be based on this paper (Evan)