Big Data and Sketching at Simons Laufer / IBM
The Simons Laufer Mathematical Institute (previously known as MSRI) hosts two-week programs for graduate students across the US to study special topics in mathematics. Typically, they also provide funding and housing for students to attend, so I highly recommend applying if there's a topic of interest to you (see their website for a full list of programs).
In July 2023, I was a TA for SLMath 1064, Mathematics of Big Data and Sketching. There were graduate students from across the United States, and even a few international ones. Lior Horesh, Kenneth Clarkson, Misha Kilmer, Shashanka Ubaru, and Tamara Kolda were the instructors for the school, which took place at the beautiful IBM Research campus in Almaden, CA. I had the pleasure to work with fellow TAs Yijun Dong and Rachel Minster.
Problem Sets and Curriculum
Each of the two problem sets assigned per day was comparable in length to a weekly university homework assignment. The students worked in groups so that they could finish the problems in the short time alotted, while the TAs roamed between the groups to help. Given two lectures (roughly 2.5-3 hours) and 3 hours of homework per day, I estimate that the summer school covered roughly the same content as a standard quarter-long mathematics course in just two weeks. Everyone was tired by the end, but the course content was valuable.
The first week of the summer school covered the basics of linear algebra and the mathematics of randomization and sketching, tools used to decrease the computational cost of expensive linear algebra primitives. The second week covered tensors, which are generalize matrices and vectors to higher dimensions.
I work at the intersection of these topics. In addition to TAing, I was gratified to meet some of the heavyweights in both fields, and we had many productive discussions.
Logistics
The students stayed at the dormitories of San Jose State university and took a bus to the summer school every day, which took place over two weeks in an auditorium on the Almaden research campus. There was a breakfast of fresh fruit and muffins for students and staff, and each morning there was a lecture for slightly more than an hour. After a break, the students received a problem set to work on until lunch at noon, which we usually ate outside under a leafy canopy atop a hill. Temperatures regularly exceeded 80 Farenheit outside, but the auditorium was air-conditioned.
The afternoon session was a mirror of the morning: a lecture, followed by a break and problem sets (there was a tea snack provided!). At the end of the day, dinners were provided in brown paper bags for the students before they boarded the bus back to the dorm.
They fed us well! But the work made us hungry, and we needed it.
Research Seminar and Career Panel
By student request, the last day of the program was a seminar of research talks given by the students; 17 of the participants shared their research, and all three of us TAs presented our work as well.
I think the students really enjoyed the feedback from the instructors - I certainly did. The last two hours consisted of a career panel, where the instructors and the other two TAs (who were postdocs) shared advice for the students. I usually sleep through career panels, so I was really surprised by how engaged the students were. They asked so many questions that we ran out of time.
If you have the chance to attend one of these summer schools, it's a wonderful experience. IBM Almaden was also one of the most quiet, beautiful tech campuses I have ever seen, surrounded by the serene Santa Teresa Hills. I hope to go back one day.