By Henri Linus Breloer (UiT)
The SIAM conference in algebraic geometry took place in Madison, Wisconsin, this year. For this month’s newsletter, I would like to share my experience of attending the conference.
It started in January, when I was given the opportunity to hold a talk at the conference, but had to come up with an abstract on short notice. I had a couple of hours to decide whether I wanted to travel to the US in the summer and give a talk. Evidently, I decided to go, even though, as the time drew near, I grew a bit apprehensive because of multiple high-profile cases of researchers and tourists being denied entry into the US. In the end, the travel and immigration to the United States went well for me, though it was quite difficult to find a reasonable flight from Tromsø to Madison, and I had to spend a night at the Munich airport. For the conference guests, there was housing organized at the Witte residence hall, which during the semester is a dormitory for the students of the University of Wisconsin-Madison, including a very american all-you-can-eat breakfast buffet.
For a conference in algebraic geometry, and from all the conferences I have experienced, SIAM AG is quite large. This year, there were more than 400 participants registered, even though a lot of people canceled their participation on short notice. With plenary talks in the morning and afternoon and parallel sessions with up to 14 talks at the same time, there was a lot going on at all times. The topics ranged from applications in biology, like phylogenetic networks, and algebro-geometric methods in machine learning to coding theory and tensors. With many cancellations and new replacement talks, there was a lot of reshuffling of talks and timelines, so always having an eye on the online schedule was important. I mostly visited the mini-symposium on tensors, which took place from Tuesday to Friday, with a couple of interesting talks on metric algebraic geometry and applications in computer vision and machine learning in between. I also met people a few people from the TENORS network and, in particular, my fellow DC from TENORS, Francesco, who gave an interesting talk about discriminants from the Kuramoto model in the discriminants session.
All in all, I was positively surprised by the understandability and information density of the talks. The parallel session talks went on for only 25 minutes, but still managed to convey a lot of mathematics that was new to me. I especially enjoyed a series of talks on the different types of tensor rank, namely the slice and partition rank as well as a talk on infinite symmetric tensors and their behavior. On the second-to-last day, the evening program consisted of the presentation and subsequent vote on the bids for the next SIAM AG conference host. The decision to give out wine and beer beforehand convinced a lot of people to stay and made the discussion of the bids quite lively. In the end, more people voted for Bologna than Dresden, but it was by a narrow margin. The vote was non-binding and only served as a indication of interest, so we’ll see where the next SIAM AG conference in two years will take place.
My own talk was during the last parallel session on Friday, on the topic of my recent preprint, “Rational invariants of even degree polynomials under the orthogonal group.” The aim of the talk was to present a concrete generating set for rational invariants for the action of the orthogonal group on polynomials of even degree. Working out the details of the construction unearths a surprising connection to graph theory and the graph isomorphism problem.
On the evening of the last conference day, I went with a group of other mathematicians to a nearby barbecue, when we were surprised by a heavy thunderstorm that came with weather warnings of flash floods and even tornadoes. Everyone got home safe and even mostly dry, but it was an eventful evening nonetheless.