Congrats to C. Y. Chang, a number theorist working on transcendence in function field arithmetic (FFA)! He has been awarded a silver medal by the International Congress of Chinese Mathematicians. See this link for more.
He and his collaborators have determined all algebraic relations among various objects such as the Carlitz zeta values, and special values of an analog of the gamma function in FFA, among other things. Nothing like their work has been done yet for number fields.
Those interested in these things should again see my notes on log-algebraicity (linked just below) where some of these things are discussed briefly with references. I also recommend an internet search for Chang and his collaborators. It’s fairly easy to get a good sense of their work from the introductions to their papers.
On Tuesday I gave a talk on Anderson’s log-algebraicity at Ohio State University to an audience of mostly grad students and advanced undergrads in a seminar entitled What is…?. I used the extremely powerful transcendence results of M. Papanikolas and others as motivation for where log-algebraicity can take you. There are also applications of Anderson’s results to the new constructions of L. Taelman that we’ve been studying on this blog, but these are not mentioned below.
Notes for the talk are attached are linked RIGHT HERE. Any comments, corrections, hints, tips, or tricks are welcome.
Clearly, we’ve already been taking a bit of a break, and I (Rudy) will be away from the office for the next month. This means I won’t have a space to make any videos until later in the month of May. I plan to continue when I return, so check back in around May 20th.
We’re planning a new video for next week. Sorry about the delay, we’re all just a bunch of swamped graduate students!
Actually, we have two videos in the works. In the first, Tim All will tell us some more about L. Taelman’s constructions – in particular his class module and the relation to Goss-Carlitz zeta values. In the second, we’ll have a guest Brad Waller tell us some about the peculiarities of p-adic measures and distributions. Eventually I’ll get my act together and post another video as well.
Stay tuned for the next video in our lecture series, which I plan to have up in the next week. Our next topic will be motivation for the Carlitz module via zeta values in positive characteristic.