Yesterday I came across a photo of two gentlemen sitting outside of my old grad-school student lounge. They are Sasha Beilinson and Vladimir Drinfeld, two mathematicians from my alma mater who were awarded this year’s Wolf Prize in Mathematics.
The CS department at the University of Chicago shared space with Mathematics and Statistics in my day, so it was not unusual to encounter mathematicians while having lunch (or a nap) in the lounge. There have been many useful collaborations and intersections between these departments.
I have no idea what Sasha or Vladimir do. I tried to understand. I glanced at their ground breaking work, a book called Chiral algebras. They state in the introduction “Chiral algebras have their origin in mathematical physics;” and “Chiral algebras are “quantum” objects.” Ok.
Drinfeld and Beilinson still run the Geometric Langlands Seminar that of course captures the essence of what they care about most. As best I can figure, Langlands, himself a 1996 Wolf prize recipient, is a mathematician who envisioned building links between algebra and modern physics. Drinfeld and Beilinson have extended that work. Maybe the best explanation of this undertaking is provided by Edward Frenkel.
He seems to be a celebrity in his own right. I enjoyed how he connects Solaris to universals of number theory!
If Frenkel is still too abstract for you, then Mitya Boyarchenko suggests that this poem that I include below might be of use in understanding the Langlands talks
A man called Pakhomych, shaking as he rode on the carriage footboards,
Carried a bunch of forget-me-nots.
He got corn on his heels,
And treated them at home with camphor.
Reader! Having discarded the fable’s forget-me-nots,
Which were put here as a joke,
You can arrive at only a single conclusion:
If you get corns
And you want to rid yourself of the pain,
You, like our friend Pakhomych,
Should treat them with camphor.