Organizer: V. Harizanov and A. Shlapentokh
For link contact [email protected]
Friday, December 18, 12:00-1:00 ET on Zoom
Speaker: Yuri Matiyasevich, Saint Petersburg State University
and Russian Academy of Sciences
Title: 60 years of DPR-theorem and 50 years of DPRM-theorem
Abstract: I will start by considering different ways to prove these two theorems and some of their improvements.
These theorems, originally aimed at the (negative) solution of Hilbert’s 10th problem, found numerous applications, mainly for establishing impossibility of something else (today the literature totals more than 1000 items). I’ll discuss a few of such applications in various branches of mathematics. The selection is personal, for example, I won’t touch numerous extensions of Hilbert’s 10th problem to other rings (there were many brilliant talks about them during this semester).
A few (most likely, very difficult) related open problems will be discussed as well.
Note: Matiyasevich (M), building on the work of Davis, Putnam and J. Robinson (DPR) solved Hilbert’s Tenth Problem, 70 years after it was posed.