General (Main) Seminar MSRI program on DDC-60 years of DPR-theorem and 50 years of DPRM-theorem

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.