Thursday, March 17, 2016
4:00 PM, CC Little 2502 (note the nonstandard building/room!)
Hilbert’s tenth problem, which asks if there exists an algorithm that decides whether a given polynomial equation with integral coefficients has integer solutions or not, has been answered in the negative by Matiyasevich. However, many variants of this problem are still open, and we explain the connections between these variants and certain decidability problems. In particular, we will show that the complement of the ring of integers of a number field admits a Diophantine definition inside the number field.