# Lech's conjecture

Tuesday, April 11, 2017 -

4:30pm to 5:30pm

A long-standing conjecture of Lech states that the Hilbert-Samuel multiplicity does not drop for faithfully flat extensions of local rings. This conjecture was known in dimension less than or equal to two and remains open in higher dimensions. In this talk we will use Hilbert-Kunz theory to obtain estimates on the multiplicities under faithfully flat extension, and in particular we can prove the conjecture in dimension three, in equal characteristic.

Speaker:

Linquan Ma

University of Utah

Event Location:

Fine Hall 322