Monday, February 6, 2023
Time  Items 

All day 

4:00pm 
02/06/2023  4:00pm A wellknown conjecture of Margulis predicts the existence of a uniform lower bound on the systole of any irreducible arithmetic locally symmetric space. In joint work with F. Thilmany, we proved that this conjecture is equivalent to a weak version of the Lehmer conjecture, a wellknown problem from Diophantine geometry. Location: 02/06/2023  4:30pm This is a report on work of my graduate student Cristian Rodriguez. A QFano 3fold is a complex projective variety with mild singularities such that its 1st Chern class is positive. QFano 3folds with b_2=1 arise as end products of Mori's minimal model program. Thousands of families are expected, whereas there are only 17 in the smooth case. We will describe mirror symmetry for QFano 3folds in terms of the StromingerYauZaslow conjecture and Kontsevich's homological mirror symmetry conjecture, building on work of Auroux. The mirror of a QFano 3fold is a K3 fibration over the affine line such that the total space is log CalabiYau and some power of the monodromy at infinity is maximally unipotent. In 95 cases the QFano is realized as a hypersurface in weighted projective space and we describe the mirror K3 fibration explicitly. Location:
LOM 214
