### 1:30- 2:20

#### Derived Categories

I will discuss the derived categories of Fano varieties of Picard number 1, degree 10, and coindex 3. In particular, I will describe an interesting semiorthogonal component of the derived category of such a variety, and discuss its behavior for some birationally special families of fourfolds. This is joint work with Alexander Kuznetsov.

### 2:30 - 3:20

#### Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points

Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic curves, the Ogg-Saito formula shows that (the negative of) the Artin conductor equals the minimal discriminant. In the case of genus two curves, equality no longer holds in general, but the two invariants are related by an inequality. We investigate the relation between these two invariants for hyperelliptic curves of arbitrary genus.

### 4:00 - 4:50

#### Interpolation for normal bundles of general curves.

This talk will address the following question: When does there exist a curve of given degree d and genus g, passing through n general points p_1, p_2,..., p_n in P^r?

### 5:00 - 5:50

#### Canonical Models for Symmetric Spaces

We show that canonical models can be defined over number fields for certain locally symmetric spaces arising from some unitary groups.

Organized by Ken Ascher, Dori Bejleri, Mamikon Gulian, and Laura Walton at the Brown Math Department

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