## Mathematics## Seminar |

## Rocky Mountain Algebraic Combinatorics Seminar

### Cubic surfaces over $\mathbb{F}_{13}$

Fatma Karaoglu

University of Sussex (UK)

Given five skew lines *a*_{1}, *a*_{2}, *a*_{3} , *a*_{4}, *a*_{5} with a single
transversal
*b*_{6} such that each set of four *a*_{i} omitting *a*_{j} (*j* = 1, …, 5)
has a unique further transversal
*b*_{j}, then the five lines *b*_{1}, *b*_{2}, *b*_{3}, *b*_{4}, *b*_{5} also have a transversal
*a*_{6}. These twelve lines form a double-six.
The double six lies on a unique cubic surface with 15 further lines
*c*_{ij} given by [*a*_{i},*b*_{j}] ∩[*a*_{j}, *b*_{i}].

*F*

_{4}, \mathbb

*F*

_{7}, \mathbb

*F*

_{8}, and \mathbb

*F*

_{9}. Sadeh in 1985 classified the cubic surfaces in

*PG*(3,11). In this talk, we classify cubic surfaces with twenty-seven lines over the finite field of thirteen elements by classifying 6-arcs not lying on a conic in the plane, although projectively distinct arcs do not necessarily represent projectively distinct surfaces.

### Covers of Symplectic Dual Polar Spaces

Eric Moorhouse

University of Wyoming

For q ≡ 1 mod 4, the symplectic dual polar graph of type G=Sp(2n,q) admits a double cover admitting 2×G as a group of automorphisms (M. and Williford, 2015). I will describe how this construction works over the field of real numbers (and possibly also mentioning more general fields). Here the group 2×G is replaced by the relevant metaplectic group, an extension of Sp(2n,F) which is not necessarily split. Here, as in our original finite case, the Maslov index plays a crucial role.

Weber 223

4–6 pm

Friday, February 17, 2017

(Refreshments in Weber 117, 3:30–4 pm)

Colorado State University

This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly. Anyone interested is welcome to join us at a local restaurant for dinner after the talks.