MathematicsSeminar |
Rocky Mountain Algebraic Combinatorics Seminar
Cubic surfaces over $\mathbb{F}_{13}$
Fatma Karaoglu
University of Sussex (UK)
Given five skew lines a1, a2, a3 , a4, a5 with a single transversal b6 such that each set of four ai omitting aj (j = 1, …, 5) has a unique further transversal bj, then the five lines b1, b2, b3, b4, b5 also have a transversal a6. These twelve lines form a double-six. The double six lies on a unique cubic surface with 15 further lines cij given by [ai,bj] ∩[aj, bi].
Hirschfeld in 1964 discussed the existence and the properties of the cubic surfaces over the finite fields of odd and even order and classified over \mathbbF4, \mathbbF7, \mathbbF8, and \mathbbF9. 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.