CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Frank Sottile, University of Massachusetts, Amherst

Time:          Wednesday, March 20, at 4:30pm, 

Place:         Earth Science Bldg 152A, University at Albany

Title:         Common transversals and tangents in P^3 


Abstract: 

The following geometric problem has its origins in
computational vision: Determine the (degenerate)
configurations of two lines l_1 and l_2 and two spheres
in R^3 for which there are infinitely many lines
simultaneously transversal to l_1 and l_2 and tangent
to both spheres. We generalize this, replacing the
spheres by quadric surfaces in P^3. In this setting,
the question has an amazing answer. Fixing the two
lines to be skew and one quadric, the set of degenerate
second quadrics is a curve of degree 24 in the P^9 of
quadrics which is in fact the union of 12 plane conics!
Moreover, there are examples where all 12 degenerate
families are real. We describe the symbolic computation
behind this result and give some vivid pictures.

This is joint work with Gabor Megyesi and Thorsten Theobald


Refreshments at 4:15 pm in ES 152.