Michael Zeng, University of Washington
-
PDL C-401
(This talk will be given as a Socratic Seminar.)
- How many roots does a polynomial have over the complex numbers? How about over the reals? Over any field?
- How many circles are simultaneously tangent to 3 circles in the plane, over C? How about over R? Over k?
- How many lines simultaneously meet 4 skew lines in 3-space?
- How many lines are there on a smooth cubic surface in 3-space? How many different types of lines are there?
- How many lines are there in a pencil of quartic surfaces in 3-space? What are the types of these lines?
- How many genus 1 curves are there on a (3,3)-Calabi-Yau threefold in 5-space?
- How do we know for sure???