Date & Time: Wednesday, April 07, 2010, 16:00-17:00.
Venue: Ramanujan Hall
Title: Three Thousand Two Hundred and Sixty-Four
Speaker: Jaydeep Chipalkatti, University of Manitoba and IIT Bombay
Abstract: Suppose we are given five randomly positioned conics C1,C2,...,C5 in the projective plane. How many conics can we find which are simultaneously tangent to each of the Ci? The 19th century geometer Jakob Steiner owns the credit for posing this problem, and also for giving the 'correct' incorrect answer to it.
Two ideas are needed to clarify the issue: (i) Blow-ups, and (ii) Intersection Rings. In this talk, I will give an elementary introduction to these themes. No substantial knowledge of algebraic geometry will be assumed.