Description
Mathematics Colloquium
Date and Time: 5:00pm, Wednesday 26 June, 2019.
Venue: Room No.105 Department of Mathematics
Speaker: Dilip Patil, IISc, Bangalore.
Title: On the number of rational points on real algebraic varieties.
ABSTRACT. The main result of this colloquium is the equality of the
number of K-rational points with the signature of the trace form of a
finite K-algebra over a real closed field K. The main tools are symmetric
bilinear forms, Hermitian forms, trace forms, generalized trace forms and
their types and signatures. Further, we prove a criterion for the
existence of K-rational points by using generalized trace forms. As an
application we prove the Pederson-Roy-Szpirglas theorem about counting
common real zeros of real polynomial equations.