Wed, June 26, 2019
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5:00pm [5:00pm] Dilip Patil, IISc, Bangalore: Mathematics Colloquium
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.
6:00pm