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[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 Krational points with the signature of the trace form of a
finite Kalgebra 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 Krational points by using generalized trace forms. As an
application we prove the PedersonRoySzpirglas theorem about counting
common real zeros of real polynomial equations.


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