Date and Time: Monday 14 October, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Vector bundles, stability and Harder-Narasimhan filtration.
Abstract: Vector bundles in geometry generalize projective modules in
algebra. They are the simplest sort of coherent sheaves. We will introduce
the all important notion of stability of vector bundles. The stable
bundles have nice properties, and luckily, most bundles are stable. But
even those bundles that are not stable can be analysed in terms of stable
bundles. This is done by the notion of the Harder-Narasimhan filtration of
a bundle. We will give a sketch of the theory and illustrate it with
examples.
Time:
5:30pm-7:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Probability and Statistics seminar.
Speaker: Probal Chaudhuri.
Affiliation: ISI Kolkata.
Date and Time: Tuesday 15 October, 05:30 pm - 07:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Learning Mahalanobis distance from C R Rao.
Time:
2:15pm-3:15pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Mathematics Colloquium.
Speaker: Probal Chaudhuri.
Affiliation: ISI Kolkata.
Date and Time: Wednesday 16 October, 2:15 pm - 3:15 pm.
Date and Time: Friday 18 October, 4:15 pm - 5:15 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Introduction to the Polynomial Method in Combinatorics II (Lower
bounds on Kakeya sets over finite fields).
Abstract: For a finite field F, a Kakeya set is a subset of F^n that
contains a line in every direction. We will discuss a result of Dvir
showing a lower bound of C_n*q^n on the size of any Kakeya set over F^n,
where C_n only depends on n and F is a finite field of size q.