Wed, September 25, 2019
Public Access

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25
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2:00pm [2:45pm] Amalendu Krishna :TIFR, Mumbai
Description:
Mathematics Colloquium Talk II. Speaker: Amalendu Krishna. Affiliation: TIFR, Mumbai. Date and Time: Wednesday 25 September, 2:45 pm - 3:45 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: Revisiting Bertini theorems. Abstract: The classical Bertini theorem in algebraic geometry says that a general hyperplane section of a smooth quasi-projective subvariety of a projective space over an algebraically closed field is also smooth. It was already known long time ago that such a result holds over any infinite field. However, this turned out to be false over finite field, as Katz showed. Poonen then showed that Bertini theorem can be salvaged over finite fields by allowing hypersurfaces of large degree rather than just hyperplanes. In this talk, we shall revisit these Bertini theorems. In particular, we shall prove new Bertini theorems for normal and integral schemes over finite fields. This is based on a joint work with Mainak Ghosh.

3:00pm
4:00pm [4:00pm] Omprokash Das: TIFR, Mumbai
Description:
Mathematics Colloquium Talk III. Speaker: Omprokash Das. Affiliation: TIFR, Mumbai. Date and Time: Wednesday 25 September, 4:00 pm - 5:00 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: Birational classification of algebraic varieties. Abstract: Algebraic varieties are common solutions of bunch of multi-variable polynomials equations, for example, straight line, circle, cuspidal curve, nodal curve, sphere, etc. Classifying all algebraic varieties up to isomorphism is the ultimate goal of algebraic geometry. Of course, this is nearly impossible achieve, so we consider various weaker form of classification, and classifying varieties ‘Birationally’ is of those tools. In this talk I will explain what it means to classify varieties birationally, what are the difficulties in higher dimensions and the role of Minimal Model Program (MMP) in birational classification.
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