December 16, 2019 - December 20, 2019
Public Access Category: All |
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- Time:
- 4:00pm-5:00pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Analysis seminar.
Speaker: Sudeshna Basu.
Affiliation: Ramakrishna Mission Vivekananda Educational and Research
Institute, Belur.
Date and Time: Monday 16 December, 4:00 pm - 5:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Linear Hahn Banach Extension of module homomorphisms in Hilbert
and Banach modules.
Abstract: The notion of linear Hahn-Banach extension operator was first
studied in detail by Heinrich and Mankiewicz (1982). Previously, J.
Lindenstrauss (1966) studied similar versions of this notion in the
context of non separable reflexive Banach spaces. Subsequently, Sims and
Yost (1989) proved the existence of linear Hahn-Banach extension operators
via interspersing subspaces in a purely Banach space theoretic set up. In
this paper, we study similar questions in the context of Banach modules
and module homomorphisms, in particular, Banach algebras of operators on
Banach spaces. Based on Dales, Kania, Kochanek, Kozmider and
Laustsen(2013), and also Kania and Laustsen (2017), we give complete
answers for reflexive Banach spaces and the non-reflexive space
constructed by Kania and Laustsen from the celebrated Argyros-Haydon's
space with few operators.
- Time:
- 4:00pm-5:00pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Mathematics Colloquium.
Speaker: Hossein Movasati.
Affiliation: IMPA, Rio de Janeiro.
Date and Time: Wednesday 18 December, 4:00 pm - 5:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Ramanujan's relations between Eisenstein series.
Abstract: In 1916 S. Ramanujan discovered three identities involving the
Eisenstein series $E_2,E_4,E_6$ and their derivatives. This can be seen as
a vector field in the moduli space of an elliptic curve $E$ enhanced with
a certain frame of the de Rham cohomology of $E$. For this one needs
algebraic de Rham cohomology, cup product and Hodge filtration developed
by Grothendieck and Deligne among many others. Viewed in this way,
Ramanujan's differential equation can be generalized to an arbitrary
projective variety. If time permits I will explain two generalizations of
this picture in the case of Abelian varieties and Calabi-Yau threefolds.