Wed, January 22, 2020
Public Access Category: All |
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- Time:
- 11:00am-12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics Seminar.
Speaker: S. Venkatesh.
Affiliation: Department of Mathematics, IIT Bombay.
Date and Time: Wednesday 22 January, 11:00 am - 12:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Improved Bounds for the Sunflower Lemma.
Abstract: For a positive integer r, an r-sunflower is a collection of r
finite sets such that the intersection of any two sets is the intersection
of all. The Erdos-Rado Sunflower conjecture states that for any fixed
positive integer r, there exists a constant c>0 such that the following
holds for eventually all positive integers w: for every collection of at
least c^w sets, each having size w, there exists a subcollection which is
an r-sunflower.
Erdos and Rado (1960), while posing the Sunflower conjecture, showed that
every collection with at least about w^w sets, each having size w, will
contain an r-sunflower. In this talk, we will see an improvement by
Alweiss, Lovett, Wu and Zhang (2019), who show that every collection with
at least about (log w)^w sets, each having size w, will contain an
r-sunflower.
- Time:
- 2:30pm-3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Geometry and Topology seminar.
Speaker: Pratulananda Das.
Affiliation: Jadavpur University.
Date and Time: Wednesday 22 January, 02:30 pm - 03:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Characterized subgroups of the Circle.
Abstract: In this talk the history and the developments of the notion of
characterized subgroups of the circle group would be discussed along with
some of the main observations obtained over the years. This would be
followed by presentation of certain very recent developments in this area
carried out by using a more general method of convergence.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.
Speaker: Bata Krishna Das.
Affiliation: IIT Bombay.
Date and Time: Wednesday 22 January, 04:00 pm - 05:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Model of operators and their characteristic functions.
Abstract:
Dilations of Hilbert space operators is a basic and useful tool which is used to understand non-normal operators. In this talk, we will discuss Sz.-Nagy’s unitary dilations of contractions and some of its far reaching consequences in function theory and operator theory. This inparticular will include a functional model for a class of contractions and their charac- teristic functions. If time permits we will also discuss a recently developed multivariate analogue of these notions.