July 2017
Public Access Category: All |
11am» Prof. N. S. Narasimha Sastry, IIT Dharwad- Time:
- 11:00am
- Location:
- Ramanujan Hall
- Description:
- Speaker: Prof. N. S. Narasimha Sastry, IIT Dharwad
Title: Ovoids in finite projective 3-space
Date & Time: 5th July 2017, at 11 am
Venue: Ramanujan Hall
Abstract: In a finite projective 3-space considered as an incidence
geometry, an ovoid is the analogue of the sphere in Euclidean 3-space,
introduced independently by Segre and Tits. Elliptic quadrics are
generic examples of ovoids. A projectively nonequivalent family of
ovoids were constructed by Tits which is closely related to the
Suzuki groups and Moufang sets. These are the only known families of
ovoids.
Apart from being objects of intrinsic interest, they are fundamentally
related to some important combinatorial structures like inversive
planes, generalised quadrangles, permutation polynomials, group
divisible designs, etc. Their classification and understanding their
distribution in the projective 3-space are the fundamental problems
regarding them. However, several first questions about them are yet
to be settled. To name a few: the structure of the intersection of
any two of them, packing the projective 3- space by ovoids, the number
of such objects, up to projective equivalence.
As an introduction to this topic, we discuss some interesting results
and mention some open problems.
I will make an effort to keep the talk elementary.
- Time:
- 11:00am
- Location:
- Ramanujan Hall
- Description:
- Speaker: Matjaz Kovse, LaBRI, France
Title: Vertex Decomposition of Steiner Wiener Index and Steiner Betweenness Centrality
ABSTRACT. The Steiner diversity is a type of multi-way metric measuring the size of a Steiner tree between vertices of a graph and it generalizes the geodetic distance. The Steiner Wiener index is the sum of all Steiner diversities in a graph and it generalizes the Wiener index. Recently the Steiner Wiener index has found an interesting application in chemical graph theory as a molecular structure descriptor composed of increments representing interactions between sets of atoms, based on the concept of the Steiner diversity. Amon other results a formula based on a vertex contributions of the Steiner Wiener index by a newly introduced Steiner betweenness centrality, which measures the number of Steiner trees that include a particular vertex as a non-terminal vertex, will be presented. This generalizes Krekovski and Gutman's Vertex version of the Wiener Theorem and a result of Gago on the average betweenness centrality and the average distance in general graphs.
- Time:
- 2:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Stiefel-Whitney Classes of Representations
Abstract: Given a compact group G and a real representation pi of G, there
is a sequence of interesting invariants of pi which lie in the group
cohomology of G, called the Stiefel-Whitney classes. The first class gives
the determinant of pi, and the second class is related to the spinoriality
of pi, that is whether it lifts to the spin group. We survey work on this
problem when G is a connected Lie group, and also when G is the symmetric
group. This is joint work with my Ph.D. students Rohit Joshi and Jyotirmoy
Ganguly.
- Time:
- 4:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Neha Prabhu, IISER Pune
Title & abstract: Attached.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Punit Sharma, University of Mons, Belgium
Title and abstract: Attached
- Time:
- 4:00pm - 6:30pm
- Location:
- Room 216, Department of Mathematics
- Description:
- Title: Local Fields
Abstract: This is the first in a series of lectures on class field theory.
We begin with Chapter 1 in Cassels and Frohlich.
- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Extension and Regularity of CR Functions near CR Singularities
Abstract:
CR functions are certain generalizations of holomorphic functions and CR
manifolds are those that support CR functions. For instance, a
pseudoconvex hypersurface in $\mathbb{C}^N$ is a CR manifold and CR
functions are locally boundary values of holomorphic functions. We will
begin by describing this holomorphic extension result before proceeding to
discuss the codimension two case. Codimension two submanifolds of
$\mathbb{C}^N$ generically have isolated CR singularities and we are
interested in studying the behaviour of the extension of CR functions near
CR singularities. We prove that under certain nondegeneracy conditions on
the CR singularity this extension is smooth up to the CR singularity. This
is joint work with Jiri Lebl and Alan Noell.