Wed, October 9, 2019
Public Access Category: All |
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- Time:
- 10:15am-11:15am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics seminar
Speaker: Sudeep Stephen.
Affiliation: National University of Singapore.
Date and Time: Wednesday 09 October, 10:15 am - 11:15 am.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Zero Forcing in Graphs.
Abstract: Fo a two-colouring of the vertex set of a simple graph G = (V,E), consider the following colour-change rule: a red vertex is converted to blue if it is the only red neighbour of some blue vertex. A vertex set S ⊆ V is called zero-forcing if, starting with the vertices in S blue and the vertices in the complement V \ S red, all the vertices can be converted to blue by repeatedly applying the colour-change rule. The minimum cardinality of a zero-forcing set for the graph G is called the zero-forcing number of G, denoted by Z(G). This concept was introduced by the AIM Minimum Rank –Special Graphs Work Group in [1] as a tool to bound the minimum rank of matrices associated with the graph G. In this talk, I shall give an overview of the zero forcing problem along with some of the results that we have obtained during my Ph.D candidature. To conclude, I shall state few open problems that I intend to tackle along with my mentors. References [1] AIM Minimum Rank –Special Graphs Work Group. Zero forcing sets and the minimum rank of graphs. Linear Algebra and its Applications, 428(7):16281648, 2008.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.
Speaker: Charu Goel.
Affiliation: IIIT Nagpur.
Date and Time: Wednesday 09 October, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Nonnegative Polynomials and Sums of Squares
Abstract:
Abstract. Sums of squares representations of polynomials is of fundamental importance in real algebraic geometry and goes back to the 1888 seminal paper of Hilbert. The main theorem in his paper is a full characterisation of all pairs (n,d) for which every nonnegative polynomial of a fixed degree d in a given number of variables n is a sum of squares of polynomials. Ninety years later, Choi and Lam asserted that this characterisation remains unchanged for symmetric forms. In this talk first some key observations and problems related to Hilbert’s theorem will be discussed. We then complete the above assertion of Choi-Lam. Along the way, we shall also discuss briefly how test sets for positivity of symmetric polynomials play an important role in establishing this assertion.