Student Seminar
Speaker: Garima Khetawat, IIT Bombay
Host: Santanu Dey
Title: Independence attractors of graphs
Time, day and date: 2:00:00 PM – 2:45:00 PM, Thursday, October 09
Venue: Room 113
Abstract: By an independent set in a simple graph G, we mean a set of pairwise non-adjacent vertices in G. The independence polynomial of G is defined as IG(z) = a0+a1z+a2z 2+ · · · + aβz β , where ai is the number of independent sets in G with cardinality i and β denotes the cardinality of a largest independent set in G, known as the independence number of G. Let Gm denote the m-times lexicographic product of G with itself. The independence attractor of G, denoted by A (G), is defined as A (G) = limm→∞{z : IGm(z) = 0}, where the limit is taken with respect to the Hausdorff metric on the space of all compact subsets of the plane. In this talk, we discuss some results (without proofs) regarding the possibility of independence attractors being circles or line segments.

Student Seminar
Speaker: Aditya Dwivedi, IIT Bombay
Host: Santanu Dey
Title: TBA
Time, day and date: 2:45:00 PM – 3:30:00 PM, Thursday, October 09
Venue: Room 113
Abstract: TBA

Seminar
Speaker: Professor Ori Davidov (Department of Statistics, The University of Haifa)
Host: Siuli Mukhopadhyay
Title: Safe hypotheses testing with application to order restricted inference
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, October 09
Venue: Ramanujan Hall
Abstract: Hypothesis testing problems are fundamental to the theory and practice of statistics. It is well known that when the union of the null and the alternative does not encompass the full parameter space the possibility of a Type III error arises, i.e., the null hypothesis may be rejected when neither the null nor the alternative are true. In such situations, common in the context of order restricted inference, the validity of our inferences may be severely compromised. The study of the geometry of the distance test, a test widely used in constrained inference, illuminates circumstances in which Type III errors arise and motivates the introduction of \emph{safe tests}. Heuristically, a safe test is a test that is free of Type III errors at least asymptotically. A novel safe test is proposed and studied. The new testing procedure is associated with a \emph{certificate of validity}, a pre--test indicating whether the original hypotheses are consistent with the data. Consequently, Type III errors can be addressed in a principled way, and constrained tests can be carried out without fear of systematically incorrect inferences. Although we focus on testing problems arising in order restricted inference, the underlying ideas are more broadly applicable. The benefits associated with the proposed methodology are demonstrated through simulations and analysis of illustrative examples

Commutative Algebra seminar
Speaker: Prof. R. V. Gurjar, TIFR Bombay (Retd.)
Host: Tony Puthenpurakal
Title: Resolution of singularities of algebraic or analytic varieties.
Time, day and date: 4:00:00 PM - 5:00:00 PM, Thursday, October 09
Venue: Ramanujan Hall
Abstract: First I will show how to resolve curve singularities (this must be well-known to many). Then discuss Jung-Hirzebruch argument to get the equation of a surface in three variables in a very simple form, and then resolve its singularities. This will complete the proof of resolution of singularitiies of surfaces. Next I will discuss some easy but useful results about resolution type results (resolution of indeterminacies, principalization, general notion of resolution of singularities, and their relations to each other).