Date and time: Tuesday, 29 November at 2.30 pm

Venue: Room 215

Speaker: Arindam Banerjee, IIT Kharagpur

Title: A binomial type formula for integral closures of powers of 
monomial ideals.

Abstract: Let I and J be two ideals in two polynomial rings 
A=K[x_1,....,x_m] and B=[y_1,...,y_n] respectively. Tai Ha et al. proved 
a binomial formula for $(I+J)^(n)$ in (A \tensor B) in terms of symbolic 
powers I^(t) and J^(t') where t and t' are less than or equal to n. A 
similar formula fails for integral closures of powers of ideals, even 
for monomial ideals. It has been shown in a recent joint work with Tai 
Ha that for monomial ideals some binomial type formula holds for 
integral closures of powers of (I+J).

Using this formula we have also shown some formulas for regularity (and 
depth) of integral closures of powers of (I+J) in terms of regularity 
(and depth) of integral closures of lower powers of I and J. In this 
talk, we plan to discuss this work and some potential problems.

Statistics seminar

Date and time: Tuesday, 29th November at 3:00 pm

Venue:  Ramanujan Hall.

Speaker: Subrata Kundu, George Washington University (USA),

Title: Some remarks on generalizations of the likelihood function and the likelihood principle

Abstract:  The sufficiency principle (SP), the weak conditionality principle (WCP), the likelihood function (LF), and the likelihood principle (LP) for a general statistical inference problem are discussed. It is argued that a general statistical problem can be regarded as a prediction problem by treating the quantity (z) of inferential interest as the realized but unobserved value of a random vector Z. The LF is defined as the density of the data given z and the unknown fixed parameters of the model, considered as a function of z and θ. The SP and WCP are modified such that they are equivalent to the LP based on the proposed LF.

(Joint work with Tapan K. Nayak)