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.