Thu, August 2, 2018
Public Access

Category: All

August 2018
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2:00pm [2:00pm] Dr. Vivek Mukundan
Speaker : Dr. Vivek Mukundan Title : Implicitization problem and the defining ideal of the Rees algebra. When : Thursday, 2 Aug 2.00-3.30 pm Venue: Room 215 ============= Abstract: Consider a rational map from P^{n-1}—>P^n parametrized by homogeneous polynomials f_0,\dots,f_n of degree d. We study the equations defining the graph of the map whose coordinate ring is the Rees algebra of the ideal generated by f_0, .., f_n. We provide new methods to construct these equations using work of Buchsbaum and Eisenbud. Furthermore, for certain classes of ideals, we show that our construction is general. These classes of examples are interesting, in that, there are no known methods to compute the defining ideal of the Rees algebra of such ideals. These new methods also give rise to effective criteria to check that φ is birational onto its image.

[3:00pm] Prof. K.B. Athreya
Title: General Glivenko- Cantelli. Theorem. Speaker: Prof. K.B. Athreya Venue: Ramanujan Hall Time: 3:00 pm to 4:00 pm Abstract: The classical version of Glivenko Cantelli theorem says: let X sub I , i = 1, 2, 3, real valued r.v. with cdf F(x) then the empirical cdf based on X sub i , i = 1,2,3,....n converges wp1 as n goes to infinity to F uniformly over R. In this talk this theorm is generalised to cover Markov chains, exchangeable sequences and regenerative sequences. Some open problems will also be posed.