8:00am 


9:00am 


10:00am 


11:00am 
[11:45am] Amit Kumar Singh: IIT Madras
 Description:
 Speaker: Amit Kumar Singh.
Affiliation: IIT Madras.
Date and Time: Thursday 24 October, 11:45 am  12:45 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Semistability of certain vector bundles on elliptic curves.
Abstract: Abstract Let L be a line bundle of degree d on an elliptic curve C and ϕ : C → P
n
is a morphism
given by a sublinear system of the complete linear system L of dimension n + 1. When d = 4, n
= 2, we prove that ϕ
∗TPn is semistable if deg(ϕ(C)) > 1. Moreover, we prove that ϕ
∗TPn is isomorphic to direct sum of two isomorphic line bundles if and only if deg(ϕ(C)) = 2. Conversely, for any
rank two semistable vector bundle E on an elliptic curve C of degree 4, there is a nondegenerate
morphism ϕ :C → P
n
such that ϕ
∗TPn (−1) = E. More precisely, E is isomorphic to direct sum of two
isomorphic line bundles if and only if deg(ϕ(C)) = 2. Further E is either indecomposable or direct
sum of nonisomorphic line bundles if and only if deg(ϕ(C)) = 4. When d = 5, n = 3, we compute
the HarderNarasimhan filtration of ϕ
∗TPn .


12:00pm 

1:00pm 


2:00pm 


3:00pm 
[3:30pm] Tony J. Puthenpurakal
 Description:
 Commutative Algebra seminar II.
Speaker: Tony Puthenpurakal.
Affiliation: IIT Bombay.
Date and Time: Thursday 24 October, 3:30 pm  5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Triangulated categoriesI,II,III.
Abstract: We define and give elementary properties of triangulated
categories. We also give an application of triangulated categories to
linkage theory in commutative algebra.


4:00pm 

5:00pm 


6:00pm 

