Schedule

1. Friday's talk will be in Lecture Hall 1, during 14:00-14:50 and 15:00-15:50. Back
2. All the other talks are in the Seminar Hall.

Tue 2013-Jan-15

R. Srinivasan Vasanth, E_0-semigroups on factors. 3pm

Abstract: I will survey the recent developments in the theory of semigroup of *-endomorphisms on factors, basically related to my work.

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Wed 2013-Jan-16

Samir Datta, Computing Bits of Algebraic Numbers. 3pm

Abstract:

Abhijit Pal, Cannon-Thurston Maps for Trees of Relatively Hyperbolic Metric Spaces. 4pm

Abstract: Let $i:X\to Y$ be a proper embedding between (relatively) hyperbolic metric spaces $X,Y$. A Cannon-Thurston map is said to exists for $i$ if there exists a continuous extension of i to the (relative) hyperbolic boundaries of $X$ and $Y$. In this talk, I will prove that if X is a tree of (relatively) hyperbolic spaces such that X is also (relatively) hyperbolic then a Cannon-Thurston map exists for the embedding of a vertex space into the tree of space X.

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Thu 2013-Jan-17

Ananya Lahiri, Integrated volatility estimation for a finance model with fractional Brownian motion. 3pm

Abstract: In recent past, to capture long range dependence of stock price in reality, fractional Brownian motion (FBM) has been introduced as a replacement of Brownian motion (BM) for modelling the same. Integrated volatility (IV), which appears in different finance studies, plays an important role as a measure of variability of the data. The common practice of estimating IV is from sum of frequently sampled squared data, in case of BM setup. In present case we are interested to find some similar result for FBM setup, find the estimate and study its properties.

Upendra Kulkarni, TBA. 4pm

Abstract:

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Fri 2013-Jan-18

R. Sridharan, TBA. 2pm

Abstract:

Senthamarai Kannan, An analogue of Bott's theorem for Schubert varieties-related to torus semi-stable points. 3pm.

Abstract: Let $G$ be a simple, simply connected and simply laced algebraic group. Let $B$ be a Borel subgroup of $G$ containing a maximal torus $T$ of $G$. Let $E$ denote the Tangent Bundle of $G/B$. Then, we know that by Bott's theorem all the higher cohomologies of $E$ vanish. He also further showed that its global sections is the adjoint representation of $G$. So, it is a natural question to ask for which Schubert variety $X(\tau)$ Bott's theorem holds. In this context, we show the following:

\begin{enumerate}
\item
$H^{i}(X(\tau), E)=(0)$ for every 
$i\geq 1$.
\item
$H^{0}(X(\tau) , E)=\mathfrak{g}$
if and only if the set of semi-stable points
$X(\tau^{-1})_{T}^{ss}(\mathcal{L}_{\alpha_{0}})$ with respect to the line 
bundle associated to the highest root $\alpha_{0}$ is non-empty.
\end{enumerate}

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Mon 2013-Jan-21

Sundar S., Inverse semigroups and the\240Cuntz-Li\240algebras. 3pm

Abstract: Let R be an integral domain such that every non-zero quotient R/mR is finite. Consider the unitaries and isometries on \ell^{2}(R) induced by the addition\240 and the multiplication operation of the ring R. The C*-algebra generated by these unitaries and isometries is called\240 the ring C*-algebra and was studied by\240Cuntz\240and\240Li. In my talk, I will explain how inverse semigroups can be\240 used to understand these C*-algebras. Also some generalisation of the ring C*-algebras will\240 be discussed.

Manoj Kummini, Hilbert Functions and hypersurface restriction theorems. 4pm.

Abstract: We look at the poset of Hilbert functions of graded ideals in a graded ring. Sometimes, it can be realized as a sub-poset of the poset of graded ideals in the ring. We study how this behaves under polynomial extensions, and prove an analogue of the hyperplane restriction theorem of M. Green, and its generalizations to hypersurfaces by J. Herzog and D. Popescu and by V. Gasharov. This is joint work with G. Caviglia.