
Ghosh, Soma
Mycobacterium tuberculosis (M.tb), the causative agent of tuberculosis (TB), has remained the largest killer among infectious diseases for over a century. The increasing emergence of drug resistant varieties such as the multidrug resistant (MDR) and extremely drug resistant (XDR) strains are only increasing the global burden of the disease. Available statistics indicate that nearly onethird of the world’s population is infected, where the bacteria remains in the latent state but can reactivate into an actively growing stage to cause disease when the individual is immunocompromised. It is thus immensely important to rethink newer strategies for containing and combating the spread...

Bhattacharya, Atreyee
We discuss two topics in this talk. First we study compact Ricciflat four dimensional manifolds without boundary and obtain point wise restrictions on curvature( not involving global quantities such as volume and diameter) which force the metric to be flat. We obtain the same conclusion for compact Ricciflat K¨ahler surfaces with similar but weaker restrictions on holomorphic sectional curvature.
Next we study the reaction ODE associated to the evolution of the Riemann curvature operator along the Ricci flow. We analyze the behavior of this ODE near algebraic curvature operators of certain special type that includes the Riemann curvature operators of various(locally)...

Saha, Subhamay
In this thesis we investigate single and multiplayer stochastic dynamic optimization problems. We consider both discrete and continuous time processes. In the multiplayer setup we investigate zerosum games with both complete and partial information. We study partially observable stochastic games with average cost criterion and the state process being discrete time controlled Markov chain. The idea involved in studying this problem is to replace the original unobservable state variable with a suitable completely observable state variable. We establish the existence of the value of the game and also obtain optimal strategies for both players. We also study a continuous time...

Singh, Samar B
Stochastic differential equations(SDEs) play an important role in many branches of engineering and science including economics, finance, chemistry, biology, mechanics etc. SDEs (with mdimensional Wiener process) arising in many applications do not have explicit solutions, which implies the development of effective numerical methods for such systems. For SDEs, one can classify the numerical methods into three classes: fully implicit methods, semiimplicit methods and explicit methods. In order to solve SDEs, the computation of Newton iteration is necessary for the implicit and semiimplicit methods whereas for the explicit methods we do not need such computation.
In this thesis the common theme is...

Ravi Prasad, K J
Diffuse optical tomography (DOT) is one of the promising imaging modalities that pro
vides functional information of the soft biological tissues invivo, such as breast and brain tissues. The near infrared (NIR) light (6001000 nm) is the interrogating radiation, which is typically delivered and collected using fiber bundles placed on the boundary of the tissue. The internal optical property distribution is estimated via modelbased image reconstruction algorithm using these limited boundary measurements.
Image reconstruction problem in DOT is known to be nonlinear, illposed, and some times underdetermined due to the multiple scattering of NIR light in the tissue. Solving this inverse...

Kumar, Sumit
Let H be a separable Hilbert space over the complex field. The class
S := {NM : N is normal on H and M is an invariant subspace for Ng of subnormal operators. This notion was introduced by Halmos. The minimal normal extension Ň of a subnormal operator S was introduced by
σ (S) and then Bram proved that
Halmos. Halmos proved that σ(Ň)
(S) is obtained by filling certain number of holes in the spectrum (Ň) of the minimal normal extension Ň of a subnormal operator S.
Let σ (S) := σ (Ň) be the spectrum of the minimal normal extension...

Hota, Tapan Kumar
In this report we survey some recent developments of relationship between Hausdorﬀ moment sequences and subnormality of an unilateral weighted shift operator. Although discrete convolution of two Haudorﬀ moment sequences may not be a Hausdorﬀ moment sequence, but Hausdorﬀ convolution of two moment sequences is always a moment sequence. Observing from the Berg and Dur´an result that the multiplication operator on
Is subnormal, we discuss further work on the subnormality of the multiplication operator on a reproducing kernel Hilbert space, whose kernel is a pointwise product of two diagonal positive kernels. The relationship between infinitely divisible matrices and moment sequence...

Maity, Soma
Given a compact smooth manifold Mn without boundary and n ≥ 3, the Lpnorm of the curvature tensor,
defines a Riemannian functional on the space of Riemannian metrics with unit volume M1. Consider C2,αtopology on M1 Rp remains invariant under the action of the group of diffeomorphisms D of M. So, Rp is defined on M1/ D. Our first result is that Rp restricted to the space M1/D has strict local minima at Riemannian metrics with constant sectional curvature for certain values of p. The product of spherical space forms and the product of compact hyperbolic manifolds are also critical...

Divakaran, D
Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the GromovHausdorﬀ distance, is a theorem with many applications. In this thesis, we give a generalisation of this landmark result, more precisely, we give a compactness theorem for the space of distance measure spaces equipped with the generalised GromovHausdorﬀLeviProkhorov distance. A distance measure space is a triple (X, d,µ), where (X, d) forms a distance space (a generalisation of a metric space where, we allow the distance between two points to be infinity) and µ is a finite Borel measure.
Using this...

Rao, Balaji R
In this thesis we present a formalization of the combinatorial part of the proof of FeitHigman theorem on generalized polygons. Generalised polygons are abstract geometric structures that generalize ordinary polygons and projective planes. They are closely related to finite groups.
The formalization is carried out in Agda, a dependently typed functional programming language and proof assistant based on the intuitionist type theory by Per MartinLöf.

Porwal, Kamana
The main emphasis of this thesis is to study a posteriori error analysis of discontinuous Galerkin (DG) methods for the elliptic variational inequalities. The DG methods have become very popular in the last two decades due to its nature of handling complex geometries, allowing irregular meshes with hanging nodes and different degrees of polynomial approximation on different elements. Moreover they are high order accurate and stable methods. Adaptive algorithms reﬁne the mesh locally in the region where the solution exhibits irregular behaviour and a posteriori error estimates are the main ingredients to steer the adaptive mesh reﬁnement.
The solution of...

Rungta, Satya Prakash
A hallmark of human behaviour is that we can either couple or decouple our thoughts, decision and motor plans from actions. Previous studies have reported evidence of gating of information between intention and action that can happen at different levels in the central nervous system (CNS) involving the motor cortex, subcortical structures such as the basal ganglia and even in the spinal cord. In my research I examine the extent of this gating and its modulation by task context. I will present results obtained by data collected from (a) neck muscles and neural recording from frontal eye field (FEF) in...

Nanda Kishore Reddy, S
In this thesis, we study the exact eigenvalue distribution of product of independent rectangular complex Gaussian matrices and also that of product of independent truncated Haar unitary matrices and inverses of truncated Haar unitary matrices. The eigenvalues of these random matrices form determinantal point processes on the complex plane. We also study the limiting expected empirical distribution of appropriately scaled eigenvalues of those matrices as the size of matrices go to infinity. We give the first example of a random matrix whose eigenvalues form a nonrotation invariant determinantal point process on the plane.
The second theme of this thesis is infinite...

Ruhi, Ankit
Turbulence is an open and challenging problem for mathematical approaches, physical modeling and numerical simulations. Numerical solutions contribute significantly to the understand of the nature and effects of turbulence. The focus of this thesis is the development of appropriate numerical methods for the computer simulation of turbulent flows. Many of the existing approaches to turbulence utilize analogies from kinetic theory. Degond & Lemou (J. Math. Fluid Mech., 4, 257284, 2002) derived a k✏ type turbulence model completely from kinetic theoretic framework. In the first part of this thesis, a numerical method is developed for the computer simulation based on this...

Prathamesh, Turga Venkata Hanumantha
Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories implementable in a computer. This process is termed formalisation of mathematics. Two among the many ways of mechanising are:
1 Generating results using automated theorem provers.
2 Interactive theorem proving in a proof assistant which involves a combination of user intervention and automation.
In the first part of this thesis, we reformulate the question of equivalence of two Links in first order logic using braid groups. This...

Sanki, Bidyut
Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this thesis is: which fat graphs are systolic graphs for some surface we call such graphs admissible. This is motivated in part by the observation that we can naturally decompose the moduli space of hyperbolic surfaces based on the associated systolic graphs.
A systolic graph has a metric on it, so that all cycles on the graph that correspond to...

Reza, Md. Ramiz

Reza, Md. Ramiz

Bera, Sayani
We use transcendental shiftlike automorphisms of Ck, k > 2 to construct two examples of nondegenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck, k>2 whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of DixonEsterle in C2. The second example shows the existence of a FatouBieberbach domain in Ck,k > 2 that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and RosayRudin.
In the second part we compute the order and type of entire...

Bera, Sayani
We use transcendental shiftlike automorphisms of Ck, k > 2 to construct two examples of nondegenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck, k>2 whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of DixonEsterle in C2. The second example shows the existence of a FatouBieberbach domain in Ck,k > 2 that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and RosayRudin.
In the second part we compute the order and type of entire...