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IMSc Theses/ Dissertations: Recent submissions

  • Aspects of high energy scattering in Abelian and non Abelian Gauge theories 
    Tapobrata Sarkar (, 2009-10-06)
    This thesis reviews certain aspects of high energy scattering in abelian and non abelian gauge theories. This subject has been extensively studied over the last few decades, using perturbative techniques. Recently it has ...
  • Scalar-Tensor Theory for gravity in D Dimensions 
    Arjun Bagchi (, 2009-10-05)
    The general theory of Relativity and the scalar-Tensor theory are studied in general D dimensions stressing on Cosmology and the static spherically Schwarzchild solution. General Relativity is dealt with in Brief. Different ...
  • On Polynomial Identity Testing and Related Problems[HBNI Th12] 
    Partha Mukhopadhyay (The Institute of Mathematical Sciences, 2009)
    The polynomial identity Testing problem and its connection to several other important complexity theoretic problems are studied in this thesis. Polynomial identity testing problem is considered over commutative and non ...
  • Parameterized field theories and Loop Quantization[HBNI Th10] 
    Alok Laddha (The Institute of Mathematical Sciences, 2009)
    This thesis shows how two dimensional parametrized field theories constitute perfect toy models for Loop Quantum Gravity. Two dimensional massless scalar field theories on a Minkowskian plane and show how various aspects ...
  • Modelling Biological clocks: a study of the Repressilator 
    Somdeb Ghosh (The Institute of Mathematical Sciences, 2009-09-29)
    Biological clocks are found everywhere in the natural world. From circadian rhythms to pacemakers of the heart, biological clocks are an essential part of the smooth functioning of living organisms. They are composed of ...
  • Geometry of Quantum States 
    Sandeep, K. Goyal (, 2009-09-25)
    Understanding the geometry of state space is of fundamental interest in the field of quantum information, in particular to study entanglement. The states of a d-dimensional system form a convex set in the d^2 - 1 dimensional ...
  • Brusselator as a Reaction-Diffusion system 
    Rajeev Singh (, 2009-09-24)
    In this work the Brusselator model is studied, which is a minimal mathematical model, for chemical oscillations. The mean field analysis for the model and the traditional way of adding the effect of diffusion is reviewed. ...
  • Cosmological Perturbation Theory 
    Sabapathy, KrishnaKumar (2009-09-24)
    This study is a review of Cosmological perturbation theory. The theory aims to model the physical universe by perturbing about a background Friedmann-Robertson-Walker cosmological model. Two approaches are highlighted, ...
  • Complexity upper bounds using permutation group theory 
    Kurur, Piyush P. (2009-09-23)
    This thesis studies the Graph Isomorphism and problems that arise in Galois theory. It is targeted to use structural properties of permutation groups together with other algebraic techniques to prove complexity upper ...
  • Studies in Loop Quantization of cosmological models[HBNI Th9] 
    Kinjal Banerjee (The Institute of Mathematical Sciences, 2009)
    This thesis presents some studies on the Loop Quantization of cosmological models. The effect of loop quantization of FRW cosmology in the context of effective equations and WKB approximation are studied in the first ...
  • Complexity Theoretic aspects of Rank Rigidity and circuit evaluation[HBNI Th8] 
    Jayalal Sarma, M. N. (The Institute of Mathematical Sciences, 2009)
    This thesis studies some combinatorial, topological and linear algebraic parameters associated with Boolean and arithmetic circuits. It is divided into two parts, the first describes a study of combinations of graph ...
  • Phenomenology of a B Meson and CP violation[HBNI Th7] 
    Sharma, Chandradew (The Institute of Mathematical Sciences, 2009)
    The New Physics, the Physics beyond the Standard Model, shows that New Physics which affects B decays with any topological amplitude can be absorbed by redefinitions of the SM amplitudes. This thesis studies the B → K∗ρ ...
  • Exact Algorithms for Optimization and parameterized versions of some graph theoretic problems[HBNI Th6] 
    Saket Saurabh (The Institute of Mathematical Sciences, 2009)
    The class of NP-hard combinatorial optimization problems, need to be solved exactly for various applications in theory and practice, brings the need for exact algorithms. Parameterized complexity is an exact algorithmic ...
  • Classifying certain algebraic problems using Logspace counting classes[HBNI Th5] 
    Vijayaraghavan, T. C. (The Institute of Mathematical Sciences, 2009)
    In this thesis the results showing a finer classification of the complexity of several algebraic problems that have efficient polynomial time algorithms are obtained. The problems based on Group theory and Linear Algebra ...
  • Studies in SU(2) Savvidy model of QCD[HBNI Th4] 
    Alok Kumar (The Institute of Mathematical Sciences, 2009)
    Quantum Chromo Dynamics is accepted as the theory of strong interaction of quarks and gluons. It is a gauge theory with the gauge group as SU(3)C1 the unbroken color group. In this thesis the author examines the ground ...
  • Some explicit minimal graded free resolutions[HBNI Th2] 
    Aaloka, Kanhere (The Institute of Mathematical Sciences, 2009)
    This thesis has three parts. In the first part an irreducible curve C in P^2 is considered. The Veronese map is used for mapping it to P^5 and the resolutions are computed. In the second part, looking into two distinct ...
  • Acyclic edge colouring: Bounds and algorithms[HBNI Th3] 
    Rahul Muthu (The Institute of Mathematical Sciences, 2009)
    An acyclic edge colouring of a graph is an assignment of colours to its edges in such a way that incident edges get distinct colours, and the edges of any cycle use atleast three distinct colours. The latter condition is ...
  • Planar Algebra of the Subgroup-Subfactor[HBNI Th1] 
    Ved Prakash, Gupta (The Institute of Mathematical Sciences, 2009)
    An identification between the planar algebra of the subgroup-subfactor R x H subset of R x G is given and the G-invariant planar subalgebra of the planar algebra of the bipartite graph *n (the graph with 1 odd and n even ...
  • Explicit integral Galois Module structure for low degree abelian extensions 
    Manisha, V. Kulkarni (, 2009-09-14)
    'Let M be a finite abelian extension of of Q. Then the ring of integers OM of M is a free, rank one module over the associated order AM/Q'. There is no method for constructing a Z(G) basis for OM when OM is free over Z(G). ...
  • Asymptotic behaviour of some Optimal Control Problems 
    Muthukumar, T. (, 2009-09-14)
    The theory of homogenization of partial differential equations is a concept that deals with the study of the macroscopic behaviour of a composite medium through its microscopic properties. The aim of this thesis is to ...

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