Research conducted at the School of Mathematics draws inspiration from and connects to different areas within the discipline. Under the broad traditional headers of Mathematics, research pursued at the school can be classified as:

- Group theory, Homological Algebra, Commutative Algebra;
- Geometric aspects of Syzygies;
- Preserver problems on Spaces of Matrices;
- Representation theory of Finite-dimensional Algebras;
- Algebraic, Analytic and Combinatorial Number theory;
- Elliptic curves, Modular forms and Galois representations.

**Faculties members involved:** Sachindranath Jayaraman, Srilakshmi Krishnamoorthy, Sarbeswar Pal, Geetha Thangavelu, Viji Z. Thomas.

- Analysis of Julia sets of holomorphic maps;
- Ergodic theory of simultaneous actions;
- Dynamics of holomorphic correspondences;
- Control, existence and uniqueness results of nonlinear PDE’s;
- Nonlinear functional analysis, Semi-group theory, Monotone operator theory;
- Harmonic analysis, Sampling and reconstruction;
- Stochastic analysis, Stochastic PDE’s;
- Dynamics of nonhomogeneous products of positive operators.
- Nonlinear analysis; Topological and Variational methods in PDE

**Faculties members involved: ** P. Devaraj, Sachindranath Jayaraman, Utpal Manna, M. P. Rajan, Dhanya Rajendran, Dharmatti Sheetal, Shrihari Sridharan.

- Control of fluid flow problem in particular phase field models;
- Finite element methods for differential equations;
- Graph theory, Combinatorial PDE's, Spectral graph theory, Distance matrices on graphs;
- Navier-Stokes theory, Liquid crystals, Ferromagnetism;
- Wavelet analysis, Applied cryptography;
- Positivity classes of matrices arising in optimization problems;
- Hyperbolic systems of conservation laws and thier numerical solutions;
- Computational fluid dynamics;
- Lyapunov exponents and other invariants in structurally stable dynamical systems;
- Computational mathematics;
- Math-Bio.

**Faculties members involved:** K. R. Arun, P. Devaraj, Sachindranath Jayaraman, Dond Asha Kisan, Sudarshan Kumar K, Utpal Manna, Sumit Mohanty, M. P. Rajan, Dharmatti Sheetal, Shrihari Sridharan.

- Geometry of curves, surfaces and moduli spaces of vector bundles on them;
- Geometry of Gerbes, stacks and Lie groupoids;
- Geometry of semi-group action generated by finitely many maps;
- Stochastic geometric PDE's.

**Faculties members involved:** Saikat Chatterjee, Utpal Manna, Sarbeswar Pal, Shrihari Sridharan.

- Topological properties of moduli space of vector bundles;
- Grothendieck topology;
- Topological dynamical systems.

**Faculties members involved:** Saikat Chatterjee, Sarbeswar Pal, Shrihari Sridharan.

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