The major theme of this thesis is the study of multiplicity results for fractional elliptic equations and the system of equations. The thesis is mainly divided into three parts. In the first part, the existence and ...

We will compute the boundary asymptotics of the Carathéodory and Kobayashi-Eisenman vol- ume elements on convex finite type domains and Levi corank one domains in C n using the standard scaling techniques. We will show ...

In this thesis, we estimate the contribution of symmetric cube transfer and tensor product transfer to the cuspidal cohomology of ${\rm{GL}_4}$. Let $\mathbb{E}=\mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic extension ...

Orthogonal representations \pi of a finite group G have invariants w_i(\pi), living in the ith degree cohomology group H^i(G, Z/2Z), called Stiefel-Whitney Classes (SWCs). Their sum is known as the total SWC of \pi. There ...

In first half of the work we prove the \A^1 connectivity of moduli stack of vector bundles on a curve, as a consequence of which we classify projective bundles on curves upto their \A^1 homotopy type. Based on joint work ...

Component-wise semi-Markov processes (CSM) constitute a larger class of pure jump processes which includes semi-Markov, and Markov pure jump processes. This thesis examines semi-Markov as well as CSM processes with dependent ...

This thesis studies some geometric properties of knots in real projective 3-space. These ideas are borrowed from classical knot theory. Since knots in $\mathbb{R}P^3$ are classified into three disjoint classes: affine, ...

In [BS19], Balasubramanyam and Sinha derived the first moment of the pair correlation function for Hecke angles lying in small subintervals of [0, 1], as one averages over large families of Hecke newforms of weight k with ...

Integro-differential operators arise naturally in biological modeling and mathematical finance. We aim to conduct an in-depth study of integro-differential operators and their regularity properties in this thesis. We start ...