The main theme of my thesis is based on non-local type elliptic equations. In particular, existence of infinitely many nontrivial solutions for a class of equations driven by non-local integro-differential operator ...

In the thesis, we have studied effective distribution of gaps between elements of one or more than one sequences. We also have studied a multiplicity one kind theorem for cusp forms.

The main focus of this thesis is to study the topology of some spaces associated with polynomial knots and determining the least polynomial degree in which a given knot can be represented. A polynomial knot is an embedding ...

A famous conjecture of Sato and Tate (now a celebrated theorem of Taylor et al) predicts that the normalised p-th Fourier coeffcients of a non-CM Hecke eigenform follow the Sato-Tate distribution as we vary the primes ...

This thesis studies three problems of mathematical finance. We address the appropriateness of the use of semi-Markov regime switching geometric Brownian motion (GBM) to model risky assets using a statistical technique. ...

One can define the notion of primitive length spectrum for a simple regular periodic graph via counting the orbits of closed reduced primitive cycles under an action of a discrete group of automorphisms. We prove that this ...

Representations of the symmetric groups can be thought of as homomorphisms to the orthogonal group. We give criteria for whether such a representation lifts to the Pin group, which is a two-fold cover of the orthogonal ...

Gabber’s presentation lemma is a foundational result in A 1 -homotopy theory. This result can be thought of as an algebro-geometric analog of the tubular neighborhood theorem in differential geometry. Similar to tubular ...

For the similitude symplectic group GSp_6 over a totally real number field F, we establish the meromorphic continuation of the standard L-function and the spin L-function which are Langlands L-functions associated to the ...