Unnathi Venkatesh
Research Fellow
Unnathi Venkatesh is an exceptionally motivated and inspired student with great passion for mathematics, theoretical physics and computer science.
Unnathi Venkatesh is, though in her 12th grade, already a scholar and researcher difficult to find combined in one individual. Her learning presents a spectacular blaze of scholarly pursuits, research studies and accomplishments.
Beginning with a solid foundation of calculus based basic physics and mathematics, she has been working on key topics in modern Mathematics and Theoretical Physics an outline of which is as follows:
1. Linear Algebra: Matrices. Product of Matrices. Triangular, Matrices. Scalar Matrices. Conjugate of a matrix. Hermitian Matrix; Direct Sum; Determinant; Minors and Cofactors. The Laplace Expansion; Rank of a matrix. Non-singular and singular matrices. Adjoint of a matrix. Inverse of a matrix. Matrices over Fields. Linear dependence of vectors. Vector spaces and linear transformations. Characteristic equation of a matrix. Hermitian form. Bilinear form. Minimum polynomial of a matrix.
2. Quantum Computation: Classical Information. Entropy and Shannon’s Information Theory. Probability Basics. Qubits and Quantum States. Inner Products. Orthonormality. Gram-Schmidt Orthogonalization. The Cauchy-Schwartz and Triangle Inequalities. Observables. The Pauli Operators. Hermitian, Unitary, and Normal Operators. Eigenvalues and Eigenvectors. Spectral Decomposition. The Trace of an Operator. Tensor Products .Density Operator. Projective Measurements. Measurements on Composite Systems. Generalized Measurements. Entanglement. Bell’s Theorem. Bipartite Systems and the Bell Basis. Quantum Gates and Circuits. Hadamard Gates. The Phase Gate. Matrix Representation of Serial and Parallel Operations.
3. Quantum Computer Music: Foundations and Initial Experiments: Gate-Based Quantum Computing. Algorithmic Computer Music. Musical Quantum Walks (1-D and 3-D). Basak-Miranda Algorithm, Constructive and Destructive Interference, Amplitude Remixing.
4. The Physics of Music: The Nature of Sound. Force, Vibration and Resonance. Intensity and Loudness. Pitch. Musical Quality. The Ear. Vibrations of Strings. Organ Pipes. Dissonance and Consonance. Scales and Temperament. Recording and Production of Sound. Halls and Concert Rooms.
Research Publications
Unnathi Venkatesh and Charu Gupta - Voice Leading Space of Triads, To Be Submitted for Publication
