In a distinguished scientific life that had spanned over five decades, AlladiRamakrishnan made significant contributions to probability and statisticselementary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Inspired by his visit to the Institute of Advanced Study during 1957-1958, and the direct influences of Robert Oppenheimer, Niels Bohr, Sir C.V. Raman, S. Chandrasekhar, and other notable contemporaries, he later founded the Institute of Mathematical Sciences (MATSCIENCE) in Madras, India.In the spirit of Alladi Ramakrishnan's profound interest and contributions to three fields of science - Mathematics, Statistics, and Physics - this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan's illustrious career of special interest are included as well.

- PrefacePart I. The Legacy of Alladi Ramakrishnan Contributions of Alladi Ramakrishnan to the Mathematical Sciences. Alladi Ramakrishnan's Theoretical Physics Seminar. Telegrams received for the MATSCIENCE inauguration. The miracle has happened, speech given by Alladi Ramakrishnan at the inauguration of MATSCIENCE. Overseas Trips of Alladi Ramakrishnan. List of publications of Alladi Ramakrishnan. List of PhD students of Alladi Ramakrishnan.Part II. Pure Mathematics Inversion and invariance of characteristic terms - part I (Abhyankar). Partitions with non-repeating odd parts and q-hypergeometric identities (Alladi). q-Catalan identities (Andrews). Completing Brahmagupta's extension of Ptolemy's theorem (Askey). A transformation formula involving the gamma and Riemann zeta functions in Ramanujan's Lost Notebook (Berndt and Dixit). Ternary quadratic forms, modular equations, and certain positivity conjectures (Berkovich and Jagy). How often is n! a sum of three squares? (Deshouillers and Luca).- Crystal symmetry viewed as zeta symmetry - II (Kanemitsu and Tsukuda). Eulerian polynomials: From Euler's time to the present (Foata). Crystal symmetry viewed as zeta symmetry II (Kanemitsu and Tsukada). Positive homogeneous minima for a system of linear forms (Raghavan). The divisor matrix, Dirichlet series, and SL(2,Z)(Sin and Thompson). Proof of a conjecture of Alladi Ramakrishnan on circulants (Waldschmidt).Part III. Probability and Statistics Branching random walks (Athreya). A commentary on the logistic distribution (Ghosh, Choi, and Li). Entropy and cross entropy characterizations and applications (Rao). Optimal weights for a class of rank tests for censored bivariate data (Rao, Raychaudhuri, and Wu). Connections between Bernoulli strings and random permutations (Sethuraman and Sethuraman). Storage models for a class of master equations with separable kernels (Vittal, Jayasankar, and Muralidhar).Part IV. Theoretical Physics and Applied Mathematics Inverse consistent deformable image registration (Chen and Ye). A statistical model for the quark structure of the nucleon (Devanathan and Karthiyayini). On generalized Clifford algebras and their physical applications (Jagannathan). (p,q)-Rogers-Szegö polynomial and the (p,q)-oscillator (Jagannathan and Sridhar). Rethinking renormalization (Klauder). Magnetism, FeS celluloids, and origins of life (Mitra-Delmotte and Mitra). The Ehrenfest theorem in quantum field theory (Parthasarathy).