Symmetries And Singularity Structures

Proceedings of the Workshop, Bharathidasan University, Tiruchirapalli, India, November 29 - December 2, 1989

This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould's analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field.

This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model. Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, $p$-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field. The volume also contains several research articles by leading researchers, showcasing new developments in the field.

This volume is the seventh in a series of proceedings on theoretical physics related to various aspects of the structure of condensed matter and to appropriate mathematical methods for adequate description. Three main topics are considered: conformal symmetry, central charge, condensation of flux; rigged string configurations, YangOCoBaxter equations and their applications in solid state physics; and energy band structure in solids."

This volume is the seventh in a series of proceedings on theoretical physics related to various aspects of the structure of condensed matter and to appropriate mathematical methods for adequate description. Three main topics are considered: conformal symmetry, central charge, condensation of flux; rigged string configurations, Yang–Baxter equations and their applications in solid state physics; and energy band structure in solids. Contents:Path Integral Representations for a Constrained System (Y Ohnuki)Finite Quantum Systems and Their Applications to Quantum Information Processing (A Vourdas)The Vandermonde Determinant Revisited (B G Wybourne)Fascinating Properties of Carbon Nanotubes (M Czechowska et al.)Scale Invariant Behaviour in Growing and Coalescing Droplets (J A Blackman & J Poulter)Rigged Configuration and the Bethe Ansatz (A Schilling)Towards a General Solution of the Linear Heisenberg Problem (W J Caspers et al.)Skew Gelfand–Tsetlin Patterns, Lattice Permutations, and Skew Pattern Polynomials (J D Louck)Transport Properties of Domain Walls in Ferromagnets (J Barnas & V K Dugaev)and other papers Readership: Researchers, academics, graduate students and upper level undergraduates in condensed-matter, theoretical and semiconductor physics. Keywords:

The phase structure of particle physics shows up in matter at extremely high densities and/or temperatures as they were reached in the early universe, shortly after the big bang, or in heavy-ion collisions, as they are performed nowadays in laboratory experiments. In contrast to phase transitions of condensed matter physics, the underlying fundamental theories are better known than their macroscopic manifestations in phase transitions. These theories are quantum chromodynamics for the strong interaction part and the electroweak part of the Standard Model for the electroweak interaction. It is their non-Abelian gauge structure that makes it a big challenge to predict the type of phase conversion between phases of different symmetries and different particle contents. The book is about a variety of analytical and numerical tools that are needed to study the phase structure of particle physics. To these belong convergent and asymptotic expansions in strong and weak couplings, dimensional reduction, renormalization group studies, gap equations, Monte Carlo simulations with and without fermions, finite-size and finite-mass scaling analyses, and the approach of effective actions as supplement to first-principle calculations. Contents:General Background from Statistical PhysicsField Theoretical Framework for Models in Particle PhysicsAnalytic Methods on the Lattice and in the ContinuumNumerical Methods in Lattice Field TheoriesEffective Actions in the ContinuumPhenomenological Applications to Relativistic Heavy-Ion Collisions Readership: Theoretical and high energy physicists. Keywords: