New Books in the Science Libraries March-April 2023
Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts by Matthew Emerton; Toby GeeA foundational account of a new construction in the p-adic Langlands correspondence Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize étale (ϕ, Γ)-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. These stacks are then used to show that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and indeed admit crystalline lifts. The book explicitly describes the irreducible components of the underlying reduced substacks and discusses the relationship between the geometry of these stacks and the Breuil-Mézard conjecture. Along the way, it proves a number of foundational results in p-adic Hodge theory that may be of independent interest.
Call Number: QA1 .A63 no.215
Publication Date: 2022-12-13
The Logical Approach to Automatic Sequences by Jeffrey ShallitAutomatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.
Call Number: QA164 .S53 2023
Publication Date: 2022-09-29
Pseudo-Bosons and Their Coherent States by Fabio BagarelloThis book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.
Call Number: QC174.17 .C6 B144 2022
Publication Date: 2022-04-23
Laurentia by Steven J. Whitmeyer; Michael L. Williams; D. A. Kellett; Basil Tikoff"This Memoir focuses on 7 turning points that had specific and lasting impacts on Laurentian evolution: The Neoarchean, characterized by cratonization; the Paleoproterozoic and the initial assembly of Laurentia; the Mesoproterozoic southern margin of Laurentia; the Midcontinent rift and the Grenville orogeny; the Neoproterozoic breakup of Rodinia; the mid-Paleozoic phases of the Appalachian-Caledonian orogen; and the Jurassic-Paleogene assembly of the North American Cordillera"--
Double Helix of Phyllotaxis by Boris Rozin"This book is devoted to anyone who is in search of a beauty in mathematics and mathematics in the beauty around us. Attempting to combine mathematical rigor and magnificence of the visual perception, author is presenting the mathematical study of phyllotaxis, the most beautiful phenomenon of the living nature. The distinctive feature of this book is an animation feature that explains the work of mathematical models and the transformation of 3D space. The analysis of the phyllotactic pattern as a system of discrete objects together with the mathematical tools of generalized sequences made it possible to find a universal algorithm for calculating the divergence angle. In addition, it is serving as a new proof of the fundamental theorem of phyllotaxis and analytically confirming well-known formulas obtained intuitively earlier as well as casting some doubts on a few stereotypes existing in mathematical phyllotaxis. The presentation of phyllotaxis morphogenesis as a recursive process allowed the author to formulate the hydraulic model of phyllotaxis morphogenesis and propose a method for its experimental verification. With the help of artificial intelligence, the author offered methodology for the digital measurement of phyllotaxis allowing a transition to a qualitatively new level in the study of plant morphogenesis. Due to the successful combination of mathematical constructions and their visual presentation, the materials of this study are comprehensible to readers with high school advanced mathematical levels"--