Format: Hardback, 390 pages, height x width: 235x155 mm, 10 Tables, color; 28 Illustrations, color;
12 Illustrations, black and white; X, 390 p. 40 illus., 28 illus. in color., 1 Hardback
Series: Springer INdAM Series 53
Pub. Date: 14-Feb-2023
ISBN-13: 9789811982804
An incredible season for algebraic geometry flourished in Italy between 1860, when Luigi Cremona was assigned the chair of Geometria Superiore in Bologna, and 1959, when Francesco Severi published the last volume of the treatise on algebraic systems over a surface and an algebraic variety. This century-long season has had a prominent influence on the evolution of complex algebraic geometry - both at the national and international levels - and still inspires modern research in the area. "Algebraic geometry in Italy between tradition and future" is a collection of contributions aiming at presenting some of these powerful ideas and their connection to contemporary and, if possible, future developments, such as Cremonian transformations, birational classification of high-dimensional varieties starting from Gino Fano, the life and works of Guido Castelnuovo, Francesco Severi's mathematical library, etc. The presentation is enriched by the viewpoint of various researchers of the history of mathematics, who describe the cultural milieu and tell about the bios of some of the most famous mathematicians of those times.
1. Gilberto Bini (Palermo), Introduction.-
2. Claudio Fontanari (Trento), Stefano Gattei (Trento), Francesco Severi's Mathematical Library.-
3. Angelo Guerraggio (Milano), Francesco Severi and the Fascist Regime.-
4. Maria Giulia Lugaresi (Ferrara), Fabio Conforto (1909-1954).His Scientific and Academic Career at the University of Rome.-
5. Livia Giacardi (Torino), Alessandro Terracini (1889-1968). Teaching and Research from the University Years to the Racial Laws.-
6. Marco Andreatta (Trento), Higher Dimensional Geometry from Fano to Mori and Beyond.-
7. Livia Giacardi (Torino), Erika Luciano (Torino), Elena Scalambro(Torino), Gino Fano (1871-1952). The scientific Trajectory of an Italian Geometer between Internationalism and Persecution.-
8. Alessandro Verra (Roma), From Enriques Surface to Artin-Mumford Counterexample.-
9. Ciro Ciliberto (Roma), The Theorem of Completeness the Characteristic Series: Enriques' Contribution.-
10. Edoardo Sernesi (Roma), Severi, Zappa and the Characteristic System.-
11. Ciro Ciliberto (Roma), Claudio Fontanari (Trento). Two letters by Guido Castelnuovo.-
12. Claudio Fontanari (Trento), Guido Castelnuovo and his Heritage: Geometry, Combinatorics, Teaching.-
13. Enrico Rogora (Roma), Guido Castelnuovo (1865-1952).-
14. Nicla Palladino (Perugia), Maria Alessandra Vaccaro (Palermo), The Genesis of the Italian School of Algebraic Geometry through the Correspondence between Luigi Cremona and Some of his Students.-
15. Aldo Brigaglia (Palermo), Veronese, Cremona and the Mystical Hexagram.
Format: Paperback / softback, 260 pages, height x width: 235x155 mm,
29 Illustrations, black and white; X, 260 p. 29 illus.
Series: UNITEXT 141
Pub. Date: 12-Apr-2023
ISBN-13: 9783031197376
The book addresses the rigorous foundations of mathematical analysis. The first part presents a complete discussion of the fundamental topics: a review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation and integration according to Riemann.
The second part provides a more mature return to these topics: a possible axiomatization of set theory, an introduction to general topology with a particular attention to convergence in abstract spaces, a construction of the abstract Lebesgue integral in the spirit of Daniell, and the discussion of differentiation in normed linear spaces.
The book can be used for graduate courses in real and abstract analysis and can also be useful as a self-study for students who begin a Ph.D. program in Analysis. The first part of the book may also be suggested as a second reading for undergraduate students with a strong interest in mathematical analysis.
Part I First half of the journey.- 1 An appetizer of propositional logic.- 2 Sets, relations, functions in a naive way.- 3 Numbers.- 4 Elementary cardinality.- 5 Distance, topology and sequences on the set of real numbers.- 6 Series.- 7 Limits: from sequences to functions of a real variable.- 8 Continuous functions of a real variable.- 9 Derivatives and differentiability- 10 Riemann's integral.- 11 Elementary functions.- Part II Second half of the journey.- 12 Return to Set Theory.- 13 Neighbors again: topological spaces.- 14 Differentiating again: linearization in normed spaces.- 15 A functional approach to Lebesgue integration theory.- 16 Measures before integrals.
Format: Paperback / softback, 216 pages, height x width: 235x155 mm, XII, 216 p., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2325
Pub. Date: 19-Feb-2023
ISBN-13: 9783031226830
This book systematically develops the theory of continuous representations on p-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces.
This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.
Part I : Banach space representations of p-adic Lie groups
Chapter
1. Iwasawa algebras: The purpose of the chapter is to define Iwasawa algebras and study their properties. As a preparation, we first cover projective limits of topological spaces, finite groups, and linear-topological modules. After that, we explain in detail Iwasawa algebras and their topology.
Chapter
2. Distributions: We review basic definitions and properties of locally convex vector spaces. We study the algebra of continuous distributions and establish an isomorphism with the corresponding Iwasawa algebra. We discuss different topologies on the algebra of continuous distributions, among them the weak topology and the bounded-weak topology.
Chapter
3. Banach space representations: We prove some fundamental theorems in nonarchimedean functional analysis and introduce Banach space representations. We give an overview of the Schikhof duality between p-adic Banach spaces and compactoids. Then, we present the theory of admissible Banach space representations by Schneider and Teitelbaum and their duality theory. Part II: Principal series representations of reductive groups
Chapter
4. Reductive Groups: In this chapter, we give an overview of the structure theory of split reductive Z-groups, with no proofs. The purpose of this chapter is to help a learner navigate through the literature and to explain different objects we need in
Chapters 6 and 7, such as roots, unipotent subgroups, and Iwahori subgroups. We also review important structural results, such as Bruhat decomposition, Iwasawa decomposition, and Iwahori factorization.
Chapter
5. Algebraic and smooth representations: In our study of Banach space representations, we also encounter algebraic and smooth representations. Namely, continuous principal series representations may contain finite dimensional algebraic representations or smooth principal series representations. In this chapter, we review some basic properties of these representations.
Chapter
6. Continuous principal series: We establish some basic properties of the continuous principal series representations. In particular, we prove that they are Banach. After that, we work on the dual side and study the corresponding Iwasawa modules.
Chapter
7. Intertwining operators: In this chapter, we present the main results and proofs from a recent joint work with Joseph Hundley. The purpose is to describe the space of continuous intertwining operators between principal series representations. As before, we apply the Schneider-Teitelbaum duality and work with the corresponding Iwasawa modules.
Format: Hardback, 346 pages, height x width: 235x155 mm,
105 Illustrations, black and white; IV, 346 p. 105 illus
Series: Simons Symposia
Pub. Date: 12-Mar-2023
ISBN-13: 9783031215490
This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning non-abelian aspects This volume contains both original research articles as well as articles that contain both new research as well as survey some of these recent developments.
A. Abbes and M. Gros: The Relative Hodge-Tate Spectral Sequence - An Overview.- L. A. Betts and D. Litt: Semisimplicity of the Frobenius action on .- H. Diao, K.-W. Lan, R. Liu, X. Zhu.- Logarithmic adic spaces: some foundational results.- M. Gros, B. Le Stum and A. Quiros: Twisted Differential Operators and q-Crystals.- J. Lurie: Full Level Structures on Elliptic Curves.- A. Ogu: The saturated de Rham-Witt complex for schemes with toroidal singularities.
Format: Hardback, 173 pages, height x width: 235x155 mm, 32 Illustrations, color;
1 Illustrations, black and white; XII, 173 p. 33 illus., 32 illus. in color.
Series: Mathematical Physics Studies
Pub. Date: 11-Feb-2023
ISBN-13: 9789811985393
This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold.
This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface.
The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory.
This work is intended for advanced students in mathematical physics and researchers alike.
Introduction.- Geometric preliminaries.- Ricci flow background.- Ricci flow conjugation of initial data sets.- Concluding remarks.
Format: Paperback / softback, 150 pages, height x width: 235x155 mm,
1 Tables, color; 10 Illustrations, color; XIII, 150 p. 10 illus. in color
Series: Compact Textbooks in Mathematics
Pub. Date: 02-Mar-2023
ISBN-13: 9789811985430
Designed as a self-contained text, this book covers a wide spectrum of topics on portfolio theory. It covers both the classical-mean-variance portfolio theory as well as non-mean-variance portfolio theory. The book covers topics such as optimal portfolio strategies, bond portfolio optimization and risk management of portfolios. In order to ensure that the book is self-contained and not dependent on any pre-requisites, the book includes three chapters on basics of financial markets, probability theory and asset pricing models, which have resulted in a holistic narrative of the topic. Retaining the spirit of the classical works of stalwarts like Markowitz, Black, Sharpe, etc., this book includes various other aspects of portfolio theory, such as discrete and continuous time optimal portfolios, bond portfolios and risk management.
The increase in volume and diversity of banking activities has resulted in a concurrent enhanced importance of portfolio theory, both in terms of management perspective (including risk management) and the resulting mathematical sophistication required. Most books on portfolio theory are written either from the management perspective, or are aimed at advanced graduate students and academicians. This book bridges the gap between these two levels of learning. With many useful solved examples and exercises with solutions as well as a rigorous mathematical approach of portfolio theory, the book is useful to undergraduate students of mathematical finance, business and financial management.
Chapter
1. Mechanisms of Financial Markets.
Chapter
2. Fundamentals of Probability Theory.
Chapter
3. Asset Pricing Models.
Chapter
4. Mean-Variance Portfolio Theory.
Chapter
5. Utility Theory.
Chapter
6. Non-Mean-Variance Portfolio Theory.
Chapter
7. Optimal Portfolio Strategies.
Chapter
8. Bond Portfolio Optimization.
Chapter
9. Risk Management of Portfolios.