Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture
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| Author | : Joel Friedman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 124 |
| Release | : 2014-12-20 |
| Genre | : Mathematics |
| ISBN | : 1470409887 |
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.
| Author | : C. M. Campbell |
| Publisher | : Cambridge University Press |
| Total Pages | : 510 |
| Release | : 2019-04-11 |
| Genre | : Mathematics |
| ISBN | : 1108602835 |
This volume arises from the 2017 edition of the long-running 'Groups St Andrews' conference series and consists of expository papers from leading researchers in all areas of group theory. It provides a snapshot of the state-of-the-art in the field, and it will be a valuable resource for researchers and graduate students.
| Author | : Benjamin Steinberg |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 418 |
| Release | : 2024-10-21 |
| Genre | : Mathematics |
| ISBN | : 3110984326 |
This reference discusses how automata and language theory can be used to understand solutions to solving equations in groups and word problems in groups. Examples presented include, how Fine scale complexity theory has entered group theory via these connections and how cellular automata, has been generalized into a group theoretic setting. Chapters written by experts in group theory and computer science explain these connections.
| Author | : Paul Seidel |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 142 |
| Release | : 2015-06-26 |
| Genre | : Mathematics |
| ISBN | : 1470410974 |
The author proves Kontsevich's form of the mirror symmetry conjecture for (on the symplectic geometry side) a quartic surface in C .
| Author | : Svante Janson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 124 |
| Release | : 2015-10-27 |
| Genre | : Mathematics |
| ISBN | : 1470414651 |
The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.
| Author | : Weiwei Ao |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 100 |
| Release | : 2016-01-25 |
| Genre | : Mathematics |
| ISBN | : 1470415437 |
Click here to view the abstract. IntroductionProof of Theorem 1.1 in the caseProof of Theorem 1.1 in the caseAppendixBibliography
| Author | : P. Cannarsa |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 225 |
| Release | : 2016-01-25 |
| Genre | : Mathematics |
| ISBN | : 1470414961 |
Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conceived to introduce the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.
| Author | : Timothy C. Burness, |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 100 |
| Release | : 2016-01-25 |
| Genre | : Mathematics |
| ISBN | : 1470414945 |
Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .
| Author | : Tetsu Mizumachi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 110 |
| Release | : 2015-10-27 |
| Genre | : Mathematics |
| ISBN | : 1470414244 |
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as . He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward . The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.
| Author | : M. Dickmann |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 148 |
| Release | : 2015-10-27 |
| Genre | : Mathematics |
| ISBN | : 1470414686 |
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.
