1.

Record Nr.

UNINA9910480624203321

Autore

Goldman William Mark

Titolo

Rank one Higgs bundles and representations of fundamental groups of Riemann surfaces / / William M. Goldman, Eugene Z. Xia

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , [2008]

©2008

ISBN

1-4704-0510-5

Descrizione fisica

1 online resource (86 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 904

Disciplina

516.3/6

Soggetti

Surfaces, Deformation of

Riemann surfaces

Geometry, Differential

Geometry, Algebraic

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"May 2008, volume 193, number 904 (fourth of 5 numbers)."

Nota di bibliografia

Includes bibliographical references (pages 67-69).

Nota di contenuto

""Contents""; ""Introduction""; ""1. Equivalences of deformation theories""; ""2. The Betti and de Rham deformation theories and their moduli spaces""; ""2.1. The Betti groupoid""; ""2.2. The de Rham groupoid""; ""2.3. Equivalence of de Rham and Betti groupoids""; ""3. The Dolbeault groupoid""; ""3.1. Holomorphic line bundles""; ""3.2. The moduli spaces""; ""3.3. Geometric structure of the Dolbeault moduli space""; ""4. Equivalence of de Rham and Dolbeault groupoids""; ""4.1. Construction of the equivalence""; ""4.2. Higgs coordinates""; ""4.3. Involutions""

""5. Hyperkahler geometry on the moduli space""""5.1. The quaternionic structure""; ""5.2. The Riemannian metric""; ""5.3. Complex-symplectic structure""; ""5.4. Quaternionization""; ""6. The twistor space""; ""6.1. The complex projective line""; ""6.2. The twistor space as a smooth vector bundle""; ""6.3. A holomorphic atlas for the twistor space""; ""6.4. The twistor lines""; ""6.5. The real structure on the twistor space""; ""6.6. Symplectic geometry of the twistor space""; ""6.7. The lattice quotient""; ""6.8. Functions and flows""; ""7. The moduli space



and the Riemann period matrix""

""7.1. Coordinates for the Betti moduli space""""7.2. Abelian differentials and their periods""; ""7.3. Flat connections""; ""7.4. Higgs fields""; ""7.5. The C*-action in terms of the period matrix""; ""7.6. The C*-action and the real points""; ""Bibliography""

2.

Record Nr.

UNINA9910349323803321

Titolo

Trends in Control Theory and Partial Differential Equations / / edited by Fatiha Alabau-Boussouira, Fabio Ancona, Alessio Porretta, Carlo Sinestrari

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019

ISBN

3-030-17949-4

Edizione

[1st ed. 2019.]

Descrizione fisica

1 online resource (276 pages)

Collana

Springer INdAM Series, , 2281-5198 ; ; 32

Disciplina

515.353

Soggetti

Differential equations

Mathematical optimization

Calculus of variations

Game theory

Differential Equations

Calculus of Variations and Optimization

Game Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

1 P. Albano, Some remarks on the Dirichlet problem for the degenerate eikonal equation -- 2 V. Basco and H. Frankowska, Lipschitz continuity of the value function for the infinite horizon optimal control problem under state constraints -- 3 P. Cannarsa et al., Herglotz' generalized variational principle and contact type Hamilton-Jacobi equations -- 4 P. Cannarsa et al., Observability inequalities for transport equations through Carleman estimates -- 5 I. Capuzzo Dolcetta, On the weak maximum principle for degenerate elliptic operators -- 6 P. Cardaliaguet, On the convergence of open loop Nash equilibria in mean



field games with a local coupling -- 7 E. Fernández-Cara and D. A. Souza, Remarks on the control of a family of b-equations -- 8 G. Leugering et al., 1-d wave equations coupled via viscoelastic springs and masses: boundary controllability of a quasilinear and exponential stabilizability of a linear model -- 9 P. Loreti and D. Sforza, A semilinear integro-differential equation: global existence and hidden regularity -- 10 M. Mazzola and K. T. Nguyen, Lyapunov's theorem via Baire category -- 11 D. Pighin and E. Zuazua, Controllability under positivity constraints of multi-d wave equations -- 12 C. Pignotti and I. Reche Vallejo, Asymptotic analysis of a Cucker-Smale system with leadership and distributed delay -- 13 J. Vancostenoble, Global non-negative approximate controllability of parabolic equations with singular potentials.

Sommario/riassunto

This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.