The two volumes of Algebra, Arithmetic and Geometry: In Honor of Y.I. Manin are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70 th birthday.

Contributed articles are written by distinguished and invited prominent researchers in the field Broad collection of topics reveals Y.I. Manin's wide range of research and influence The subjects covered range from mathematical logic to theoretical physics Includes supplementary material: sn.pub/extras

Autorentext
The two volumes of Algebra, Arithmetic and Geometry: In Honor of Y.I. Manin are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70 th birthday.

Klappentext
Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists of invited expository and research articles on new developments arising from Manin's outstanding contributions to mathematics. Contributors in the first volume include: K. Behrend, V.G. Berkovich, J.-B. Bost, P. Bressler, D. Calaque, J.F. Carlson, A. Chambert-Loir, E. Colombo, A. Connes, C. Consani, A. Dabrowski, C. Deninger, I.V. Dolgachev, S.K. Donaldson, T. Ekedahl, A.-S. Elsenhans, B. Enriquez, P. Etingof, B. Fantechi, V.V. Fock, E.M. Friedlander, B. van Geemen, G. van der Geer, E. Getzler, A.B. Goncharov, V.A. Iskovskikh, J. Jahnel, M. Kapranov, E. Looijenga, M. Marcolli, B. Tsygan, E. Vasserot, M. Wodzicki.

Inhalt
Preface.- Introduction.- K. Behrend, B. Fantecci, Gerstenhaber and Batalin-Vilkovisky structures on Lagrangian intersections.- V. Berkovich, A non-Archimedean interpretation of the weight zero subspaces of limit mixed Hodge structures.- J.-B. Bost, A. Chambert-Loir, Analytic curves in algebraic varieties over number fields.- P. Bressler, M. Kapranov, B. Tsygan, E. Vasserot, Riemann-Roch for real varieties.- E. Colombo, B. van Geemen, E. Looijenga, Del Pezzo moduli via root systems.- A. Connes, C. Consani, M. Marcolli, The Weil proof and the geometry of the adeles class space.- A. Dabrowski, M. Wodzicki, Elliptic curves with large analytic III(E).- C. Deninger, p-adic entropy and a p-adic Fuglede - Kadison determinant.- S. Donaldson, Lie algebra theory without algebra.- T. Ekedahl, G. van der Geer, Cycle classes of the E-O stratification on the moduli of abelian varieties.- A.-S. Elsenhans, J. Jahnel, Experiments with general cubic surfaces.- V.V. Fock, A. Goncharov, Cluster ensembles, quantization and the dilogarithm II: The intertwiner.- E. Getzler, Operads revisited.- M. Harris, Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications.- D. Kaledin, Cyclic homology with coefficients.- M. Kapranov, Noncommutative geometry and path integrals.- N. Katz, Another look at the Dwork family.- R. Kaufmann, Graphs, strings and actions.- J. Kollár, M. Larsen, Quotients of Calabi-Yau varieties.- M. Kontsevich, Notes on motives in finite characteristic.- L. Merel, Symboles de Manin et valeurs de fonctions L.-M. Markl, A. Voronov, PROPped up graph cohomology.- S. Merkulov, Graph complexes with loops and wheels.- M. Movshev, Yang-Mills theory and a superquadric.- E. Mukhin, V. Tarasov, A. Varchenko, A generalization of the Capelli identity.- J.Nekovar, Hidden symmetries of the theory of complex multiplication.- V. Nikulin, Correspondences of a K3 surface with itself via moduli of sheaves, I.-O. Ogievetsky, V. Schechtman, Uneintersection des quadriques liée à la suite de Sturm.- F. Oort, Foliations in moduli spaces of abelian varieties and dimension of leaves.- D. Orlov, Derived categories of coherent sheaves and triangulated categories of singularities.- A. Panchishkin, K. Vankov, Rankin's lemma of higher genus and explicit formulas for Hecke operators.- A. Polishchuk, Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations.- A. Vishik, Fields of $u$-invariant $2^r+1$.- Y. Zarhin, Cubic surfaces and cubic threefolds, jacobians and intermediate jacobians.- Index.