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Details of project

  
Identifier
42769
Type K
Principal investigator Böröczky, Károly
Title in Hungarian Algebrai Geometria
Title in English Algebraic Geometry
Panel Mathematics and Computing Science
Department or equivalent Alfréd Rényi Institute of Mathematics
Participants Braun, Gábor
Frenkel, Peter
Némethi, András
Szabó, Endre
Szamuely, Tamás
Szenes, András
Starting date 2003-01-01
Closing date 2006-12-31
Funding (in million HUF) 6.647
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
A Cambridge University Press-nél megjelent könyvet írtak centrális egyszerű algebrákról és Galois-kohomologiáról ''Central simple algebras and Galois cohomology'' címmel. A könyv a legújabb, eddig csak folyóiratcikkben megjelent eredményeket tárgyalja, és átfogó összefoglalást ad a témakörről. Az alacsony, kettő, három vagy nény dimenziós sokaságok és szingularitások elmélete több olyan invariánst vizsgál, melyek a fizikából származnak. Tübb olyan eredményt sikerült elérni, melyek az ún. Seiberg-Witten és Casson invariánsokról adott alpvetően új összefüggéseket. A kifejlesztett módszerek a projektív algebrai görbék klasszikus elméletében is lényeges új eredményekre vezettek. Az ún. Newton diagram segítségével algoritmust is tudtak adni bizonyos szingularitások invariánsainak kiszámolásához. Sokaságok vagy varietások huroktere szintén fizikai indíttatású fogalom. Belátták, hogy egy racionálisan összefüggő varietás huroktere is racionálisan összefüggő.
Results in English
They have written a monograph entitled "Central simple algebras and Galois cohomology". The monograph discusses the most recent related results that appeared only in research articles, and provides a comprehensive and easy to digest survey about the topic. The theory of low (two, three or four) dimensional manifolds and their singularities uses various invariants that originate from physics. Many fundamental results have been achieved, which provide new information about the so-called Seiberg-Witten and Casson invariants. The methods developed led togroundbreaking results in the classic theory of projective algebraic curves, as well. ith the help of the so-called Newton diagram, even an algorithm has been provided to calculate invariants of certain type of singularities. The loop space of a manifold or a variety is another notion that originates from physics. It has been proved that the loop space of a rationally connected variety is rationally connected, as well.
Full text http://real.mtak.hu/785/
Decision
Yes





 

List of publications

  
Némethi, A.; Luengo, I.; Melle-Hernández, A.: Links and analytic invariants of superisolated singularities, Journal of Algebraic Geometry, 14, 543-565., 2005
Némethi A., L. I. Nicolaescu: Seiberg-Witten invariants and surface singularities II (singularities with good C*-action), Journal of London Math. Soc. (2), 69, 593-607., 2004
Némethi A., L. McEwan: The zeta-function of a quasi-ordinary singularity, Compositio Math. 140, 667-682., 2004
ifj. Böröczky K.: Finite packing and covering, Cambridge Tracts in Mathematics, Cambridge University Press, 2004
Réti T., ifj. Böröczky K.: Topological Characterization of Cellular Structures, Acta Polytechnica Hungarica, 1, 59--85., 2004
ifj. Böröczky K., M. Reitzner: Approximation of Smooth Convex Bodies by Random Circumscribed Polytopes, Annals of Applied Prob., 14, 239--273, 2004
Braun G.: A proof of Higgin's conjecture, Bull. Austral. Math. Soc., 70, 207-212., 2004
Domokos M., Frenkel P. E.: On orthogonal invariants in characteristic 2, J. of Algebra, 274, 662--688., 2004
Domokos M., Frenkel P. E.: Mod 2 indecomposable orthogonal invariants, Adv. Math., 192, 209-217., 2005
Némethi A.: Invariants of normal surface singularities, Contemporary Mathematics, 354 , 161-208., 2004
Némethi A., A. Dimca: Hypersurface complements. Alexander modules and monodromy, Contemporary Mathematics, 354, 19-43., 2004
Elek G., Szabó E.: Sofic groups and direct finiteness, Journal of Algebra, 280, 426-434., 2004
Szamuely T.: Groupes de Galois de corps de type fini (daprès Pop), Astérisque 294, 403-431., 2004
Szenes, A., M. Vergne: Toric reduction and a conjecture of Batyrev and Materov, Invent. Math., 158, 453-495., 2004
ifj. Böröczky K.; Réti T.: Topological characterization of finite cellular systems represented by 4-dimensional polytopes., Materials Science Forum, 473-474, 381-388, 2005
ifj. Böröczky K.: Finite coverings in the hyperbolic plane, Discrete and Comp. Geometry, 33, 165-180., 2005
Némethi, A.: On the Heegaard Floer homology of S^3_{-d}(K) and unicuspidal rational plane curves, Fields Institute Communications, 47., 2005
ifj. Böröczky K.: The stability of the Rogers-Shephard inequality, Adv. Math., 190, 47-76., 2005
Braun, G.; Blass, A.: Random orders and gambler's ruin, Electronic Journal of Combinatorics, 12, R23., 2005
Braun, G.; Göbel, R.: E-algebras whose torsion part is not cyclic., Proc. Amer. Math. Soc. 133, no.8, 2251-2258, 2005
Némethi, A.; Mendris, R.: The link of {f(x,y)+z^n=0} and Zariski's Conjecture., Compositio Math., 141, 502-524., 2005
Braun, G.: Characterization of matrix types of ultramatricial algebras, New York Journal of Mathematics, 11, 21-33., 2005
Némethi, A.; McNeal, J.D.: The order of contact of a holomorphic ideal in C^2, Math. Zeitschrift, 250, 873-883., 2005
Némethi, A.: On the Ozsváth-Szabó invariant of negative definite plumbed 3-manifolds, Geometry and Topology, 9, 991-1042., 2005
Szabó, E.; Elek, G.: Hyperlinearity, essentially free actions and L^2-invariants. The sofic property., Mathematische Annalen, 332, 421-441., 2005
Szamuely, T.; Harari, D.: Arithmetic duality theorems for 1-motives, J. reine angew. Math., 578, 93-128., 2005
Szenes, A.; Vergne, M.: Mixed toric residues and tropical degenerations, Topology, 45, no. 3, 567-599., 2006
Némethi, A.; de Bobadilla, F.J.; Luengo, I.; Melle-Hernandez, A.: On rational cuspidal projective plane curves, Proc. of London Math. Soc. 92 (3), 99-138., 2006
Némethi, A.; Horváth, A: On the Milnor fiber on non-isolated singularities, Studia Sci. Math. Hungarica, 43 (1), 131-136., 2006
Némethi, A.; Rimányi, R; Fehér, L.: Coincident root loci of binary forms, Michigan Math. J. 54(2), 375-392., 2006
Némethi, A.; Caubel, C.; Popescu-Pampu, P.: Milnor open books and Milnor fillable contact 3-manifolds, Topology, 45 (3), 673-689., 2006
Szamuely, T.; Gille, Ph.: Central simple algebras and Galois cohomology, Cambridge University Press, 2006
Böröczky, K.J.; Réti, T.; G. Wintsche: On the combinatorial characterization of quasicrystals, J. Geometry and Physics, 57, 39-52., 2006
Böröczky, K.J.; Pach, J.; Tóth, G.: Planar crossing numbers of graphs embeddable in another surface, International Journal of Foundations of Computer Science, 17, 1005-1017., 2006
Böröczky, K.; Böröczky, Jr., K.; Wintsche, G.: Typical faces of extremal polytopes with respect to a thin three-dimensional shell., Periodica Math. Hung., 53, no. 1-2, 83-102., 2006
Böröczky, Jr., K.; Fábián, I.; Wintsche, G.: Covering the crosspolytope by equal balls, Periodica Math. Hung., 53, no. 1-2, 103-113., 2006
Frenkel, P.E.: Character formulae for classical groups, Central European J. of Math, 4, no 2., 242-249, 2006
Braun, G.; Lippner, G.: Characteristic numbers of multiple-point manifolds, Bull. London Math. Soc. 38, no. 4, 667-678., 2006
Szabó, E; Elek, G.: On sofic groups, J. Group Theory 9, no. 2, 161-171., 2006



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