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"Where there is matter, there is geometry." Johannes Kepler (1571-1630)

Archived preprints:

• V. Mathai, W. Zhang (with appendix by U. Bunke), Geometric quantization for proper actions, 20 pages [0806.3138v2]
• V. Mathai, Siye Wu, Analytic torsion for twisted de Rham complexes, 25 pages, [0810.4204]
• K. Hannabuss, V. Mathai, Noncommutative principal torus bundles via parametrised strict deformation quantization, 15 pages, [0911.1886]
• J. C. Hurtubise and M. K. Murray, Loop groups and holomorphic bundles, 31 pages, [0812.3684v1]
• F. Larusson, The homotopy theory of equivalence relations, 12 pages, [math.0611344]
• F. Larusson, Affine simplices in Oka manifolds, 6 pages, [0905.0532]
• T. Leistner, P. Nurowski, Conformal structures with $G_{2(2)}$-ambient metrics, 13 pages, [0904.0186] .
• V. Cortes, T. Leistner, L. Schafer, F. Schulte-Hengesbach, Half-flat Structures and Special Holonomy, 40 pages, [0907.1222] .

Refereed publications (2009) :

• V. Mathai and J. Rosenberg, A noncommutative sigma-model, J. Noncommutative Geometry, (to appear) 29 pages, [0903.4241]
• V. Mathai, R.B. Melrose, I.M. Singer, The index of projective families of elliptic operators: the decomposable case, Asterisque, 327 (2009) 251-292, [0809.0028]
• P. Bouwknegt, V. Mathai, T-Duality as a Duality of Loop Group Bundles, J. Physics A: Math. Theor. (Fast Track Communications), 42 no.16 (2009) 162001, 8 pages, [0902.4341]
• P. Bouwknegt, K. Hannabuss, V. Mathai, C*-algebras in tensor categories, Clay Mathematics Proceedings, 12 (2009) 39 pages, (in press). [math.QA/0702802]
• R. Green, V. Mathai, Harmonic Cheeger-Simons characters with applications, J. Geometry and Physics, 59 no.5 (2009) 663-672. [0803.1874]
• P. Chakraborty, V. Mathai, The geometry of determinant line bundles in noncommutative geometry, J. Noncommutative Geometry, 3 no.4 (2009) 559-578. [0804.3232v2]
• J. Brodzki, V. Mathai, J. Rosenberg, R. Szabo, Noncommutative correspondences, duality and D-branes in bivariant K-theory, Advances in Theoretical and Mathematical Physics, 13 no. 2 (2009) 497-552. [0708.2648]
• M. K. Murray, An Introduction to Bundle Gerbes, volume in honour of Nigel Hitchin's birthday (to appear) [0712.1651v3]
• F. Larusson, Applications of a parametric Oka principle for liftings, in Complex Analysis - Several complex variables and connections with PDE theory and geometry, refereed volume in honour of Linda P. Rothschild, Trends in Mathematics series, Birkhauser, to appear. [0901.4388]
• F. Larusson, R. Sigurdsson, Siciak-Zahariuta extremal functions, analytic discs and polynomial hulls, Math. Annalen, 345 (2009) 159-174. [0808.3304v1]
• F. Larusson, R. Shafikov, Schlicht envelopes of holomorphy and foliations by lines, J. Geometric Analysis, 19 (2009) 373-389.
• D.K. Butler and S.G. Barwick. A characterizations of the lines external to a quadric cone of PG(3,q), q odd. Innovations in Incidence Geometry, 8 (2009) 39-48.
• S.G. Barwick and D.K. Butler. A Characterisation of the Lines External to an Oval Cone in PG(3,q), q even. J. Geometry, 93 (2009), no. 1-2, 21--27.
• S.G. Barwick and D.J. Marshall. Unitals and Replaceable t-nests. Aust. J. Combin., 43 (2009), 115--126..
• D. V. Alekseevsky, V. Cortes, A. Galaev and T. Leistner, Cones over semi-Riemannian manifolds and their holonomy, Journal fur die reine und angewandte Mathematik (Crelle's Journal) , 635 (2009), 23-69. [0707.3063]
• T. Leistner, A. J. Di Scala, Connected subgroups of SO(2,n) acting irreducibly on $\mathbb{R}^{2,n}$, to appear in Israel Journal of Mathematics, 22 pages [0806.2586]
• T. Leistner, P. Nurowski, Ambient metrics for $n$-dimensional $pp$-waves, Commun. Math. Phys., (to appear) 17 pages, [0810.2903]
• A. Galaev, T. Leistner, Recent developments in pseudo-Riemannian holonomy theory, to appear in Handbook of Pseudo Riemannian Geometry, Institut de Recherche Mathematique Avancee Lectures in Mathematics and Theoretical Physics, 38 pages.
• A. J. Di Scala, T. Leistner, T. Neukirchner, Geometric applications of irreducible representations of Lie groups to appear in Handbook of Pseudo Riemannian Geometry, Institut de Recherche Mathematique Avancee Lectures in Mathematics and Theoretical Physics, 21 pages [math/0507047]

Refereed publications (2008) :

• J. Brodzki, V. Mathai, J. Rosenberg, R. Szabo, D-branes, KK-theory and duality on noncommutative spaces, J. Physics: Conference Series, 103 (2008) 012004, 13 pages. [0709.2128]
• V. Mathai, R.B. Melrose, I.M. Singer, Equivariant and fractional index of projective elliptic operators, J. Differential Geom., 78 no.3 (2008) 465-473. [math.DG/0611819]
• J. Brodzki, V. Mathai, J. Rosenberg, R. Szabo, D-Branes, RR-Fields and Duality on Noncommutative Manifolds, Commun. Math. Phys., 277, no.3 (2008) 643-706. [hep-th/0607020]
• M. K. Murray, D. Stevenson, The basic bundle gerbe on unitary groups, J. Geometry and Physics, 58 (11), (2008), 1571-1590.
• F. Larusson,T. Sadykov, Dessins d'enfants and differential equations, St. Petersburg Mathematical J. 19 (2008), 1003-1014.
• N. Buchdahl, Algebraic deformations of compact Kahler surfaces. II. Math. Z. 258 (2008), no. 3, 493--498.
• S. Barwick, W-A. Jackson, Geometric constructions of optimal linear perfect hash families. Finite Fields Appl. 14 (2008), no. 1, 1-13.
• S. Barwick, G. Ebert, Unitals in projective planes. Springer Monographs in Mathematics. Springer, New York, 2008. xii+193 pp.
• David Roberts, Urs Schreiber, The inner automorphism 3-group of a strict 2-group, J. Homotopy and Related Structures, vol. 3(1), (2008), 193-245. [0708.1741]
• Rongmin Lu, The Gamma-hat-genus and a regularization of an S^1-equivariant Euler class, J. Phys. A: Math. Theor. 41 (2008) 425204, 14 pages. [0804.2714]
• M. Eastwood, T. Leistner, Higher symmetries of the square of the Laplacian. In, Symmetries and overdetermined systems of partial differential equations, 319--338, IMA Vol. Math. Appl., 144, Springer, New York, 2008.
• A. Galaev, T. Leistner, Holonomy groups of Lorentzian manifolds: classification, examples, and applications. In, Recent developments in pseudo-Riemannian geometry, 53--96, ESI Lect. Math. Phys., Eur. Math. Soc., Zurich, 2008.

Refereed publications (2007) :

• V. Mathai, T-duality in type II string theory via noncommutative geometry and beyond, Progress of Theoretical Physics Supplement, 171, (2007) 237-257.
• V. Mathai, D. Stevenson, Entire cyclic homology of stable continuous trace algebras, Bull. London Math. Soc., 39 no. 1 (2007) 71-75 , [math.KT/0412485]
• F. Larusson, R. Sigurdsson, Siciak-Zahariuta extremal functions and polynomial hulls, Annales Polonici Mathematici 91 (2007) 235-239.
• S. Barwick, W-A. Jackson, A sequence approach to linear perfect hash families. Des. Codes Cryptogr. 45 (2007), no. 1, 95-121.
• T. Leistner, On the classification of Lorentzian holonomy groups. J. Differential Geom. 76 (2007), no. 3, 423--484.
• S. Armstrong, T. Leistner, Ambient connections realising conformal tractor holonomy. Monatsh. Math. 152 (2007), no. 4, 265--282.