Alexander invariants of hypersurface
complements (Ph.D. Advisor: Julius Shaneson).
Papers and Preprints:
- Intersection
homology and Alexander modules of hypersurface complements,
Comment. Math. Helv. 81 (2006), no. 1, 123-155.
- A decomposition theorem for the Peripheral Complex associated with
hypersurfaces,
Int. Math. Res. Not. 43 (2005), 2627-2656.
- Multivariable
Alexander invariants of hypersurface complements (with A. Dimca),
Trans. Amer. Math. Soc.
359 (2007), no. 7, 3505-3528.
- Higher-order Alexander invariants of plane algebraic curves (with C. Leidy),
Int. Math. Res. Not., Volume 2006 (2006), Article ID 12976, 23 pages.
- On the Alexander invariants of hypersurface
complements,
in Singularity Theory, Proceedings of the 2005 Marseille Singularity School and
Conference (Denis Cheniot et al, ed.),
World Scientific, 2007, 725-744.
- Euler characteristics of algebraic varieties (with S. Cappell and J. Shaneson),
Comm. Pure Appl. Math. 61 (2008), no. 3, 409-421.
- Hodge genera of algebraic varieties, I. (with S. Cappell and J. Shaneson),
Comm. Pure Appl. Math. 61 (2008), no. 3, 422-449.
- Obstructions on fundamental groups of plane curve complements (with C. Leidy),
in Real and Complex Singularities, Contemporary Mathematics 459 (2008), pp. 117-130.
- Hodge genera and characteristic classes of complex algebraic
varieties. (with S. Cappell, A. Libgober and J. Shaneson),
Electron. Res. Announc. Math. Sci. 15 (2008), 1-7.
- Hodge genera of algebraic varieties, II. (with S. Cappell, A. Libgober and J. Shaneson),
this is an updated version of the archive preprint math.AT/0702380.
- L2-Betti numbers of plane algebraic curves (with S. Friedl and C. Leidy),
arXiv:0704.3388, accepted for publication in Michigan Math. Journal.
- Hodge-theoretic Atiyah-Meyer formulae and the stratified multiplicative property (with J. Schürmann),
arXiv:0707.0129, accepted for publication in the Proceedings of the School and Workshop on the Geometry and Topology of Singularities, (J.-P. Brasselet et al, ed.), 2007.
- Intersection cohomology invariants of complex algebraic varieties.
(with S. Cappell and J. Shaneson)
accepted for publication in the Proceedings of the School and
Workshop on the Geometry and Topology of Singularities, (J.-P. Brasselet et al, ed.), 2007.
- Equivariant genera of complex algebraic varieties. (with S. Cappell and J. Shaneson),
preprint 2008.
Notes, Surveys:
Notes on motivic integration and characteristic
classes. these notes reflect my attempt to learn this luring theory.
What groups can/cannot be fundamental groups of plane curve complements ?
this is a short survey based on
few of my talks, in which I try to relate paper #4 in the list above to previous works on
fundamental groups of plane curve complements. This survey became part of paper #8 above.
Alexander invariants of hypersurface complements. these are notes for a series of lectures
I gave at Tokyo University of Sciences and The University of Tokyo, Japan (Summer of 2006).
Video talks:
Intersection Homology and Alexander Modules of Hypersurface Complements, MSRI Workshop on "Topology of Arrangements and Applications", October 2004.
Genera of complex varieties and singularities of proper maps,
MSRI Workshop on "Recent Developments in Arrangements
and Configuration Spaces", August 2006.