Transactions of the American Mathematical Society, Vol. 359, No. 1 (Jan., 2007), pp. 333-348 (16 pages) In this paper we study the behaviour of the Lefschetz property under the blow-up construction.

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry. In the ...

The field of complex geometry, intertwined with Lie theory, represents a vibrant area where algebraic and differential techniques converge to unravel the structure of complex manifolds and their ...

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective. Symplectic geometry is a relatively new field with ...

In this paper we present rotational symplectic geometry for use in modern biomechanics of human motion. Generalized Hamiltonian formalism has been formulated on the configuration manifold consisting ...

Russian-American mathematician and Wolf Prize laureate Yakov Eliashberg delivered a public talk at IIT Madras on Thursday, as part of the inaugural annual TNQ Distinguished Lecture in Mathematics. The ...

Complex geometry, a rich interlace of algebra, analysis and geometry, continues to unveil surprising interconnections between abstract theories and practical applications. At its core, the study of ...