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Chern numbers of algebraic varieties

Dieter Kotschick solved Hirzebruch's problem, determining that most Chern numbers depend on algebraic structure of a variety, not topological properties. The breakthrough resolves the relationship between flexible and rigid geometric objects.

SourceLudwig-Maximilians-Universität München·JournalProceedings of the National Academy of Sciences·DateJun 10, 2009
Apple AirPods Pro (2nd Generation, USB-C)

Apple AirPods Pro (2nd Generation, USB-C) provide clear calls and strong noise reduction for interviews, conferences, and noisy field environments.

Mathematician's insight helps unravel knotty problem

Shelly Harvey's discovery applies to a longstanding problem within knot theory, but its significance lies in the broader context of topology. The underlying structure she uncovered uses algebraic structures to describe similarities and differences between knotted shapes, offering a new approach to proving equivalency.

SourceRice University·JournalGeometry & Topology·DateDec 5, 2005