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Hidden symmetries in geometry, arithmetic, and physics

Brent Doran
(ETH Zürich)
Seminar
Tirsdag, 24 maj, 2016, at 10:00-11:00, in Aud. D2 (1531-119)
Abstrakt:
Moduli problems often arise via a symmetry that is "visible" in the problem's description. However, there are many objects – and not just moduli – where "invisible" symmetries underlie important refined structures, which may be encoded in simpler, naturally attached spaces of higher dimension. These invisible symmetries are often non-reductive. Generalizing methods from the reductive case, we can then address a host of seemingly unrelated questions across geometry, arithmetic, and physics. These include: "What is the minimal degree curve passing through n given points in the plane?", "How many integer points are in a region bounded by a height function?", "When is a homology class represented by an algebraic subvariety?", and "How can one robustly characterize entangled states in quantum information theory?".

NOTE: This talk is aimed at a general audience of mathematicians.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen