140 episodes

Algebraic geometry is a key area of mathematical research of international significance. It has strong connections with many other areas of mathematics (differential geometry, topology, number theory, representation theory, etc.) and also with other disciplines (in the present context, particularly theoretical physics). Moduli theory is the study of the way in which objects in algebraic geometry (or in other areas of mathematics) vary in families and is fundamental to an understanding of the objects themselves. The theory goes back at least to Riemann in the mid-nineteenth century, but moduli spaces were first rigorously constructed in the 1960s by Mumford and others. The theory has continued to develop since then, perhaps most notably with the infusion of ideas from physics after 1980.

Read more at: http://www.newton.ac.uk/programmes/MOS/

Moduli Spaces Cambridge University

    • Education

Algebraic geometry is a key area of mathematical research of international significance. It has strong connections with many other areas of mathematics (differential geometry, topology, number theory, representation theory, etc.) and also with other disciplines (in the present context, particularly theoretical physics). Moduli theory is the study of the way in which objects in algebraic geometry (or in other areas of mathematics) vary in families and is fundamental to an understanding of the objects themselves. The theory goes back at least to Riemann in the mid-nineteenth century, but moduli spaces were first rigorously constructed in the 1960s by Mumford and others. The theory has continued to develop since then, perhaps most notably with the infusion of ideas from physics after 1980.

Read more at: http://www.newton.ac.uk/programmes/MOS/

    • video
    Vector bundles and coherent systems on nodal curves

    Vector bundles and coherent systems on nodal curves

    Bhosle, U (TIFR)
    Thursday 09 June 2011, 14:00-15:00

    • 52 min
    • video
    Higgs bundles and quaternionic geometry

    Higgs bundles and quaternionic geometry

    Hitchin, NJ (Oxford)
    Friday 01 July 2011, 11:30-12:30

    • 1 hr 5 min
    • video
    Moduli spaces of locally homogeneous geometric structures

    Moduli spaces of locally homogeneous geometric structures

    Goldman, W (Maryland)
    Friday 01 July 2011, 10:00-11:00

    • 1 hr 4 min
    • video
    Bridgeland stability conditions and Fourier-Mukai transforms

    Bridgeland stability conditions and Fourier-Mukai transforms

    Yoshioka, K (Kobe)
    Thursday 30 June 2011, 16:30-17:30

    • 1 hr 3 min
    • video
    Deligne-Hodge polynomials for SL(2,C)-character varieties of genus 1 and 2.

    Deligne-Hodge polynomials for SL(2,C)-character varieties of genus 1 and 2.

    Logares, M (ICMAT)
    Thursday 30 June 2011, 15:20-15:50

    • 29 min
    • video
    Derived equivalences of Azumaya algebras on K3 surfaces

    Derived equivalences of Azumaya algebras on K3 surfaces

    Khalid, M (St. Patrick's College Drumcondra)
    Thursday 30 June 2011, 14:40-15:10

    • 30 min

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