Basic Notions

  • 2020 Jan 30

    Basic Notions: Cy Maor (HUJI) "Infinite dimensional Riemannian geometry in hydrodynamics and shape analysis".

    4:00pm to 5:15pm

    Location: 

    Ross 70
    In the mid-18th century,Euler derived his famous equations of motion of an incompressible fluid, one ofthe most studied equations in hydrodynamics. More than 200 years later, in1966, Arnold observed that they are, in fact, geodesic equations on the(infinite dimensional) Lie group of volume-preserving diffeomorphisms of amanifold, endowed with a certain right-invariant Riemannian metric.
  • 2020 Jan 16

    Basic Notions: Cy Maor (HUJI) "Infinite dimensionalRiemannian geometry in hydrodynamics and shape analysis".

    4:00pm to 5:15pm

    Location: 

    Ross 70
    In the mid-18th century, Euler derived hisfamous equations of motion of an incompressible fluid, one of the most studiedequations in hydrodynamics. More than 200 years later, in 1966, Arnold observedthat they are, in fact, geodesic equations on the (infinite dimensional)Lie group of volume-preserving diffeomorphisms of a manifold, endowed with acertain right-invariant Riemannian metric.
  • 2020 Jan 09

    Basic Notions: Menachem Magidor (HUJI) "Regularity properties of subsets of the real line and other polish spaces"

    4:00pm to 5:15pm

    Location: 

    Ross 70
    Using the axiom of choice one can construct set of reals which are
    pathological in some sense. Similar constructions can be produce such
    "pathological" subsets of any non trivial Polish space (= a complete
    separable metric space).
    A "pathological set" can be a non measurable set , a set which does
    not have the property of Baire (namely it is not a Borel set modulo a
    rst category set).
    A subset of the innite subsets of natural numbers,
    can be considered to be "pathological" if it is a counter example to
  • 2019 Dec 26

    Basic Notions: Menachem Magidor (HUJI) "Regularity properties of subsets of the real line and other polish spaces"

    4:00pm to 5:15pm

    Location: 

    Ross 70
    Using the axiom of choice one can construct set of reals which are
    pathological in some sense. Similar constructions can be produce such
    "pathological" subsets of any non trivial Polish space (= a complete
    separable metric space).
    A "pathological set" can be a non measurable set , a set which does
    not have the property of Baire (namely it is not a Borel set modulo a
    rst category set).
    A subset of the innite subsets of natural numbers,
    can be considered to be "pathological" if it is a counter example to
  • 2019 Dec 19

    Basic Notions: Yoel Groman (HUJI) "Hamiltonian dynamics and classical mirror symmetry".

    4:00pm to 5:15pm

    Location: 

    Ross 70
    Physicists have observed in the '80s that Calabi-Yau manifolds come in pairs so that quantum cohomology on the one is related to period integrals on the other. This phenomenon, known as mirror symmetry, has since evolved into a deeper understanding that symplectic geometry on a manifold is typically encoded in the complex geometry of another, its mirror. I will discuss in some simple examples of how the relation arises naturally from the study of Hamiltonian Floer cohomology associated with invariant sets of an integrable system.
  • 2019 Dec 12

    Basic Notions: Yoel Groman (HUJI) "Hamiltonian dynamics and classical mirror symmetry".""

    4:00pm to 5:15pm

    Location: 

    Ross 70
    Physicists have observed in the '80s that Calabi-Yau manifolds come in pairs so that quantum cohomology on the one is related to period integrals on the other. This phenomenon, known as mirror symmetry, has since evolved into a deeper understanding that symplectic geometry on a manifold is typically encoded in the complex geometry of another, its mirror. I will discuss in some simple examples how the relation arises naturally from the study of Hamiltonian Floer cohomology associated to invariant sets of an integrable system.
  • 2019 Nov 28

    Basic Notions: Eran Nevo (HUJI) "Algebraic Combinatorics a la Stanley".

    4:00pm to 5:15pm

    Location: 

    Ross 70

    The basic idea is to associate with a combinatorial object Xan algebraic structure A(X), and derive from algebraic properties of A(X)combinatorial consequences for X. For example, Stanley's proof of the UpperBound Theorem for simplicial spheres uses the Cohen-Macaulay property of theface ring associated with a simplicial complex.

    We will review the basics of Stanley's theory, illustrate themon examples, and time permitting, discuss more recent advances of this theory.

    (All needed terms and background will be given in thetalk.)   

  • 2019 Nov 21

    Basic Notions: Jake Solomon (HUJI), "Enumerative geometry over an arbitrary field"

    Repeats every week every Thursday, 2 times .
    4:00pm to 5:15pm

    Location: 

    Ross Building, Room 70
    Counting problems in algebraic geometry over an algebraically closed field have been studied for centuries. More recently, it was discovered that there are interesting counting problems over the real numbers. Topology took the place of algebraic closedness. However, the question remained whether there are interesting counting problems over more general fields where the tools of classical topology are not available. I will describe some results in this direction.
     

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