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Alessandro Chiodo - Towards global mirror symmetry (Part 3)


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Alessandro Chiodo - Towards global mirror symmetry (Part 3)

Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathe-

matics and physics in the last twenty years; we will review here a number of results going from the enumerative
geometry of curves to homological algebra. These advances justify the introduction of new techniques, which
are interesting in their own right. Among them, Gromov{Witten theory and its variants allow us to provide a
re ned statement of mirror symmetry. Of course this leads to further open questions (despite much e ort and
progress, Gromov{Witten theory remains unknown in high genus for the quintic threefold). In this course, we
will illustrate the natural problem of moving beyond the local mirror symmetry statement and completing a
framework of global mirror symmetry which is gradually taking shape. We will show how the missing piece in
this picture comes unexpectedly from a classical subject in algebraic geometry: the theory of curves with level
structures.
 

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 Lars Andersson - Geometry and analysis in black hole spacetimes (Part 4)
 Lars Andersson - Symmetry operators and energies
 Alessandro Giacomini - Free discontinuity problems and Robin boundary conditions
 Bernd Kirchheim - Equidimensional isometric maps
 Gian Paolo Leonardi - Towards a unified theory of surface discretization
 Bruno Lévy - A numerical algorithm for L2 semi-discrete optimal transport in 3D
 Xiangyu Liang - An example of proving Almgrem's minimality by product of paired calibrations
 Andrew Lorent - The Aviles-Giga functional: past and present
 Francesco Maggi - A quantitative description of almost constant mean curvature hypersurfaces
 Matteo Novaga - Nonlocal isoperimetric problems
 Guy David - Minimal sets (Part 2)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 1)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 2)
 Guy David - Minimal sets (Part 3)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 3)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 4)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 5)
 Joseph Fu - Integral geometric regularity (Part 1)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 1)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 2)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 3)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 4)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 5)
 Tatiana Toro - Geometry of measures and applications (Part 1)
 Tatiana Toro - Geometry of measures and applications (Part 2)
 Tatiana Toro - Geometry of measures and applications (Part 3)
 Tatiana Toro - Geometry of measures and applications (Part 4)
 Tatiana Toro - Geometry of measures and applications (Part 5)
 Joseph Fu - Integral geometric regularity (Part 2)
 Joseph Fu - Integral geometric regularity (Part 3)
 Joseph Fu - Integral geometric regularity (Part 4)
 Joseph Fu - Integral geometric regularity (Part 5)
 Andrea Braides - Geometric measure theory issues from discrete energies
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 2)
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 3)
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 4)
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 5)
 Nicholas Alikakos - On the structure of phase transition maps : density estimates and applications
 Elie Bretin - About phase field method to approximate the willmore flow
 Guy David - Minimal sets (Part 1)
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 1)
FMSH
 
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