Description
The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy is organizing an Advanced School and Workshop on Moduli Spaces, Mirror Symmetry and Enumerative Geometry, to be held in Trieste from 1 to 19 August 2016.

TOPICS
Moduli spaces and enumerative geometry are important classical topics in algebraic geometry. In recent years they have received important new input from theoretical physics, among others with the advent of mirror symmetry, which made surprising predictions for classical problems in enumerative geometry. Mirror symmetry has since developed further and is a subject of intense study. Many powerful tools and techniques have been introduced in recent years in part to understand these predictions. These involve moduli spaces of maps, Gromov-Witten invariants, Donaldson-Thomas and Pandharipande-Thomas invariants, stability conditions on derived categories and their moduli spaces. At the same time important progress was made in the understanding of the geometry and topology of moduli spaces of curves. This school and workshop will introduce the participants to these fascinating subjects.

COURSES
The first two weeks (August 1-12 2016) will be devoted to an Advanced School. The third week will be a Workshop where the most recent developments will be presented.

The lecturers at the Advanced School are:
Alexander Kuznetzov (Steklov Institute, Moscow and Laboratory of Algebraic Geometry and Its Applications, Higher School of Economics, Moscow) - Derived categories and moduli spaces
Arend Bayer (University of Edinburgh) - Stability conditions on derived categories and applications to geometry
Yukinobu Toda (University of Tokyo) - Stable pair invariants and derived categories
Aaron Pixton (MIT) - Tautological rings of moduli spaces of curves
Alessio Corti (Imperial College, London) and
Alexander Kasprzyk  (University of Nottingham) - Mirror symmetry for Fano orbifolds
Paul Hacking (University of Massachusetts, Amherst) - Cluster algebras and Mirror Symmetry

The list of speakers of the Workshop includes:
Sebastian Y. Casalaina-Martin (University of Colorado)
Maksym Fedorchuk (Boston College) (TBC)
Michael Kemeny (Humboldt University, Berlin)
Martijn Kool (Utrecht University)
Marti Lahoz (University of Paris 7)
Melissa Liu (Columbia University)
Emanuele Macri (Northeastern University)
Alina Marian (Northeastern University) (TBC)
Andrei Negut (MIT)
Georg Oberdieck (MIT) (TBC)
Aaron Pixton (MIT)
Jorgen Rennemo (Oxford University)
Vivek Shende (University of California at Berkeley)
Paolo Stellari (University of Milan)
Jacopo Stoppa (University of Pavia)
Michael Wemyss (University of Edinburgh)

GRANTS
A limited number of grants are available to support the travel and living expenses of selected participants, with priority given to participants working in a developing country and who are at the early stages of their career

HOW TO APPLY
The application form can be accessed until  1 April 2016 through the link below.
Once you access the online application system, comprehensive instructions will guide you step-by-step, on how to fill out and submit online the application form. Recommendation letters are not mandatory, but will help you in the admission process.
Go to day
  • Monday, 1 August 2016
    • 08:45 - 16:30 Monday, 1 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 08:45 Registration formalities 2h5' ( Leonardo Building - Lobby )
      • 10:50 Opening Remarks 10'
        Speaker: F. Rodriguez Villegas (ICTP)
      • 11:00 Stability conditions on derived categories and applications to geometry 1h0'
        Speaker: A. Bayer (University of Edinburgh)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Stable pair invariants and derived categories 1h0'
        Speaker: Y. Toda (The University of Tokyo)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Derived categories and moduli spaces 1h0'
        Speaker: A. Kuznetzov (Steklov Institute, Moscow and Laboratory of Algebraic Geometry, Higher School of Economics, Moscow)
        Material: Video
  • Tuesday, 2 August 2016
    • 09:30 - 16:30 Tuesday, 2 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Stability conditions on derived categories and applications to geometry 1h0'
        Speaker: A. Bayer (University of Edinburgh)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Stable pair invariants and derived categories 1h0'
        Speaker: Y. Toda (The University of Tokyo)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Derived categories and moduli spaces 1h0'
        Speaker: A. Kuznetzov (Steklov Institute, Moscow and Laboratory of Algebraic Geometry, Higher School of Economics, Moscow)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Exercises 1h0'
        Speaker: A. Bayer, A. Kuznetzov (University of Edinburgh; Steklov Institute Moscow and Laboratory of Algebraic Geometry, Higher School of Economics, Moscow)
  • Wednesday, 3 August 2016
    • 09:30 - 16:30 Wednesday, 3 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Stability conditions on derived categories and applications to geometry 1h0'
        Speaker: A. Bayer (University of Edinburgh)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Stable pair invariants and derived categories 1h0'
        Speaker: Y. Toda (The University of Tokyo)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Derived categories and moduli spaces 1h0'
        Speaker: A. Kuznetzov (Steklov Institute, Moscow and Laboratory of Algebraic Geometry, Higher School of Economics, Moscow)
        Material: Video
      • 15:00 Coffee Break 30'
      • 15:30 Mirror symmetry for Fano orbifolds 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London and University of Nottingham)
        Material: Video
  • Thursday, 4 August 2016
    • 09:30 - 16:30 Thursday, 4 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Stability conditions on derived categories and applications to geometry 1h0'
        Speaker: A. Bayer (University of Edinburgh)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Stable pair invariants and derived categories 1h0'
        Speaker: Y. Toda (The University of Tokyo)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Derived categories and moduli spaces 1h0'
        Speaker: A. Kuznetzov (Steklov Institute, Moscow and Laboratory of Algebraic Geometry, Higher School of Economics, Moscow)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Mirror symmetry for Fano orbifolds 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London and University of Nottingham)
        Material: Video
  • Friday, 5 August 2016
    • 09:30 - 16:30 Friday, 5 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Stability conditions on derived categories and applications to geometry 1h0'
        Speaker: A. Bayer (University of Edinburgh)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Stable pair invariants and derived categories 1h0'
        Speaker: Y. Toda (The University of Tokyo)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Derived categories and moduli spaces 1h0'
        Speaker: A. Kuznetzov (Steklov Institute, Moscow and Laboratory of Algebraic Geometry, Higher School of Economics, Moscow)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Mirror symmetry for Fano orbifolds 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London and University of Nottingham)
        Material: Video
  • Monday, 8 August 2016
    • 09:30 - 14:00 Monday, 8 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Tautological rings of moduli spaces of curves 1h0'
        Speaker: A. Pixton (MIT)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Mirror symmetry for Fano orbifolds 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London and University of Nottingham)
        Material: Video
      • 12:00 Lunch Break 2h0'
    • 14:30 - 14:31 Dirac Medal Ceremony
  • Tuesday, 9 August 2016
    • 09:30 - 16:30 Tuesday, 9 August 2016
      • 09:30 Cluster algebras and Mirror Symmetry 1h0'
        Speaker: P. Hacking (University of Massachusetts, Amherst)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Tautological rings of moduli spaces of curves 1h0'
        Speaker: A. Pixton (MIT)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Mirror symmetry for Fano orbifolds 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London and University of Nottingham)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Cluster algebras and Mirror Symmetry 1h0'
        Speaker: P. Hacking (University of Massachusetts, Amherst)
        Material: Video
  • Wednesday, 10 August 2016
    • 09:30 - 16:30 Wednesday, 10 August 2016
      • 09:30 Tautological rings of moduli spaces of curves 1h0'
        Speaker: A. Pixton (MIT)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Cluster algebras and Mirror Symmetry 1h0'
        Speaker: P. Hacking (University of Massachusetts, Amherst)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Mirror symmetry for Fano orbifolds 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London and University of Nottingham)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Exercises 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London; University of Nottingham)
  • Thursday, 11 August 2016
    • 09:30 - 16:30 Thursday, 11 August 2016
      • 09:30 Tautological rings of moduli spaces of curves 1h0'
        Speaker: A. Pixton (MIT)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Cluster algebras and Mirror Symmetry 1h0'
        Speaker: P. Hacking (University of Massachusetts, Amherst)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Mirror symmetry for Fano orbifolds 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London and University of Nottingham)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Exercises 1h0'
        Speaker: P. Hacking (University of Massachusetts, Amherst)
  • Friday, 12 August 2016
    • 09:30 - 16:30 Friday, 12 August 2016
      • 09:30 Tautological rings of moduli spaces of curves 1h0'
        Speaker: A. Pixton (MIT)
        Material: Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Cluster algebras and Mirror Symmetry 1h0'
        Speaker: P. Hacking (University of Massachusetts, Amherst)
        Material: Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Mirror symmetry for Fano orbifolds 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London and University of Nottingham)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Exercises 1h0'
        Speaker: A. Corti and A. Kazprzyk (Imperial College, London; University of Nottingham)
  • Monday, 15 August 2016
    • 09:30 - 16:30 Monday, 15 August 2016
      • 09:30 Holomorphic differentials and Witten's r-spin class 1h0'
        Speaker: A. Pixton (MIT)
        Material: Abstract
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Stable pairs of local surfaces with smooth canonical divisor 1h0'
        Speaker: M. Kool (Utrecht University)
        Material: Abstract
      • 12:00 Lunch Break 2h0' ( )
      • 14:00 Topological and motivic invariants for generalized Kummer schemes 1h0'
        Speaker: J. Shen (ETH Zurich)
        Material: Abstract
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Curve counting on elliptically fibered Calabi-Yau threefolds 1h0'
        Speaker: G. Oberdieck (MIT)
        Material: Abstract
  • Tuesday, 16 August 2016
    • 09:30 - 16:30 Tuesday, 16 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Geometric structures on some spaces of stability conditions 1h0'
        Speaker: J. Stoppa (Università degli Studi di Pavia)
        Material: Abstract
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Adjoints to Fourier-Mukai functors 1h0'
        Speaker: A. Rizzardo (SISSA)
        Material: Abstract
      • 12:00 Lunch Break 2h0'
      • 14:00 A derived category approach to some moduli spaces on cubic threefolds and fourfolds 1h0'
        Speaker: P. Stellari (Università degli Studi di Milano)
        Material: Abstract
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Bridgeland stability for semiorthogonal decompositions 1h0'
        Speaker: M. Lahoz (Institut de Mathématiques Jussieu)
        Material: Abstract
  • Wednesday, 17 August 2016
    • 09:30 - 16:30 Wednesday, 17 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Brill-Noether Theory of Curves on Abelian Surfaces and Applications 1h0'
        Speaker: M. Lelli-Chiesa (Università di Pisa)
        Material: Abstract
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Descending Cohomology Geometrically 1h0'
        Speaker: S.Y. Casalaina-Martin (University of Colorado at Boulder)
        Material: Abstract
      • 12:00 Lunch Break 2h0'
      • 14:00 Hurwitz spaces and extremal Betti numbers 1h0'
        Speaker: M. Kemeny (Humboldt-Universität zu Berlin)
        Material: Abstract
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Cohomological stabilization of toroidal compactifications of A_g 1h0'
        Speaker: O. Tommasi (Chalmers University of Technology and University of Gothenburg)
        Material: Abstract
  • Thursday, 18 August 2016
    • 09:30 - 16:30 Thursday, 18 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 GW theory, FJRW theory, and MSP fields 1h0'
        Speaker: C. Liu (Columbia University)
        Material: Abstract
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Talks by Participants 1h0'
        • Cubic Hodge integrals and random matrices 15'
          Abstract: We demonstrate a recent conjectural relation between the GUE free energy and certain cubic Hodge integrals over the moduli spaces of stable algebraic curves.
          The talk is based on a joint work with Boris Dubrovin.
          Speaker: Di Yang (SISSA)
        • Lines on K3 quartic surfaces 15'
          Abstract: There are 27 lines on any smooth cubic surface in P^3. How many are there on a smooth quartic surface? What if we allow for singularities?
          The answer depends on the characteristic of the ground field: I will show you why.
          Speaker: Davide Cesare Veniani (Leibniz Universitaet Hannover)
        • A proof of Looijenga's conjecture on smoothability of cusp singularities, motivated by ideas from symplectic geometry 15'
          Speaker: Philip Engel (Harvard University)
      • 12:00 Lunch Break 2h0'
      • 14:00 Homological projective duality for Pfaffian varieties 1h0'
        Speaker: J. Rennemo (University of Oxford)
        Material: Abstract
      • 15:00 Coffee Break 30' ( Leonardo Building - Lobby )
      • 15:30 Talks by Participants 1h0'
        • Genus 1 Gromov-Witten invariants for local P^1 * P^1 15'
          Abstract: Kim and Lho calculated genus 1 Gromov-Witten invariants for quintic 3-fold  using localization on quasimap spaces and wall crossing formula. We will give a       calculation of genus 1 Gromov-Witten invariants for local P^1 * P^1 without using BCOV theory by similar method of them.
          This is joint work with Hyenho Lho.
          Speaker: Jeongseok Oh (KAIST)
        • The moduli space of twisted k-differentials 15'
          Abstract: We present the definition of the moduli spaces of twisted k-differentials,  which are closed substacks of \bar M_g,n constructed by Farkas and Pandharipande.
          We give an indication how to compute the dimension of their components and, if time   permits, a conjectural expression of their (weighted) fundamental class
          in terms of a tautological cycle studied by Pixton.
          Speaker: Johannes Schmitt (ETH Zurich)
        • Integrals over Grassmannians and enumerative geometry of lines 15'
          Abstract: The aim of this talk is to present formulas for integrals over Grassmannians of characteristic classes of the tautological bundles. An application to enumerative geometry of lines is given.
          Speaker: Dang Tuan Hiep (National Centre for Theoretical Sciences)
  • Friday, 19 August 2016
    • 09:30 - 15:00 Friday, 19 August 2016
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Hilbert schemes and knot invariants 1h0'
        Speaker: A. Negut (MIT)
        Material: Abstract
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Genus one Gromov-Witten invariants of threefolds 1h0'
        Speaker: C. Manolache (Imperial college UK)
        Material: Abstract
      • 12:00 Lunch Break 2h0'
      • 14:00 Magic windows and representations of generalized braid groups on the derived category of a GIT quotient 1h0'
        Speaker: D. Halpern-Leistner (Columbia University)
        Material: Abstract