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Description
The main focus is on recent developments in gauge theories, both in theoretical physics and in mathematics. This area is very fruitful for active interplays between Mathematics and Physics.

In theoretical physics  exact results in supersymmetric quantum field theories and superstrings on curved backgrounds prompted the interest in explicit calculations of (equivariant) Donaldson invariants also in higher rank and the possible definition of new invariants for four manifolds using non-Lagrangian theories. On the mathematical side, new results have been obtained for higher rank Donaldson invariants and Vafa-Witten invariants.  A key role is played by the interplay of with representation theory and quantum integrable systems. These developments are also expected to have impact on enumerative geometry, knot theory and representation theory of infinite dimensional algebras. A key technical tool in these developments is equivariant localization which allows the extraction of exact results.

Topics :
  • higher rank Donaldson invariants
  • Vafa-Witten invariants
  • Donaldson-Thomas invariants
  • study of the BPS spectra of (non Lagrangean) N=2 Gauge Theories and new four-dimensional invariants
  • relation to matrix models and topological strings
  • quantum Hitchin systems  and character varieties
  • gauge theories on complex toric surfaces and their instanton moduli spaces
  • surface operators in gauge theory and moduli spaces of principal bundles with parabolic structure
  • quantum cohomology of the instanton moduli space
  • K-theory of quiver varietes
  • quantum integrability, quantum Yang-Baxter equations
  • relations to knot theory and Khovanov Homology
  • higher dimensional supersymmetric gauge theories and M-theory

Lecturers:
L. GÖTTSCHE, ICTP
G. MOORE, Rudgers (tbc)
H. NAKAJIMA, Kavli IPMU
N. NEKRASOV, Simons Center
P. PUTROV, ICTP

Speakers include:
A. DAEMI, Simons Center
A. GOLAMPOUR, University of Maryland
S. GUKOV, Caltech
S. JEONG, Stony Brook
A. KLEMM, Universität Bonn
M. KOOL, Utrecht University
J. MANSCHOT, Trinity College Dublin
A. MELLIT, Universität Wien
D. OPREA, University of California, San Diego
D. PEI, Caltech
Z. RUIDONG, Tokyo University
A. SHESHMANI, Harvard University
Y. TANAKA, Oxford University
K. YOSHIOKA, Kobe Unversity

Material

School and Workshop on Gauge Theories and Differential Invariants | (smr 3326)
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  • Monday, 30 September 2019
    • 08:30 - 09:30
      • 08:30 Registration and Administrative formalities 1h0' ( Adriatico Guest House - Office n. 3 )
    • 09:30 - 16:30
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:30 Coulomb branches of 3d N=4 gauge theories 1 1h0'
        Speaker: Hiraku NAKAJIMA (University of Tokyo, Kavli Institute for the Physics and Mathematics of the Universe)
        Material: Abstract
      • 10:30 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 11:00 Invariants of manifolds from 6 dimensions 1 1h0'
        Speaker: Pavel PUTROV (ICTP)
        Material: Abstract
      • 12:00 Lunch Break 2h0'
      • 14:00 Virtual topological invariants of moduli spaces of sheaves on surfaces 1 1h0'
        Speaker: Lothar GOETTSCHE (ICTP)
        Material: Abstract Notes
      • 15:00 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 15:30 On the log-local principle for (refined) Gromov--Witten theory 1h0'
        Speaker: Andrea BRINI (University of Birmingham)
        Material: Abstract
  • Tuesday, 1 October 2019
    • 09:30 - 16:30
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:30 Coulomb branches of 3d N=4 gauge theories 2 1h0'
        Speaker: Hiraku NAKAJIMA (University of Tokyo, Kavli Institute for the Physics and Mathematics of the Universe)
        Material: Abstract
      • 10:30 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 11:00 A geometric R-matrix for the Hilbert scheme of points on a general surface 1h0'
        Speaker: Noah ARBESFELD (Imperial College London)
        Material: Abstract
      • 12:00 Lunch Break 2h0'
      • 14:00 Virtual topological invariants of moduli spaces of sheaves on surfaces 2 1h0'
        Speaker: Lothar GOETTSCHE (ICTP)
        Material: Abstract Notes
      • 15:00 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 15:30 Mocking the u-plane integral and Donaldson invariants 1 1h0'
        Speaker: Jan MANSCHOT (Trinity College Dublin)
  • Wednesday, 2 October 2019
    • 09:30 - 16:30
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:30 Coulomb branches of 3d N=4 gauge theories 3 1h0'
        Speaker: Hiraku NAKAJIMA (University of Tokyo, Kavli Institute for the Physics and Mathematics of the Universe)
        Material: Abstract
      • 10:30 Group Photo 5'
      • 10:35 Coffee break 25' ( Adriatico Guest House - Terrace )
      • 11:00 Mocking the u-plane integral and Donaldson invariants 2 1h0'
        Speaker: Jan MANSCHOT (Trinity College Dublin)
      • 12:00 Lunch Break 2h0'
      • 14:00 Virtual topological invariants of moduli spaces of sheaves on surfaces 3 1h0'
        Speaker: Lothar GOETTSCHE (ICTP)
        Material: Abstract Notes
      • 15:00 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 15:30 Invariants of manifolds from 6 dimensions 2 1h0'
        Speaker: Pavel PUTROV (ICTP)
        Material: Abstract
  • Thursday, 3 October 2019
    • 09:30 - 16:30
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:30 The curious hard Lefschetz property for character varieties 1h0'
        Speaker: Anton MELLIT (University of Wien)
        Material: Abstract Notes
      • 10:30 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 11:00 Invariants of manifolds from 6 dimensions 3 1h0'
        Speaker: Pavel PUTROV (ICTP)
        Material: Abstract
      • 12:00 Lunch Break 2h0'
      • 14:00 Virtual topological invariants of moduli spaces of sheaves on surfaces 4 1h0'
        Speaker: Lothar GOETTSCHE (ICTP)
        Material: Abstract
      • 15:00 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 15:30 Invariants of Manifolds from Non-Gauge Theories 1 1h0'
        Speaker: Du PEI (Institute for theoretical Physics, California Institute of Technology)
        Material: Abstract
  • Friday, 4 October 2019
    • 09:30 - 16:30
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:30 Invariants of Manifolds from Non-Gauge Theories 2 1h0'
        Speaker: Du PEI (Institute for theoretical Physics, California Institute of Technology)
        Material: Abstract
      • 10:30 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 11:00 Chiral Algebras from Three Dimensions 1h0'
        Speaker: Sergei GUKOV (California Institute for Technology)
        Material: Abstract Link
      • 12:00 Lunch Break 2h0'
      • 14:00 MTC[M3] and Twisted Hilbert Spaces 1h0'
        Speaker: Sergei GUKOV (California Institute for Technology)
        Material: Abstract Link
      • 15:00 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 15:30 Invariants of manifolds from 6 dimensions 4 1h0'
        Speaker: Pavel PUTROV (ICTP)
        Material: Abstract
  • Monday, 7 October 2019
    • 08:30 - 09:30
      • 08:30 Registration and Administrative formalities 1h0' ( Adriatico Guest House - Office n. 3 )
    • 09:30 - 16:40
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:30 Topological String on genus one fibered Calabi-Yau 3-folds and string dualities 50'
        Speaker: Albrecht KLEMM (University of Bonn)
        Material: Abstract
      • 10:20 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 10:50 Stable higher rank flag sheaves on surfaces 50'
        Speaker: Artan SHESHMANI (Harvard University)
        Material: Abstract
      • 11:40 Symplectic Leaves for Symplectic Singularities 50'
        Speaker: Amihay HANANY (Imperial College London)
      • 12:30 Lunch Break 2h0'
      • 14:30 DT/PT correspondence for Calabi-Yau fourfolds 50'
        Speaker: Martijn KOOL (Utrecht University)
        Material: Abstract
      • 15:20 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 15:50 Web construction for ABCDEFG and affine quivers 50'
        Speaker: Ruidong ZHU (Department of Physics, The University of Tokyo)
        Material: Abstract
  • Tuesday, 8 October 2019
    • 09:20 - 16:50
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:20 Vertical Vafa--Witten Invariants 50'
        Speaker: Pieter Ties Allerd LAARAKKER (Utrecht University)
        Material: Abstract
      • 10:10 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 10:40 Quantum Solved from Crossed and Folded I 2h0'
        Speaker: Nikita NEKRASOV (Simons Center for Geometry and Physics)
        Material: Abstract
      • 12:40 Lunch Break 2h0'
      • 14:40 Surface defects, nested instantons and flags of sheaves 50'
        Speaker: Nadir FASOLA (SISSA)
        Material: Abstract
      • 15:30 Group Photo 5'
      • 15:35 Coffee break 25' ( Adriatico Guest House - Terrace )
      • 16:00 Moduli of stable sheaves on Enriques surfaces 1 50'
        Speaker: Kota YOSHIOKA (Kobe University)
        Material: Abstract
  • Wednesday, 9 October 2019
    • 09:20 - 16:50
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:20 Virtual invariants of Quot schemes of surfaces 50'
        Speaker: Dragos OPREA (University of California at San Diego)
        Material: Abstract
      • 10:10 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 10:40 Quantum Solved from Crossed and Folded II 2h0'
        Speaker: Nikita NEKRASOV (Simons Center for Geometry and Physics)
      • 12:40 Lunch Break 2h0'
      • 14:40 q-Virasoro and partition functions 50'
        Speaker: Maxim ZABZINE (Uppsala University)
        Material: Abstract
      • 15:30 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 16:00 Boundary N=2 Theory, Floer Homologies, Affine Algebras, and the Verlinde Formula 50'
        Speaker: Meng-Chwan TAN (NUS)
        Material: Abstract Slides
  • Thursday, 10 October 2019
    • 09:30 - 16:40
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:30 Higher rank instantons and low dimensional topology 50'
        Speaker: Aliakbar DAEMI (Simons Center for Geometry and Physics)
      • 10:20 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 10:50 On two generalisations of Hitchin's equations in four dimensions from Theoretical Physics 50'
        Speaker: Yuuji TANAKA
        Material: Abstract
      • 11:40 Opers, surface defects, and Yang-Yang functional 50'
        Speaker: Saebyeok JEONG (Stony Brook University)
      • 12:30 Lunch Break 2h0'
      • 14:30 Reduced Gromov-Witten invariants from cuspidal curves 50'
        Speaker: Cristina MANOLACHE (Imperial College London)
        Material: Abstract
      • 15:20 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 15:50 Solving refined BPS invariants with blowup equations 50'
        Speaker: Jie GU (University of Geneva)
        Material: Abstract
  • Friday, 11 October 2019
    • 09:30 - 14:30
      • 09:30 On the Chow ring of holomorphic symplectic manifolds 50'
        Speaker: Alina MARIAN (Northeastern University)
        Material: Slides
      • 10:20 Coffee break 30' ( Adriatico Guest House - Terrace )
      • 10:50 Refined topological branes 50'
        Speaker: Can KOZCAZ (Bogazici University Turkey)
        Material: Abstract
      • 11:40 Quantum invariants of knots and new kinds of modularity 50'
        Speaker: Don ZAGIER (Max-Planck-Institut for Mathematics)
      • 12:30 Lunch Break 2h0'
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