The workshop aims to discuss the geometric correspondences of supersymmetric gauge theories and it address both physical and mathematical aspects of these theories. A deeper understanding of quantum field theory at strong coupling is an important challenge in theoretical physics. The embedding of strongly coupled quantum field theories in superstring theory provides a geometrical formulation of this problem. (Super)-conformal quantum field theories represent an important class describing critical phases and capturing many interesting physical phenomena. For this reason, a systematic study of (super)-conformal algebras and their representation has been pursued in the last three decades. The main focus of the workshop is on the geometrical aspects of superconformal quantum field theories on curved spaces. These can be formulated only on spacetimes of dimension less or equal to six dimensions. In the context of M-Theory the quantum field theories in 3 and 6 dimensions with the maximal amount of supersymmetry correspond to the microscopic theories of M2 and M5 branes. In particular, the (2,0) theories of M5-branes in six dimensions are the SCFTs with the maximal amount of supersymmetry in the highest dimension. These theories have been instrumental in constructing and understanding lower dimensional theories in the past, but remain themselves among the least understood ones. The study of superconformal field theories in general is a subject situated at the border between mathematics and physics. Other related topics that may be touched during the Workshop activity are supersymmetric localisation and superconformal indices, topological strings, black holes microstate countings, S-duality, mirror symmetry in three dimensional supersymmetric quantum field theories, quantum integrable systems. Over the last 30 years there have been remarkable instances where physical theories have provided a formidable input to mathematicians, offering the stimulus to the creation of new mathematical theories, and supplying strong evidence for highly nontrivial theorems. Most notable examples of this kind of interaction between mathematics and physics can be found in the theory of moduli spaces. In algebraic geometry the theory of moduli spaces goes back at least to Riemann, but moduli spaces were first rigorously constructed in the 1960s by Mumford. The theory has experienced an extraordinary development in recent decades, finding an increasing number of mathematical connections with other fields of mathematics and physics. In particular, moduli spaces of different objects (sheaves, instantons, curves, stable maps, ...) have been used to construct fine invariants (such as Donaldson, Seiberg-Witten, Gromov-Witten, Donaldson-Thomas invariants) that solve long-standing, difficult enumerative problems. During first week, August 27 - 31, 2018 there will be school which will consist of series of pedagogical lectures. Schedule (pdf) During second week, September 3 - 7, 2018 there will be the conference with the advanced talks on the subject of the workshop. Schedule (pdf) To participate to the activities, please apply by sending an email to esi18@sissa.it within July, 24. You will be contacted in due time.
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