Higher Algebra, Geometry, and Topology

The aim of the present conference is to gather mathematicians working in Algebra, Geometry, Topology, and Mathematical Physics. Created over the past 50 years, the theory of higher structures (operads, homotopy algebras, infinity-categories) has given rise recently to powerful tools which led to resolutions of open problems and prompted deep developments, for instance in algebraic topology (faithful algebraic invariants of the homotopy type of spaces), algebraic geometry (derived algebraic geometry), and deformation theory (formal moduli problems). More recent, fundamental achievements have been obtained by applying these effective and algorithmic higher algebraic methods in Lie theory (higher Lie theory), derived deformation theory (deformation theory in positive characteristic, universal deformation groups, Grothendieck–Teichmüller groups), homotopy theories (rational homotopy theories), and geometry (algebraic, complex and discrete).