Abstract: We explain the notion of shifted symplectic structure in derived algebraic geometry, in the sense of Pantev-Toen-Vezzosi-Vaquie, and show that a derived scheme with -1-shifted symplectic structure can be Zariski locally presented as the critical locus of a polynomial. If time permits, we’ll discuss analogous results for -m-symplectic derived-schemes and applications to categorification of Donaldson-Thomas invariants. This is joint work with Vittoria Bussi, Delphine Dupont, and Dominic Joyce.