**Valery Alexeev, Hülya Argüz and Pierrick Bousseau.** Algebraic geometry is the study of algebraic varieties, which are spaces defined by polynomial equations in several variables. The moduli spaces parametrizing families of algebraic varieties are of…

**Akram Alishahi, Hülya Argüz, David Gay, Peter Lambert-Cole, Gordana Matic and Mike Usher.** Symplectic and contact structures first arose from classical mechanics, and since then symplectic and contact topology has become a…

**Hülya Argüz, Pierrick Bousseau and Mike Usher.** Enumerative geometry is a branch of algebraic geometry concerned with counting solutions to geometric problems. Gromov–Witten invariants, counting curves in algebraic varieties, and their sheaf theoretic…

**Akram Alishahi, Peter Lambert-Cole and Gordana Matic.** Heegaard Floer theory is a package of powerful algebraic invariants for low dimensional objects such as 3- and 4-manifolds, knots and links, contact structures, etc. These invariants have answered…

**Akram Alishahi, David Gay, Peter Lambert-Cole and Gordana Matic.** Low-dimensional topology focuses on the study of 3- and 4-manifolds, embedded knots and surfaces in them, their diffeomorphism groups and contact and symplectic structures on them. The…

**Valery Alexeev, Hülya Argüz, Pierrick Bousseau, David Gay and Mike Usher.** Mirror symmetry is a phenomenon inspired by string theory in physics. It is in the intersection of algebraic and symplectic geometry. Particularly, it predicts that moduli…

**Mike Usher.** A longstanding technique in symplectic topology has involved using the real-valued filtrations on symplectic Floer complexes associated to the action functional to obtain information about quantitative questions such as how much energy is…