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…
