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Monday, April 14, 2014

**Abstract:** A codimension one foliation is (topologically) taut if it admits a closed 1-cycle everywhere transverse to the foliation. The theory of taut foliations is extremely rich in dimension 3, however, it less satisfactory in higher dimensions. In this talk we will discuss a different generalization of 3-dimensional taut foliati- ons to higher dimensions inspired in symplectic geometry. These are codimension one foliations which admit a closed 2-form which makes every leaf a symplectic manifold. Our main result is that on an ambient closed manifold a foliation (of class at least C^1 in the transverse direction) admitting a 2-calibration has its transverse geometry encoded in a 3-dimensional foliated submanifold. This is joint work with Álvaro del Pino and Francisco Presas (ICMAT, Madrid)