In this paper a variationally consistent trigonometric shear deformation theory is presented for the free vibration of thick isotropic square and rectangular plate. In this displacement based theory, the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in tr...

Algebraic deformations of modules over a ring are considered. The resulting theory closely resembles Gerstenhaber’s deformation theory of associative algebras.

We give an introduction to deformation theory with a special focus on the moduli space of semistable sheaves and the Quot-scheme. These are notes to a talk given during Spring 2016 at the graduate seminar on moduli of sheaves on K3 surfaces joint between MIT and NEU.

We describe a step toward quantizing deformation theory. The L∞ operad is encoded in a Hochschild cocyle ◦1 in a simple universal algebra (P, ◦0). This Hochschild cocyle can be extended naturally to a star product ⋆ = ◦0+~◦1+~ 2 ◦2+ · · · . The algebraic structure encoded in ⋆ is the properad Ω(coFrob) which, conjecturally, controls a quantization of deformation theory—a theory for which Froben...

In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the wellknown deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations and we construct sever...