This workshop, sponsored by AIM and the NSF, will bring together experts from different areas in mathematics related to applications of the Bochner technique, including Riemannian geometry, complex geometry, representation theory, and geometric flows.

The Bochner technique is a foundational tool in differential geometry which provides a deep link to topology. Recent advances include new connections to representation theory with applications to vanishing results for Betti and Hodge numbers, the resolutions of the Nishikawa conjecture, projectivity and rational connectedness results for Kähler manifold, or new Kodaira-Bochner formulae. The aim of the workshop is to both push the boundaries of these areas as well as strengthen the interaction among experts in different areas. Utilizing the versatility of the Bochner technique is a key component of the workshop. The workshop is meant to bring together leading experts as well as aspiring new researchers from all areas related to the Bochner technique.

The main topics for this workshop are

(1) Vanishing results and applications to topology and geometric flows

(2) Representation theoretic aspects and symmetric spaces

(3) The curvature operator of the second kind

(4) Nonlinear Kodaira-Bochner formulae and their applications

This conference is addressed to mathematicians and mathematical physicists interested in contemporary mechanics, physics and biology and associated mathematical questions. The application of differential geometry to find new results on manifolds, relativity, hypersurfaces, N-body problem, gauge fields, geometric quantization, rotational sequences, minimal surfaces, biophysical systems, coherent states, Dirac and Seiberg-Witten monopoles, rigid body dynamics, Toda chains dynamics, geometric algebra, Kähler calculus, thermodynamics, etc. The meeting allows participants coming from different fields to share and to interchange geometrical ideas among them with the leading role of differential geometry. The contributions presented at the conference will be invited to be submitted to the series on Geometry, Integrability and Quantization or to the Journal of Geometry and Symmetry in Physics.