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No abstract uploaded!

No abstract uploaded!

This talk will give a very brief outline how a portion of geometric analysis was carried out in relation to geometry, nonlinear partial differential equations and mathematical physics. My personal experience is that this is a beautiful subject with great depth and it touches almost all branch of mathematics.

We give bounds for various homological invariants (including Castelnuovo-Mumford regularity, degrees of local cohomology, and injective dimension) of finitely generated VI-modules in the non-describing characteristic case. It turns out that the formulas of these bounds for VI-modules are the same as the formulas of corresponding bounds for FI-modules.