February 05, 2013
939 Evans Hall
Spaces and varieties of barcodes
Speaker: Gunnar Carlsson
Persistence barcodes are very interesting and useful summaries of the shape of point cloud data sets. They can be used to understand individual data sets, or data sets whose objects themselves have shapes. The set of barcodes can be understood as a space in various ways, one as a metric space, the other as an (infinite dimensional) algebraic variety. We\'ll discuss these ideas and ask for input on more general situations.
Uniform annihilation of Ext modules and generation of derived categories
Speaker: Ryo Takahashi
This talk is based on ongoing joint work with Srikanth Iyengar. Let R be a commutative noetherian ring. We call a nonzerodivisor x of R a uniform annihilator if there exists an integer n>0 such that x annihilates Ext_R^n(M,N) for all finitely generated R-modules M and N. It follows from a result of Hsin-Ju Wang that R possesses a uniform annihilator if R is a complete local domain containing a field with perfect residue field. In this talk, we consider how to proceed in the general case. We also relate it with strong generation of the bounded derived category of finitely generated R-modules in the sense of Bondal and Van den Bergh.