If you are interested in giving a talk, please contact the organizers Emily Witt and Jonathan Montaño.

All seminar talks will take place on
Tuesday or Thursday at 2:30pm in Snow Hall 306.

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Past
Seminars

**Name:**Alessandra Costantini, Purdue University**Title:***The Cohen-Macaulay property of the Rees algebra of a module.***Abstract:**Rees algebras of ideals and modules appear frequently in Algebraic Geometry, for instance in connection with blow-up constructions, equisingularity theory and birational study of projective varieties. For an ideal I in a Cohen-Macaulay ring R, the Cohen-Macaulay property of the Rees algebra R(I) is deeply connected with the Cohen-Macaulayness of the associated graded ring gr(I). In fact, gr(I) is Cohen-Macaulay whenever R(I) is; and although the converse is not true in general, the Cohen-Macaulay property of gr(I) combined with other assumptions often implies that R(I) is Cohen-Macaulay. However, for an R-module E there is no analogue of the associated graded ring, so the study of the Cohen-Macaulay property of R(E) is more complicated. In this talk, using the technique of generic Bourbaki ideals introduced by Simis, Ulrich and Vasconcelos we will provide classes of modules whose Rees algebra is Cohen-Macaulay. Our results generalize known results of Jonhson and Ulrich, and of Goto, Nakamura and Nishida for the Rees algebra of an ideal.

**Name:**Jack Jeffries, University of Michigan**Title:***The Smith-Van den Bergh functors.***Abstract:**In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive characteristic. We will discuss formulas for the ring of differential operators as well as these derived functors of differential operators in terms of local cohomology. One can use this description to relate questions on the behavior of differential operators under base change to questions on p-torsion in local cohomology. We will also connect the vanishing of these functors to some interesting properties of singularities.

**Name:**Daniel Katz, University of Kansas**Title:***Talks in honor of the 100th birthday of D. Rees: An overview of the work of David Rees.***Abstract:**

**Name:**Justin Lyle, University of Kansas**Title:***Hom and Ext, Revisited.***Abstract:**Let be a commutative Noetherian local ring and be finitely generated R-modules. We prove a number of results of the form: if has some nice properties and for some , then (and sometimes ) must be close to free. Using these results, we are able to extend and unify a number of results in the literature.

**Name:**Hailong Dao, University of Kansas**Title:***Talks in honor of the 100th birthday of D. Rees: m-full ideals.***Abstract:**