When: Monday/Thursdays 12:15-1:15pm Where: CP 123A. Who: All are welcome. Whom to Contact: Quanlei Fang, Yunchun Hu,Parul Laul,Mehdi Lejmi |
|
Spring 2017 Schedule
Monday Feb 6: Dr. Uma Iyer, Modules over Weyl algebra, part I Abstract
I am trying to understand the paper "Weyl Algebra Modules" by
Beckert, Benkart, and Futorny available at https://arxiv.org/pdf/math/0202222v1.pdf
Thursday Feb 9: no meeting
Monday Feb 13: college is closed Feb 15 (Monday schedule): Dr. Uma Iyer, Modules over Weyl algebra, part II Thursday Feb 16: no meeting
Monday Feb 20: college is closed Thursday Feb 23: no meeting
Monday Feb 27: Dr. Uma Iyer, Modules over Weyl algebra, part III Thursday Mar 2: department meeting
Monday Mar 6: Dr. Uma Iyer, Modules over Weyl algebra, part IV Thursday Mar 9: no meeting
Monday Mar 13: Dr. Uma Iyer, Modules over Weyl algebra, part V Thursday Mar 16: Dr. Mehdi Lejmi, Conformal constant Chern scalar curvature metrics in almost Hermitian geometry, part I
Monday Mar 20: Dr. Tony Weaver, Lattices and Mobius Inversion, part I Thursday Mar 23: no meeting
Monday Mar 27: Dr. Tony Weaver, Lattices and Mobius Inversion, part II Thursday Mar 30: Dr. Philipp Rothmaler, Pure extensions, part I Abstract A subgroup A of an (additively written) abelian group B is called pure if it is relatively divisible in B, i.e., if every element from A that is divisible by a natural number in B is so already in A (Pr"ufer, 1923). (E.g., the subgroup {0,2} of the cyclic group {0,1,2,3} is NOT pure.) The exact sequence 0 --> A --> B --> B/A --> 0 is then called pure-exact (and B a pure extension of A). The importance of pure-exact sequences lies in the fact that they stay exact when tensored with any other abelian group. This latter categorical definition translates to the category of modules over any other ring (commutative or not). In the 50s, P.M. Cohn discovered a condition analogous to relative divisibility that is equivalent to purity, also over any ring. In fact, this condition, in turn, can be taken mutatis mutandis as the definition of purity in any category of algebraic structures (with tensor product or not). I will give an introduction to the concept and explain the previously mentioned features (and some more if time and interest permits).
Monday Apr 3: Dr. Tony Weaver, Lattices and Mobius Inversion, part III Thursday Apr 6: department meeting
Monday Apr 10: spring break Thursday Apr 13: spring break
Monday Apr 17 spring break Thursday Apr 20 (Monday schedule) no meeting
Monday Apr 24 (Room change: BH 226): Dr. Apoorva Khare (Stanford University), Modules over generalized Weyl algebras categorify Young diagrams Abstract
Generalized Weyl algebras (GWAs), including down-up algebras and their quantum variants, have been the focus of much recent activity. We study the BGG Category O over a triangular GWA, specifically, blocks with finitely many simple objects. We show that the endomorphism algebra of a projective generator of such a block is finite-dimensional and graded Koszul. We also show how blocks of O categorify Young diagrams, by studying projectives and tilting objects in detail. (Joint with Akaki Tikaradze.)
Thursday Apr 27: Math&Science club- student presentations
Monday May 1: Dr. Tony Weaver, Gaussian polynomials and q-analogues Thursday May 4: department meeting
Monday May 8: Dr. Philipp Rothmaler, Pure extensions, part II Abstract
Part II will be largely self-contained. I'll define purity again and derive some fundamental properties. Then I give a very short proof that, over a von Neumann regular ring, all extensions of modules are pure. The---much easier---converse also holds, which means that the property that all module extensions be pure characterizes von Neumann regularity of the ring.
Thursday May 11:Math and Science fair
Monday May 15: Dr. Philipp Rothmaler, Pure extensions, part III Thursday May 18: last day of classes/joint lunch |