When: Wednesdays/Thursdays 12:15-1:15pm Where: Wednesdays CP418/ Thursdays CP309 Who: All are welcome. Whom to Contact: Quanlei Fang,Yunchun Hu, Mehdi Lejmi |
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Spring 2018 Schedule
Thursday Feb 8: Dr. Mehdi Lejmi, Einstein-Maxwell Equations Abstract
I will discuss the Einstein-Maxwell equations, some recent results about obstruction to their existence etc. I will also discuss their existence on Lie algebras.
Notes
Wednesday Feb 14: Dr. Uma Iyer, Introduction to Quivers and Path Algebras Abstract
Following notes by William Crawley-Boevey: http://www1.maths.leeds.ac.uk/~pmtwc/quivlecs.pdf
Thursday Feb 15: no talk
Wednesday Feb 21: no talk Thursday Feb 22: Dr. Quanlei Fang, Dirac Operators for Commuting d--tuples Abstract
Given a commuting d-tuple operator on a Hilbert space there is an associated Dirac operator (defined by Arveson). We will discuss the Taylor spectrum and the notion of Fredholmness in this context.
Wednesday Feb 28: Dr. Philipp Rothmaler, Projective and injective modules and their pure versions Abstract
In this informal talk I will introduce some basic concepts of module theory (that actually work the same in any abelian category), like pushouts and pullbacks, and demonstrate their use in the very definition of injectivity and projectivity. Time permitting, I'll mention the pure versions of pure injectivity and pure projectivity. Roughly, injective module is the "correct" generalization of divisible abelian group and projective module that of free abelian group (or module). The overall purpose is to provide some preparation for the algebraic talks by my visitors coming up in the departmental seminar.
Thursday Mar 1: department meeting
Wednesday Mar 7: Dr. Philipp Rothmaler, Approximations: envelopes and covers for various classes of modules Abstract
I will introduce these concepts from scratch again and discuss them with respect to the classes of injective, projective and flat modules. While injective modules constitute a generalization of divisible modules, the injective cover that of the quotient ring (considered as a one-sided module), projective modules that of free modules (projective abelian groups are, in fact, free), flat modules constitute a generalization of torsion-free modules. They play an important role also in algebraic geometry. I will keep things down to earth though, nevertheless mention a few results without proof, like Matlis' theory on the connection between injective indecomposables and the prime spectrum of commutative noetherian rings.
Thursday Mar 8: orientation meeting for math majors
Wednesday Mar 14: Dr. Manuel Cortes Izurdiaga (University of Almeria, Spain), Some classes of modules over triangular matrix rings Thursday Mar 15: no meeting
Wednesday Mar 21: snow day Thursday Mar 22: no meeting
Wednesday Mar 28: Dr. Uma Iyer, Introduction to Quivers and Path Algebras Thursday Mar 29: no meeting
Wednesday Apr 4: spring break Thursday Apr 5: spring break
Wednesday Apr 11: Friday schedule Thursday Apr 12: department meeting
Wednesday Apr 18: Dr. Uma Iyer, Three Hopf algebras Thursday Apr 19: student presentations
Wednesday Apr 25: no meeting Thursday Apr 26: math and science fair
Wednesday May 2: Dr. Uma Iyer, Hyperrings Abstract
Hyperrings have been around for a few decades, but not that well-known. We are reading the following paper: https://arxiv.org/pdf/1001.4260.pdf
Thursday May 3: no meeting
Wednesday May 9: Dr. Philipp Rothmaler, Hiding Model Theory, beta version---with emphasis on pure exact sequences Thursday May 10: department meeting
Wednesday May 16: joint lunch
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