Events
Department of Mathematics and Statistics
Texas Tech University
Every module over a Noetherian ring \(R\) has a minimal injective
resolution that is unique up to isomorphism. Since every injective
module can be written uniquely (up to isomorphism) as a direct sum of
indecomposable injective modules, the number of summands isomorphic to
the injective hull of \(R/\mathfrak{q}\) for a given prime
\(\mathfrak{q}\) that appears in i-th stage of such a resolution is
well defined. This number is called the i-th Bass number of the module
with respect to the prime ideal \(\mathfrak{q}\). By work of Huneke
and Sharp and of Lyubeznik, the Bass numbers of the various local
cohomology modules of the ring are all finite provided \(R\) is a regular
local ring containing a field. In this talk we compute some of the
Bass number of the first nonzero local cohomology module of \(R\).
REstricted Maximum Likelihood (REML) estimators are commonly used to produce unbiased estimators for the variance components in linear mixed models. Nowadays, the dimension of the design matrix with respect to the random effects may be high, especially in genetic association studies. Originating from this, I will first introduce the high-dimensional kernel linear mixed models. The REML equations will be derived followed by a discussion on the consistency of REML estimators for some commonly used kernel matrices. The validity of the theories is demonstrated via some simulation studies.
Please virtually attend this week's Statistics seminar at 4:00 PM (UT-5) on the 29th via this zoom link
Meeting ID: 918 4011 1599
Passcode: 478843
Using previous work by Bass, Dundas, and Rognes giving a geometric model of the iterated K-theory spectrum K(ku) in terms of bundles of Kapranov-Voevodsky 2-vector spaces, and recent work by Grady and Pavlov providing a rigorous foundation for fully-extended functorial field theories, we construct a model of K(ku) in terms of 2-dimensional functorial field theories valued in KV 2-vector spaces.