Events
Department of Mathematics and Statistics
Texas Tech University
In a paper from 1968, Golod proved that the Betti sequence of the
residue field of a local ring attains the upper bound given by Serre
if and only if the homology algebra of the Koszul complex of the ring
has trivial multiplications and trivial Massey operations. This is the
origin of the notion of Golod ring. Using the Koszul complex
components as building blocks Golod also constructed a minimal free
resolution of the residue field of a Golod ring. With Van Nguyen, we
extend this construction for an arbitrary local ring, up to
homological degree five, and explicitly show how the multiplicative
structure of the homology of the Koszul algebra is involved, including
the triple Massey products. The talk will illustrate this construction
and various consequences of it.
There are similar characterizations in terms of complexes of flat
modules and complexes of injective modules.
This paper investigates advancements in the diffusion index forecasting model by incorporating time-varying factor loadings and forecasting coefficients. In the proposed model, factors are extracted from a large number of predictors using the boundary-corrected kernel method. Subsequently, these estimated factors are integrated into the time-varying forecast using the locally constant nonparametric method. An essential contribution of this study is the verification of the asymptotic consistency of the constructed forecasting target variable. Monte Carlo simulations corroborate the enhanced forecasting performance. Future work for this paper involves completing the empirical applications of the proposed model.
Please virtually attend this week's Statistics seminar at 4:00 PM (UT-5) via this zoom link.
All sorts of algebro-geometric moduli spaces (of stable curves, stable sheaves on a CY 3-folds, flat bundles, Higgs bundles...) are best understood as objects in derived geometry. Derived enhancements of classical moduli spaces give transparent intrinsic meaning to previously ad-hoc structures pertaining to, for instance, enumerative geometry and are indispensable for more advanced constructions, such as categorification of enumerative invariants and (algebraic) deformation quantization of derived symplectic structures. I will outline how to construct such enhancements for moduli spaces in global analysis and mathematical physics, that is, solution spaces of PDEs in the framework of derived ${\rm C}^\infty$ geometry and discuss the elliptic representability theorem, which guarantees that, for elliptic equations, these derived moduli stacks are bona fide geometric objects (Artin stacks at worst). If time permits some applications to enumerative geometry (symplectic Gromov-Witten and Floer theory) and derived symplectic geometry (the global BV formalism).Abstract. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction of experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity.
More recently, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties in preserving causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids.
In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues. This talk is intended for a general Math and Physics audience.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 944 4492 2197
* Passcode: applied
 | Thursday
Mar. 28
6:30 PM
MA 108
|
| Mathematics Education
Math Circle
Miraj Samarakkody
Department of Mathematics and Statistics, Texas Tech University
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Math Circle spring poster
abstract noon CDT (UT-5)