Events
Department of Mathematics and Statistics
Texas Tech University
Abstract pdf
This Job Candidate Colloquium is held in conjunction with the Biomath seminar group, and may be virtually attended via this Zoom link.
Can mathematics understand diseases of the brain and the peripheral nervous system? The modern medical perspective on neurological diseases has evolved, slowly, since the 20th century but recent breakthroughs in medical imaging have quickly transformed medicine into a quantitative science. Today, mathematical modeling and scientific computing allow us to go farther than observation alone. With the help of numerical methods and high-performance computing, experimental and data-informed mathematical models are leading to new clinical insights into serious human pathologies, that affect the nervous system, such as oedema and Alzheimer's disease. In this talk, I will discuss my work in the construction, analysis and solution of data and clinically-driven mathematical models of pathologies affecting the human nervous system. Mathematical modeling and scientific computing are indeed indispensible for cultivating a data-informed understanding of the brain, serious human diseases and for developing effective treatment.
This Job Colloquium is sponsored by the Applied Math seminar group. Please virtually attend Wednesday the 6th at 4 PM CDT (UT-5) via this Zoom link.
In this talk, we’ll discuss two themes in geometry. The first is to study the connection between the geometry and the topology of a manifold. Here, the geometry is about the shape and the measurement while the topology is about properties that are preserved under continuous deformations. We’ll mention progress in the theory of Ricci flows and advancements towards a Hopf’s conjecture and other well-known problems. Particularly, a highlighted result is a differentiable sphere theorem that resolves a conjecture proposed by S. Nishikawa in 1986.
The second theme is the search for a hierarchy of stationary surfaces, which are critical points of a certain geometric functional. In Calculus, we use derivative tests to classify critical points and determine whether one is a minimum, a maximum, or a saddle. The abstract generalization is to study the index of an operator associated with the second variation. In this direction, we’ll develop a novel mechanism when dealing with surfaces with boundaries and introduce a surprise perspective when dealing with constraints. Specifically, there is a partial resolution of a conjecture proposed by R. Schoen and A. Fraser and closely related to the Willmore conjecture.
This Third Year Review Colloquium may be attended virtually via this zoom link.
We study, in fine details, the long-time asymptotic behavior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions decay, as time tends to infinity, in a coherent way expressed by combinations of the exponential, power, logarithmic and iterated logarithmic functions. The decay may contain sinusoidal oscillations not only in time but also in the logarithm and iterated logarithm of time. It is proved that the decaying solutions admit corresponding asymptotic expansions, which can be constructed concretely. In the case of the real Euclidean spaces, the real-valued decaying solutions are proved to admit real-valued asymptotic expansions. Our results unite and extend the theory investigated in many previous works.
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here.
 | Tuesday
Oct. 5
3:30 PM
MATH 016
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| Real-Algebraic Geometry
Sheafification
David Weinberg
Department of Mathematics and Statistics, Texas Tech University
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N/A
Online video streaming is available, see https://dmitripavlov.org/geometryIn this talk, we will discuss recent results on the issue of well-posedness for the 2D generalized surface quasi geostrophic (gSQG) equation. This family of equations was introduced to the mathematical community by Chae-Constantin-Cordoba-Gancedo-Wu in 2012. Both the 2D incompressible Euler and 2D SQG equations can be realized as belonging to this family. In light of recent ill-posedness results, we positively discuss the issue of well-posedness for the gSQG family, their regularized variations, as well as the effect of instantaneous smoothing, when it is present.
Watch online via this Zoom link.
Abstract:
The Greenwood statistic Tn and its functions, including sample coefficient of variation, often arise
in testing exponentiality or detecting clustering or heterogeneity.
We provide a general result describing stochastic behavior of Tn in response to stochastic behavior
of the sample data.
Our result provides a rigorous base for con- structing tests and assuring that confidence regions are
actually intervals for the tail parameter of many power-tail distributions.
We also present a result explaining the connection between clustering and heaviness of tail for several
classes of distributions and its extension to general heavy tailed families.
Our results provide theoretical justification for Tn being an effective and commonly used statistic
discriminating between regularity/uniformity and clustering in presence of heavy tails in applied sciences.
We also note that the use of Greenwood statistic as a measure of heterogeneity or clustering is limited to
data with large outliers, as opposed to those close to zero.