Events
Department of Mathematics and Statistics
Texas Tech University
The shapes of soap bubbles and soap films are fascinating because of their beauty and elegance. In this talk, we give an approach to the mathematics that explains these shapes through experiments with soapy water and wires.
This is a Bilingual Colloquium. The slides will be in English and the speaker will deliver the talk in Spanish.
The Fourier transform is one of the most fundamental tools in classical analysis. It plays a pervasive role in several branches of theoretical mathematics and of the applied sciences. The theorem of Hausdorff-Young states that, when p is an exponent in the interval [1,2], the Fourier transform of a function in the Lebesgue class L^p belongs to the dual Lebesgue space L^p’. As such, it is only defined almost everywhere and therefore it is a priori all but clear why it should be possible to restrict it to a lower dimensional manifold, such for instance the unit sphere, which has zero Lebesgue measure. The restriction conjecture states that this is in fact possible, provided that p stays in a certain optimal subinterval of the Hausdorff-Young range [1,2]. I will give a completely self-contained presentation of such conjecture, and hint at the role that the curvature (of the sphere) plays in it. I will also highlight the celebrated Tomas-Stein theorem which completely solves the restriction problem when the target is L^2 of the unit sphere. If time permits, some notable applications will be given. Disclaimer: although it is helpful to know a bit of Lebesgue spaces, to enjoy this talk you do not need to know much about them. I will tell you the very basics.
Organism growth is often determined by multiple resources interdependently. However, growth models based on the Droop cell quota framework have historically been built using threshold formulations, which means they intrinsically involve single-resource limitations. In addition, it is a daunting task to study the global dynamics of these models mathematically, since they employ minimum functions that are non-smooth (not differentiable). To provide an approach to encompass interactions of multiple resources, we propose a multiple-resource limitation growth function based on the Droop cell quota concept and incorporate it into an existing producer–grazer model. The formulation of the producer’s growth rate is based on cell growth process time-tracking, while the grazer’s growth rate is constructed based on optimal limiting nutrient allocation in cell transcription and translation phases. We show that the proposed model captures a wide range of experimental observations, such as the paradox of enrichment, the paradox of energy enrichment, and the paradox of nutrient enrichment. Together, our proposed formulation and the existing threshold formulation provide bounds on the expected growth of an organism. Moreover, the proposed model is mathematically more tractable, since it does not use the minimum functions as in other stoichiometric models.
We will discuss the sharpness of the 2/3rds Conjecture, Brannan’s Conjecture , Smale’s Conjecture, the Sendov Conjecture, and a version of the Riemann Hypothesis. This is joint work with Kendall Richards.
A standard classification rule returns a single-valued prediction for any observation without confidence attached, which may result in severe consequences in many critical applications. In contrast, set-valued classification is a new paradigm to reduce the uncertainty in classification by reporting a set of plausible class labels to observations in highly ambiguous regions. Many existing set-valued classification methods do not consider the possibility that a new class that never appeared in the training data appears in the test data. Moreover, they are computationally expensive when the number of classes is large. In this talk, I will introduce a couple of related methods to estimate the acceptance regions while considering the possibility of a new class in the test data. The proposed classifier minimizes the expected size of the prediction set while guaranteeing that the class-specific accuracy is at least a pre-specified value. In the meantime, we show that the prediction ambiguity of our classifier attains optimality. Both theoretical analysis and numerical experiments are conducted to illustrate the effectiveness of the proposed methods.
Please virtually attend this week's Statistics seminar at 4:00 PM (CDT, UT-5) via this zoom link
Meeting ID: 904 545 1744
Extensions of the Dold-Kan correspondence for the duplicial and (para)cyclic index categories were introduced by Dwyer and Kan. Building on the categorification of the Dold-Kan correspondence by Dyckerhoff, we categorify the duplicial case by establishing an equivalence between the $\infty$-category of $2$-duplicial stable $\infty$-categories and the $\infty$-category of connective chain complexes of stable $\infty$-categories with right adjoints. I will further explain the current progress towards a conjectured correspondence between $2$-paracyclic stable $\infty$-categories and connective spherical complexes. Examples of the latter naturally arise from the study of perverse schobers. arXiv:2303.03653.
 | Wednesday
Apr. 19
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| Algebra and Number Theory
No Seminar
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Bring your own lunch and discuss (mostly) biology-related topics in math. Students, postdocs, and faculty welcome from any discipline.
Abstract. The talk focuses on a discontinuous Galerkin method for the time harmonic Maxwell system. This method is based on the use of a finite element grid, but uses plane wave solutions of Maxwell's equations on each element to approximate the global field. Because each basis function satisfies Maxwell's equations, the problem can be reduced to a coupled linear system on the faces of the grid. Arbitrarily high order of convergence can be achieved by taking more planes waves in suitable directions element by element, although ill-conditioning must be carefully controlled. Unfortunately this method has severe deficiencies when applied to some problems involving screens and transmission lines. To remedy this, we have coupled polynomial finite element methods with the plane wave scheme. I shall report on the current state of this effort.
When: 4:00 pm (Lubbock's local time is GMT -5)
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: 940 7062 3025
* Passcode: applied