Events
Department of Mathematics and Statistics
Texas Tech University
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. A simple weak Galerkin finite element method is introduced for second-order elliptic problems. First, we have proved that stabilizers are no longer needed for this WG element. Then we have proved the supercloseness of order two for the WG finite element solution. The numerical results confirm the theory.
This Job Colloquium is sponsored by the Applied Math seminar group. Please virtually attend Wednesday the 22nd at 4 PM CDT (UT-5) via this Zoom link.
This talk is based on a joint paper of Matan Mussel and Marshall Slemrod (Quarterly of Applied Mathematics, 2021) and provides two new applications of conservation laws in biology. The first is the application of the van der Waals fluid formalism for action potentials. The second is the application of the conservation laws of differential geometry (Gauss–Codazzi equations) to produce non-smooth surfaces representing Endoplasmic Reticulum.
Please virtually attend Dr. Slemrod's colloquium at noon (CDT, UT-5) on September 22nd via this Zoom link. Passcode: Slemrod
Capacity of sets and condensers in Euclidean spaces has been an object of study by researchers working in several areas of Analysis and Geometry due to its applications and the important role it plays in physics.
In the first part of this talk, we will present some basic facts about condenser capacities and their connection and applications to conformal mappings. We will also present our solution to the conjecture of J. Ferrand, G. Martin and M. Vuorinen from 1991.
In the second part we will introduce composition operators and we will examine their behavior in several Banach spaces of holomorphic functions in the unit disc. Our solution of a problem posed by J. Laitila in 2010 about isometric composition operators will be presented and we will describe the connection of the approximation numbers of an operator with condenser capacity.
Dr. Pouliasis' Third Year Review Colloquium may be virtually attended via this Zoom link. Passcode: Pouliasis Let $\varphi$ be an automorphism of the unit disc $\mathbb{D}$ and let $W_{\varphi}^{\alpha}$ be the weighted composition operator, acting on a Banach space of analytic functions in the unit disc, defined by $W_{\varphi}^{\alpha} f= (f \circ \varphi)(\varphi')^{\alpha}$ with $\alpha>0$. We observe that many common examples of Banach spaces of analytic functions like Korenblum growth classes, Hardy spaces, standard weighted Bergman and certain Besov spaces are invariant under these operators. Thus, the main goal of this talk will be to present a general approach to the spaces that satisfy this weighted conformal invariance property. Among other things, we will identify the largest and the smallest as well as the ``unique'' Hilbert space satisfying this property for a given $\alpha >0$. These results are part of a joint work together with Professor Alexandru Aleman.
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In this talk, I will state the main theorem and begin introducing the background needed to understand the statement. I will begin by briefly reviewing the theory of simplicial presheaves and their localizations. Online video streaming is available, see https://dmitripavlov.org/geometryAbstract:
Accurate estimation and optimal control of tail risk is important for building portfolios with desirable properties,
especially when dealing with a large set of assets.
We consider optimal asset allocation strategies based on the minimization of two asymmetric deviation measures,
related to quantile and expectile regression, respectively.
Their properties are discussed in relation with the ‘risk quadrangle’ framework introduced by Rockafellar and Uryasev (2013),
and compared to traditional strategies, such as the mean-variance portfolio.
In order to control estimation error and improve the out-of-sample performances of the proposed models,
we include ridge and elastic-net regularization penalties.
We also propose an application of the framework to the enhanced index replication problem,
that aims to minimize the asymmetric risk measures related to the expectile,
while controlling for the distance from a benchmark by penalizing the deviation of the portfolio weights compared to the ones in an index.
Our approach aims to address the needs of investors interested in smart beta products (systematic strategies that
aim to maintain costs smaller than traditional active strategies) in a market context where cheap ETFs are available.
The analysis is supported by an empirical study on the real data.