Events
Department of Mathematics and Statistics
Texas Tech University
Please virtually attend this week's Statistics seminar/qualifying exam at 4:15 PM Monday the 19th via this zoom link, passcode 7HxN4T
The Schwarzian derivative is intimately connected to criteria for univalence and quasiconformal extension. Recently, many of these results have been generalized from the classical (analytic) setting to harmonic mappings. In this talk we will show the existence of a quasiconformal extension to the complex plane for harmonic mappings defined on finitely connected domains whose boundary has the appropriate geometry, thus generalizing a result of Osgood (1980). Moreover, we will give two explicit quasiconformal extensions for harmonic mappings defined in the unit disk. When applied to analytic functions these extensions reduce to the one given by Ahlfors and Weill (1962).
To join the zoom meeting for the Analysis Seminar click
here.
Optimal control problems constrained by PDEs are certainly among the most interesting and challenging topics in mathematics. Not only is that the case for the practical applications, but also for the underlying theoretical and computational questions that arise in their study. We will address some of these questions for a certain class of optimal control problems where boundary data act as the steering force, and where the constraint equations are typical models in continuum mechanics.
Please virtually attend this week's PDGMP seminar at 3 PM Wednesday the 21st at this zoom link.
In this talk, I will mostly focus on large homomorphisms of local
rings introduced by Gerson Levin in 1979. Some examples and
characterization of large homomorphisms in terms of Koszul homologies
over complete intersection and Golod local rings will be
addressed. Next, I will discuss some conditions under which a
homomorphism from (or in to) a Koszul algebra is large, small, or
Golod. In the last part of the talk, I will focus on a specific class
of local rings namely minimal intersections. We will see that the
largeness or smallness of the natural maps to a minimal intersection
(R,m,k) enables us to give a formula for the Poincare series of k.
Join Zoom Meeting https://zoom.us/j/96217128540?pwd=NjU5dzE2RjZvV0prejhOOWVjVENadz09
Meeting ID: 962 1712 8540
Passcode: 474170
In this talk, we will present a method for learning interpretable, thermodynamically stable and Galilean invariant partial differential equations (PDEs) based on the Conservation-dissipation Formalism of irreversible thermodynamics. As governing equations for non-equilibrium flows in one dimension, the learned PDEs are parameterized by fully-connected neural networks and satisfy the conservation-dissipation principle automatically. In particular, they are hyperbolic balance laws and Galilean invariant. The training data are generated from a kinetic model with smooth initial data. Numerical results indicate that the learned PDEs can achieve good accuracy in a wide range of Knudsen numbers. Remarkably, the learned dynamics can give satisfactory results with randomly sampled discontinuous initial data and Sod's shock tube problem although it is trained only with smooth initial data.
Please virtually attend the Applied Math seminar on Wednesday the 21st at 4 PM (UTC - 5) via this zoom link.