Events
Department of Mathematics and Statistics
Texas Tech University
Many continuous time stochastic systems that are modeled by SDE and SPDE have been limited to noise processes being Brownian motions. Brownian motion models have a well developed stochastic calculus and limiting behaviors that reflect the martingale, Markov and Gaussian properties of Brownian motion. However for many physical systems the empirical data do not justify the use of Brownian motion as the model for random disturbances. In fact Brownian motions provide models that are often far from the physical data. Thus it is necessary to find more general noise models and tractable methods to solve the associated problems of control or adaptive control. These other noise models include more general Gaussian processes and non-Gaussian processes. The talk focuses on new developments and new challenges in noise models for stochastic control and adaptive control problems.
Dr. Pasik-Duncan's colloquium is held in conjunction with the Applied Math seminar group. Virtually attend this colloquium at 4 PM CST (UTC -5) via this zoom link. The literature on the optimal harvest of fisheries has concentrated on a single fishing area with biomass uncertainty and to a lesser degree also with price uncertainty. We develop and implement a stochastic optimal control approach to determine the harvest that maximizes the value of a fishery participating in a global market, where all the considered harvesting zones sell their production. This market is characterized by an
inverse demand function, which combines an exogenous demand shock and the aggregate harvesting of all zones. Accordingly, a fishery's harvest will be affected by the global demand shocks and the harvesting in all the competing zones through the global selling price. In addition, we decompose the biomass uncertainty into local and global biomass shocks. Through global biomass shocks, the model provides enough flexibility
to acknowledge for correlation in the biomass shocks faced by the multiple perhaps adjacent areas. When we compare our global framework with an alternative where the individual
zones are aggregated into a single optimizing fishery we find that competition will increase the global harvest and consequently reduced the resource price.
This Colloquium is co-hosted with the Mathematical Finance seminar group. Join us at 4 PM CST (UTC-5) via this zoom link, passcode 886878 The regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation is discussed in both its scalar and vector forms. In particular, we examine integrability
criteria for the regularity of solutions in terms of the scalar solution $\phi$, the vector solution $u=\nabla\phi$, as well as the divergence $div(u)=\Delta\phi$, and each component of $u$ and $\nabla u$.
To join the zoom meeting for the Analysis Seminar click
here.
This is an expository talk about a subject about which the speaker is currently learning. The theory of regularity structures was invented by Martin Hairer in 2014 (for which he won the Fields Medal). In short, many equations in physics such as Kardar-Parisi-Zhang equation, parabolic Anderson model, Phi4 model from quantum field theory, and even Navier-Stokes equations, were studied under the forcing by white noise (typically white in both space and time) which was so singular that the most fundamental question about the existence of its solution was not proven rigorously. In fact, solutions in the classical sense (or even weak sense) actually do not exist. The theory of regularity structures was a first (along with the theory of paracontrolled distributions due to Gubinelli et al.) systematic way to actually prove the existence of a limiting solution (after much work of renormalization, computing Wick products, and writing tree diagrams akin to Feynman diagrams). Its impact has been immense and has generated waves of new results in many related fields (even stochastic quantization of Yang-Mills).
Please virtually attend this seminar via this zoom link Wednesday the 14th at 3 PM.In the 1950s Serre introduced an algebraic invariant for regular local
rings to measure the geometric notion of intersection multiplicity of
curves, and proposed a number of conjectures about its
behavior. Hochster, and later Dao, studied generalizations of this
invariant for hypersurface and complete intersection rings. This talk
will focus on the case of a graded complete intersection ring, where
we will show vanishing of a closely related invariant under
assumptions on the complexity of a pair of modules. Our main tool is
to draw a connection between this invariant and work of Avramov,
Buchweitz, and Sally involving orders of Laurent series. This is on
joint work with David Jorgensen and Liana Sega.
Join Zoom Meeting https://zoom.us/j/96217128540?pwd=NjU5dzE2RjZvV0prejhOOWVjVENadz09
Meeting ID: 962 1712 8540
Passcode: 474170