Events
Department of Mathematics and Statistics
Texas Tech University
Abstract pdf
This Job Colloquium is sponsored by the Applied Math seminar group. Please virtually attend Wednesday the 20th at 4 PM CDT (UT-5) via this Zoom link.
This is a general talk about recent breakthroughs in the fields of PDEs in Fluid and Stochastic PDEs in Mathematical Physics, representative of my research interests for the past several years. Concerning the first direction, whether a solution to the three-dimensional Navier-Stokes equations starting from a smooth initial data exists uniquely for all time with kinetic energy bounds remains an outstanding open problem in Analysis of PDEs. As a significant step forward, very recently, De Lellis, Szekelyhidi Jr., Buckmaster, Vicol et al. have obtained breakthroughs proving non-uniqueness if we start from non-smooth initial data. Concerning the second direction, while there exist many PDEs in physics literature forced by space-time white noise (e.g., Kardar-Parisi-Zhang equation, Phi4 model in quantum field theory, Yang-Mills), the singularity of such noise caused the non-linear terms therein to be ill-defined. Very recently, Hairer, Gubinelli, Imkeller, Perkowski et al. have established new uniform methods to attain solution theory for such singular PDEs. This talk is intended for a general audience to provide the ideas of these research directions.
This Third Year Review Colloquium is held in tandem with the PDGMP seminar group, and may be virtually attended on the 21st via this Zoom link.
Both climate and human systems are impacting our risk of mosquito-borne diseases. To be able to forecast risk in the short term and predict change in risk longer-term, we combine mathematical and statistical models with weather, satellite, demographic, and Google Health trends data. We focus on a few areas with high-fidelity data to show that accurate predictions are possible with the help of heterogeneous, time varying data. I will also address the challenges of transferability, including integration of earth systems, mosquito population, and disease models.
This Colloquium is sponsored by the TTU chapter of SIAM. Please virtually attend Friday the 22nd at 3:00PM CDT (UT-5) via this Zoom link.
We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In view of Taylor's conjecture, this proves that there exist finite energy weak solutions to ideal MHD which cannot be attained in the infinite conductivity and zero viscosity limit. Our proof is based on a Nash-type convex integration scheme with intermittent building blocks adapted to the geometry of the MHD system. Based on joint work with Tristan Buckmaster and Vlad Vicol.
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Online video streaming is available, see https://dmitripavlov.org/geometryWe empirically examine the equity portfolio choices of investors with generalized disappointment aversion (GDA) preferences. Contrary to expected utility investors, GDA investors suffer, out-of-sample, large monetary utility losses from suboptimal portfolio choices such as equally weighted portfolios. These losses increase in the level of disappointment aversion and the number of stocks available for investment. A novel semi-parametric method based on L-moments enables us to study the impact of very high order moments on portfolio choice. Higher order moments, beyond four, are as important as lower order moments in explaining portfolio choice of investors.
Please virtually attend on Friday at 2 PM CDT (UT-5) via this Zoom link.