Events
Department of Mathematics and Statistics
Texas Tech University
A complex adaptive system (CAS) is a system that is complex in that it is a dynamic network of interactions, but the behavior of the ensemble may not be predictable according to the behavior of the components. Social insect colonies; the brain; the immune system; and human social group-based endeavors are excellent examples of complex adaptive. Mathematical models are powerful tools that can provide us quantitative approaches to
elucidate complicated ecological and evolutionary processes on the numerous spatial, temporal and hierarchical scales at which CAS such as social insect colonies and/or human groups operate. In this talk, I will review some of our recent collaborative work with biologists and psychologists regarding important and interesting questions of CAS such as how information spreads in the social insect colonies? How may we define and model trust dynamics in human and robotic teaming? I will particularly present our modeling work through ODE, SDE and evolutionary models on addressing ...
1. How do task organization and work performance scale with colony size and metabolism?
2. How does environment impact task allocation?
3. What are co-evolutionary dynamical outcomes of the interaction of social parasite and host?
This Biomath seminar may be attended Monday the 21st at 4:00 PM CST (UT-6) via this Zoom link. Meeting ID: 839 9465 7333 Passcode: BfriM6
The symmetric decreasing rearrangement (symmetrization) of a function $f$ in
$n$ variables is the unique radially decreasing function $Sf$ equimeasurable
with $f$. Classical inequalities tell us that symmetrization reduces the overall
oscillation of functions; for instance, it shrinks $L^p$-distances and decreases
gradient norms. But how does symmetrization behave with respect to mean oscillation?
In this talk, I will describe some recent results with Almut Burchard and Galia Dafni.
To join the talk on Zoom please click
here.
We consider the asymptotic limits of two dimensional incompressible stochastic Navier Stokes equation and one dimensional stochastic Schrodinger equation. These limits include large and moderate deviations, central limit theorem, and the law of the iterated logarithm. For large and moderate deviations, we will discuss both the Azencott method and the weak convergence approach and show how they can be used to derive the Strassen's compact law of the iterated logarithm. The exit problem will also be given as an application.
Watch online via this Zoom link.This is an expository/introductory talk concerning transport equation that appears in various problems of mathematical physics such as fluid mechanics and kinetic theory. The unknown of this equation is density that is transported by a given vector field. Often, the velocity that transports the density is too rough to admit the uniqueness of the solution. One of the most important works is due to DiPerna and Lions in 1989 in which they introduced a notion of ``renormalized solution'' and proved the uniqueness with a surprisingly rough vector field. While the competition to reduce the smoothness of the given vector field and still retain uniqueness was continued by many, via a new breakthrough technique called ```convex integration,'' some researchers very recently proved non-uniqueness with a surprisingly smooth vector field (even with arbitrarily strong diffusion).
Please virtually attend the Applied Math seminar via this Zoom link Wednesday the 23rd at 4 PM -- meeting ID: 937 2431 1192
Let $(R,\mathfrak{m},\Bbbk)$ be a regular local ring of dimension
3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. Buchsbaum and
Eisenbud proved that there is a skew-symmetric matrix of odd size such
that $I$ is generated by the sub-maximal pfaffians of this matrix. Let
$J$ be the ideal obtained by multiplying some of the pfaffian
generators of $I$ by $\mathfrak{m}$; we say that $J$ is a trimming of
$I$. In this paper we construct an explicit free resolution of $R/J$
with a DG algebra structure. Our work builds upon a recent paper of
Vandebogert. We use our DG algebra resolution to prove that recent
conjectures of Christensen, Veliche and Weyman on ideals of class
$\mathbf{G}$ hold true in our context.
Join Zoom Meeting https://texastech.zoom.us/j/97115201141?pwd=N0YwcDkzTDc4bC9JYS9kVFQ1bFh2UT09
Meeting ID: 971 1520 1141
Passcode: 900450
The persistence of low interest rates is spurring research on the question how to increase yields,
while limiting the variability of long-term investment payouts.
Under the benchmark approach it is possible to achieve attractive, almost riskless,
non-fluctuating long-term investment results.
Payouts of savings account units that achieve an almost riskless outcome over a long time period
can be hedged reliably as contingent claims by using a stock index and a savings account.
This dynamic asset allocation can be performed in a less expensive manner than by traditional valuation methods.
The benchmark approach is using real-world pricing,
which provides the least expensive hedging strategy for replicable contingent claims.