Project 1: Disconnected quark loops In lattice Quantum Chromodynamics (LQCD), the calculation of physical quantities from disconnected quark loop calculations have large variance due to the use of noise methods for the estimation of the trace of the inverse lattice Dirac operator. In collaboration with Dr. Ronald Morgan of the Baylor Mathematics Department, we have developed a new numerical approach which we call multilevel Monte Carlo. It combines off-diagonal subtraction via high-degree GMRES polynomials, eigenvalue deflation, multisubtraction levels, and the use of GMRES double-polynomials. Our work was presented at the Numerical Challenges Workshop at Meinerzhagen, Germany. Attached are papers which outline these techniques. High-Degree Polynomial Noise Subtraction Multi-Polynomial Monte Carlo for Trace Estimation in Lattice QCD

Project 2: Electric and magnetic polarizability of pions and protons I am presently investigating the use of an innovative lattice QCD time summation technique for directly evaluating particle electric and magnetic polarizabilities. This avoids introducing external fields on the lattice. This work is being done in collaboration with Frank X. Lee of The George Washington University. These techniques also can be used to calculate hadron structure functions. Attached below is our charged pion magnetic polarizability paper. Four-point Magnetic Polarizability

Project 3: Thomas-Fermi quark model The standard theoretical methods to investigate multiquark states is LQCD. For large nuclear systems LQCD has a major disadvantage: with increasing quark content, it becomes too computationally expensive and time-intensive to do the lattice calculations. To investigate the dynamics of such exotic states more cheaply, the Thomas-Fermi statistical quark model was developed \cite{Walter} as an alternative. I work with Profs. Suman Baral of NCCC, New York, and Gopi Kaphle, Tribhuvan University, Nepal. Our latest paper is listed below. Investigation of quark distributions in a family of pentaquarks using the Thomasâ€“Fermi quark model

Besides the above, I am working on other topics in the lattice field as well. I am indebted to many colleagues and organizations for the progress made on these subjects and other research work. Most of my computer time comes through grants from the Texas Advanced Computing Center (TACC) at the University of Texas. I have also had supporting monetary grants from the National Science Foundation (NSF).