Research Interests

Research conducted in Dr. Vasquez's group spans a broad range of topics related to the mathematical modeling of complex fluids and soft matter including multiscale modeling and simulation of viscoelastic fluid flows, viscoelastic and diffusive transport processes in biopolymers, dynamic organization of chromosomes in yeast cells, and pituitary organogenesis.

The common thread in their research is the close collaboration between mathematicians and researchers from the biology, physics, chemistry and engineering fields. Dr. Vasquez has established the Complex Fluids Lab as part of the Math Department at USC. This lab is used both as a complement to our modeling and simulation approaches and as educational tool whose main objective is to show math majors how to apply experimental principles to formulate mathematical models and to interpret the data; and to non-math majors how models provide rigorous information about a given process arising from experimental data and once formulated and solved, afford predictions beyond the experiments.

Education

• Ph.D. in Applied Mathematics, University of Delaware (2007)
• M.B.A., Goldey-Beacom College (2002)
• B.S., Facultad de Minas, Universidad Nacional de Colombia (1998)

Experience

• Associate Professor, University of South Carolina (2019 – present)
• Assistant Professor, University of South Carolina (2013 – 2019)
• Postdoctoral Fellow, University of North Carolina at Chapel Hill (2010 – 2013)
• Postdoctoral Fellow, University of Delaware (2004 – 2007)

Courses Taught

• MATH 141: Calculus I
• MATH 142: Calculus II
• MATH 172: Math Modeling for the Life Sciences
• MATH 520: Ordinary Differential Equations
• MATH 544: Linear Algebra
• MATH 550: Vector Analysis
• MATH 599: Topics in Mathematics
• BIOL 599: Topics in Biology
• MATH 709: Foundations of Computational Mathematics II
• MATH 720: Applied Mathematics I
• MATH 728: Selected Topics in Applied Mathematics

Selected Publications

• H. Kim, J. L. Bauer, P.A. Vasquez and E.M. Furst. “Structural coarsening of magnetic ellipsoid particle suspensions driven in toggled fields.” Journal of Physics D: Applied Physics, 52.18 (2019): 184002.
• C. Hult, D. Adalsteinsson, P.A. Vasquez, J. Lawrimore, M. Bennett, A. York, D. Cook, E. Yeh, M.G. Forest, and K. Bloom. “Enrichment of dynamic chromosomal crosslinks drive phase separation of the nucleolus.” Nucleic Acids Research, 45(19), 11159-11173, 2017.
• J. Lawrimore, T.M. Barry, R.M. Barry, A.C. York, B. Friedman, D.M. Cook, K. Akialis, J. Tyler, P.A. Vasquez, E. Yeh, and K. Bloom. "Microtubule dynamics drive enhanced chromatin motion and mobilize telomeres in response to DNA damage." Molecular Biology of the Cell, 28(12), 1701-1711, 2017.
• P.A. Vasquez, C. Hult, D. Adalsteinsson, J. Lawrimore, M.G. Forest, and K. Bloom. "Entropy gives rise to topologically associating domains." Nucleic Acids Research, 44(12), 5540-5549, 2016.
• M. Lysy, N.S. Pillai, D.B. Hill, M.G. Forest, J. Mellnik, P.A. Vasquez, and S.A. McKinley. "Model comparison and assessment for single particle tracking in biological fluids." Journal of the American Statistical Association, 111(516), 1413-1426, 2016.
• P.A. Vasquez, Y. Jin, E. Palmer, D.B. Hill, and G. Forest, “Modeling and Simulation of Mucus Flow in Human Bronchial Epithelial Cell Cultures – Part I: Idealized Axisymmetric Swirling Flow.” PLOS Comput Biol 12(8), e1004872, 2016.