# Applied & Computational Math

# Applied and Computational Mathematics

## Mathematical Theory, Modeling, and Computation

Across the application spectrum, theoretical modeling ranges from discrete (ODEs) to continuum (PDEs, integro-differential equations), which may be either deterministic or stochastic. Making quantitative predictions in applications often requires: the creation of models for the behavior of interest (i.e., the governing equations are not always *a priori* known); the development of analytical and computational tools and methods to solve (exactly, computationally, or asymptotically) the models and extract the relevant information from solutions; ways to visualize and learn from experimental or simulated data; and, the translation of the results of modeling, analysis, and computation to meaningful impacts on the application. These tools of analysis and computation are essential partners with experimental, clinical, and observational data toward advances in applications. All faculty in our program contribute to this fundamental, cross-cutting research area and its applications.

- David Adalsteinsson
- Roberto Camassa
- Greg Forest
- Boyce Griffith
- Kelli Hendrickson
- Jingfang Huang
- Shahar Kovalsky
- Karin Leiderman
- Richard McLaughlin
- Sorin Mitran
- Caroline Moosmueller
- Katie Newhall
- Pedro Saenz

## Mathematics Of Data Science

The field of Data Science is exploding across all dimensions of society. Mathematics lies at the heart of Data Science and is one of three pillars along with Statistics and Computer Science. Indeed, linear algebra is the workhorse behind all machine learning, deep learning, numerical optimization, image reconstruction, data compression, and many other algorithms and aspects of artificial intelligence. Learning from data has always been at the core of applied mathematics, exemplified by our Experimental Laboratories and by our collaborations with experimentalists and domain experts across science, engineering, biology, medicine, pharmacy, and health. We are furthermore deeply engaged with the new UNC School of Data Science and Society.

- David Adalsteinsson
- Greg Forest
- Jingfang Huang
- Shahar Kovalsky
- Karin Leiderman
- Sorin Mitran
- Caroline Moosmueller

## Mathematical Biology, Medicine, and Pharmacy

The research and entrepreneurial enterprises of biology, public health, medicine, and pharmacy are heavily integrated with applied and computational mathematics. Whereas historically these areas were deemed too complex for mathematical modeling and simulations, the perspective has flipped within these areas – their systems and questions, their experimental, clinical, and observational data are so complex that they cannot be understand *without* mathematical models and simulated data to orchestrate among all potential mechanisms to explain what happens, how, and what one can do to shift outcomes toward optimal and desirable versus harmful. Deep collaborations exist with colleagues in Applied Physical Sciences, Biology, Biomedical Engineering, the Blood Research Center, the Computational Medicine Program, the Eshelman School of Pharmacy, Marsico Lung Institute, McAllister Heart Institute, and Physics.

- David Adalsteinsson
- Greg Forest
- Boyce Griffith
- Karin Leiderman
- Sorin Mitran
- Caroline Moosmueller
- Katie Newhall

## Experimental Fluids and Computational Laboratories

The Joint Applied Mathematics and Marine Sciences Fluids Lab (JFL), led by Roberto Camassa and Rich McLaughlin, is an interdisciplinary research lab with the largest experimental footprint on the UNC Campus, hosting a 120 foot modular wavetank, tilting windtunnel, and many modern instruments for measuring fluid flows. The JFL is a collaborative effort spanning faculty, postdocs, graduates, undergraduates, and high school students. The Physical Mathematics Lab (PML), led by Pedro Saenz, studies problems that find motivation in physics and engineering, including hydrodynamic quantum analogs, soft and active matter, collective phenomena, and fluid mechanics. The projects are interdisciplinary and highly collaborative, in-situ experimental observations are used to inform and test the group’s mathematical theories and numerical simulations. The Cardiovascular Modeling and Simulation Lab, led by Boyce Griffith, develops methods of computational and applied mathematics, computer science, and bioengineering to develop physiological models of cardiac and cardiovascular function in health and disease.

- Roberto Camassa
- Boyce Griffith
- Kelli Hendrickson
- Jingfang Huang
- Karin Leiderman
- Rich McLaughlin
- Sorin Mitran
- Pedro Saenz