Our faculty work in a variety of areas in mathematics and statistics, which may be grouped into four main areas:

## Applied and Computational Mathematics

This research focuses on areas most important in science and engineering. Our work includes the development of both analytical and computational techniques for the solution of differential equations.

Current projects related to the analysis of PDE’s include the effect of diffusion on reaction-diffusion equations. Some basic questions in this area are:

- How does diffusion change the shape and the local stability of steady states?
- How does it change the global dynamics?
- How do we design a nano-material with a periodic structure so that it optimizes heat-protection?

In computational mathematics, our group works on several aspects of fluid motion and its interaction with elastic structures immersed in the fluid. Specifically, our projects involve:

- Biological applications of fluid motion, such as the motility of microorganisms (bacteria, cells, spermatozoa, etc.)
- The flow of liquids in flexible tubes (blood vessels)
- The evolution of biofilms and more

In addition, our group works on the design of numerical methods for the simulation of compressible flows which may contain shocks or other discontinuities.

Faculty members working in these areas include:

- Professor James (Mac) Hyman
- Professor Lisa Fauci
- Professor Ricardo Cortez
- Professor Scott McKinley
- Professor Kun Zhao
- Professor Nathan Glatt-Holtz

## Algebra and Theoretical Computer Science

The Algebra and Theoretical Computer Science group is one of the most active in the department. The group's research focuses on abstract algebra and the foundations of computer science with interests in combinatorics and symbolic computation.

### Algebra Research

Within algebra, the group's research interests include semigroups, partially ordered structures, abelian groups, rings and modules, division rings, category theory and coalgebras. Focus is on Prüfer and Prüfer-like domains, modules, and commutative semigroups.

### Theoretical Computer Science Research

Research includes domain theory, category theory, non-well-founded set theory, models for probabilistic computation, labeled Markov processes, and the semantics of concurrency. Focus is on programming semantics and models of computation, and on applications to crypto-protocols and embedded hybrid systems.

The journal **Semigroup Forum** and the electronic series Electronic Notes in Theoretical Computer Science were founded and are still edited at Tulane.

Tulane also plays a prominent role in the annual series of meetings **Mathematical Foundations of Programming Semantics**.

### Participating faculty

The group consists of regular faculty:

- Professor Mahir Can
- Professor Tài Huy Hà
- Professor Michael Mislove
- Professor Victor Moll
- Adjunct Professor Karl Hofmann

Prof. Tài Huy Hà's research interest lies in the interactions between algebraic geometry, computational algebra and combinatorics. He studies syzygies and (arithmetic) Macaulayfication of schemes, monomial ideals and edge ideals of hypergraphs, Castelnuvo-Mumford and multigraded regularity. His recent work focuses on applying techniques and methods in computational algebra to tackle problems and questions in combinatorics and optimization.

Professor Michael Mislove is the author of over 60 research articles. He is also an editor of Semi-group Forum, Theoretical Computer Science, Electronic Notes in Theoretical Computer Science, and a number of conference proceedings . His current interests include topological algebra, domain theory, non-well-founded set theory, and theoretical computation, especially the semantics of languages supporting nondeterminism and concurrency. His recent results focus on labeled Markov processes as models of probabilistic computation, and he has devised models that support both probabilistic and nondeterministic choice operators.

Professor Victor Moll is a classical analyst with longstanding interests in symbolic computation, special functions and number theory. He is the author of a book on Elliptic Curves (joint with Henry McKean) and the book "Irresistible Integrals" (joint with George Boros).

Adjunct Professor Karl Hofmann is a prominent expert on Lie groups and Lie semigroups, as well as many other areas of topological algebra. He makes regular visits to Tulane, during which he participates in both the Algebra-TCS Seminar and the Algebra Seminar.

## Topology and Geometry

The research interests of the members of the Topology & Geometry group spans a wide variety of areas. In geometry these include:

- Various questions related to the curvature properties of Riemannian manifolds
- Geometry of symplectic manifolds
- Bundle theoretic problems in algebraic geometry
- Applications of partial differential equations in geometry of complex manifolds

In topology, research centers around:

- Theory of Continua and Dynamical Systems
- Transformation Groups and Surgery Theory
- Participating Faculty

The group consists of regular faculty:

- Professor Albert Vitter III
- Professor Morris Kalka
- Professor David Yang
- Professor Rafal Komendarczyk
- Professor Albert Slawomir Kwasik

## Probability and Statistics

The group consists of regular faculty:

- Professor Michelle Lacey
- Professor Gustavo Didier
- Professor Scott McKinley
- Professor Nathan Glatt-Holtz