Research Highlights

Disproof of Wall’s Conjecture
During the June 2012 AIM workshop, “Cohomology bounds and growth rates” a counterexample was found to a group theory conjecture formulated by G. E. Wall in 1961. A mathematical group is a set along with an operation that combines two elements to form a third element […]

Distinguishing Knots
An old question in mathematics is: how can we distinguish between knots? If we imagine a knot tied out of a piece of rope, the most basic problem is to tell if the knot can be “undone” by moving the rope around without breaking it. Although it may be difficult to see immediately, the following […]

Symplectic Dynamics
During the 20112012 academic year, the School of Mathematics held a special program on Symplectic Dynamics led by Helmut Hofer and John Mather. Symplectic Dynamics is an anticipated new field focusing on Hamiltonian systems using highly integrated ideas from the theory of dynamical systems and symplectic geometry. In recent years a number […]

AI for Chemical Design
Exploration of chemical compound space unites quantum chemistry with artificial intelligence By combining quantum chemistry with artificial intelligence (AI) or Machine Learning, core participants of the long program, “Navigating Chemical Compound Space for Bio and Materials Design”, achieved a scientific breakthrough expected to aid in exploring chemical compound space, i.e. the virtual […]

Strawberry Fields Forever
How does our society conserve water resources and still enjoy an abundant food supply? The Pajaro Valley, in the Monterey Bay area of California, is ideally suited for agriculture. There one can see acres and acres of fruit trees, vegetable, berries, and flowers. In fact, the Pajaro Valley and the nearby Salinas Valley produce nearly […]

Understanding Microtubules
Microtubules are hollow rods approximately 25 nanometers in diameter. They undergo continual assembly and disassembly within a living cell and serve as longdistance “superhighways” for motorbased intracellular transport. The dynamics of microtubule selfassembly are of great interest for medical reasons since microtubule assemblypromoting drugs are used to treat cancer. More recently, they have been used […]

Math of Planet Earth
Mathematics of Planet Earth 2013 An initiative to devote the year 2013 to mathematics of the planet earth was begun by the thirteen North American mathematics institutes and now also includes mathematical societies and other scientific organizations from around the world. The goal of event is to highlight the […]

Fractal® Sound Barrier
The study of the vibrations in domains with boundaries or interfaces of irregular geometry is a complex mathematical problem, for which many questions are still unsolved. Nevertheless, it has been known for a long time that objects of irregular shape or geometry are “bad resonators.” From the seminal work of Bernard Sapoval, a physicist at […]

Galois Representations
During both terms of the 201011 year, the School of Mathematics held a special program on Galois Representations and Automorphic Forms. The program was organized by the School’s Distinguished Visiting Professor, Richard Taylor of Harvard University. The program had about 33 longterm participants and many other people visited for shorter periods. Six […]

GPS Algorithms
The Global Positioning System (GPS) is global navigation system consisting of at least twentyfour satellites orbiting in six planes around the earth. GPS is extensively used by both the military and the FAA, with growing applications in civilian markets. The importance of GPS […]