## Mathematics professor wins Fulbright Fellowship

Keith Kearnes, a professor of mathematics at the University of Colorado, has been awarded a Fulbright Fellowship for fall semester 2010 to collaborate with a group of researchers in Hungary on applications of relational clones to algebra and theoretical computer science.

“The mathematical problem I will work on is that of starting with a system of equations where one knows all solutions to each individual equation and must decide if there is a simultaneous solution to the entire system,” Kearnes said. “This is a problem that comes up all the time in mathematics and everyday life.”

“For example, I may have 100 containers of materials that must be stored in three rooms, and it may happen that some pairs of containers cannot be stored in the same room because they form a hazardous combination. If I am given a list of the hazardous pairs of containers, then I can encode the information in a system of equations,” he continued.

“Checking to see if two containers form a hazardous pair is as easy as looking at the list of such pairs, or equivalently solving one equation in my system. If a pair is hazardous, then the two containers must be stored separately, while if the pair is not hazardous they may be stored separately or together. Easy. But it is a very difficult problem to see if all 100 containers can be stored safely in only 3 rooms, a problem equivalent to finding a simultaneous solution to the entire system in a 3-valued algebraic system.”

This type of work involves algebra, combinatorics (the study of finite or countable discrete structure) and algorithm design.

Kearnes, who earned his Ph.D. from the University of California at Berkeley in 1988, is an author on more than 70 scholarly articles and co-author of the book “The Shape of Congruence Lattices.”

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