- Associate Professor Emeritus of Mathematics
David P. Kraines
Research Areas and Keywords
Dr. Kraines contributed to the theory of homology and cohomology operations, particularly to Massey products and loop operations. Among the applications of his work has been his construction of the counterexample to the transfer conjecture of Quillen. He has also studied the variational bicomplex of Vinogradov and introduced the cohomology of quantum electrodynamics. Dr. Kraines has applied game theoretical techniques to study the evolution of cooperation. With Dr. Vivian Kraines, he introduced a stochastic learning approach, dubbed the Pavlov strategy, for the iterated Prisoner's Dilemma. They show that, in a noisy environment, agents using the Pavlov strategy may achieve a higher level of cooperation than those using Tit for Tat type strategies. Using computer simulations, dynamic systems and Markov chains, they extend their analysis to the evolution of the rate of learning in a society of Pavlov type agents. Recently, they have explored the natural selection of stochastic strategies in the simultaneous and the alternating Prisoner's Dilemma and identified several evolutionarily stable strategies.
Drachman, B, and Kraines, D. "A duality between transpotence elements and Massey products." Pacific Journal of Mathematics 39.1 (October 1, 1971): 119-123. Full Text
Kraines, D. "Rational cohomology operations and Massey products." Proceedings of the American Mathematical Society 22.1 (January 1, 1969): 238-238. Full Text
Kraines, D. "Primitive chains and H*(ΩX)." Topology 8.1 (1969): 31-38.
After 45 years teaching at Duke, David Kraines will become emeritus at Duke this summer. Kraines attended Oberlin College and the University of California at Berkeley where he received his doctorate in 1965 under the supervision of Ed Spanier. After... read more »
The Blue Devils may have lost in the Sweet 16 during March Madness 2016, but a Duke team crushed more than 500 other schools in the NCAA tournament of the math world, known by mathletes as ... read more »
Six students have been named 2016 PRUV Fellows and will work on a variety of research projects from algebraic geometry and number theory to modeling biological systems. They are Trung Can, Matthew Gherman, Feng Gui, Mendel... read more »
The Duke Putnam team finished 10th among 577 colleges and universities in the 76th W.L Putnam Mathematical Competition. The student coach of the team, Alex Milu’15, received Honorable Mention (top 2%) and Trung Can ’18... read more »