Wednesday, December 9, 1530-1630. |
SPEAKER :
Aviezri Fraenkel, Weizmann Institute of Science, Israel.
TITLE : Which conjectures stimulate new directons in mathematics ?
ABSTRACT : Fermat's Last Theorem was formulated by Pierre Fermat in 1637 and was finally proved by Andrew Wiles in 1995, towering over the shoulders of many famous mathematicians who developed algebraic number theory, theories of elliptic curves over the rationals, modular and automorphic forms, representation theory, Langlands program, to offer just a few.
I'll discuss a few recent conjectures in the general area of discrete math and combinatorial number theory. Two of them were proved quickly and a third was disproved even more quickly. A fourth is an easily stated 36 years old conjecture. It concerns a problem which was completely solved for the integers, completely solved for the irrationals, but is wide open for the rationals! Will it have some influence on mathematics? In the meantime it has precipitated the Japanese remainder theorem and used notions such as balanced sequences and the discrete Fourier transform in proof attempts. The conjecture has applications in job scheduling theories, for which special cases have been solved.
Conclusion: Intriguing conjectures everybody can understand, nobody can settle, precipitate new mathematical insights over time.
Monday, December 14, 1530-1630. |
SPEAKER :
Christer Borell, Chalmers
TITLE : Convexity inequalities.
ABSTRACT :
In this talk different convexity inequalities for real functions, positive measures, equilibrium potentials, and utility functions will be discussed. Several unsolved problems in convex geometry are exhibited.