Speaker: Micha Sharir (TAU) Title: Improved bounds on counting and cutting cycles of lines in space Abstract: Given n lines in 3-space in general position, their depth relation can contain cycles, and the goal, motivated by applications to hidden surface removal in computer graphics, is to cut the lines into a small number of pieces so that all cycles are eliminated. A quadratic number of cuts is always sufficient, and there are configurations where Omega(n^{3/2}) cuts are needed. The problem was deemed in the past to be hopelessly difficult, and only very few partial and weak bounds have been obtained, using fairly complicated machinery. In this talk I will show that, using the new algebraic machinery, one can solve this problem in a fairly (and embarassingly) simple manner, and get bounds close to n^{3/2}. The approach can also be successfully applied to more involved situations. Joint work with Boris Aronov