Predavanje dr Keith Rogers-a

Dr Keith Rogers, istraživač na Institutu Matematičkih nauka u Španiji, održaće predavanje pod nazivom Improved bounds for the Kakeya conjecture using semialgebraic geometry u srijedu, 6. marta u 12h u amfiteatru 013. U nastavku je sažetak predavanja.

The Kakeya problem considers tubes which point in different directions and the extent to which they can be compressed by positioning them strategically. On the one hand, we will see that the measure of any semialgebraic set that contains the tubes must satisfy the expected bound. That is to say, the tubes cannot be compressed too much if they are positioned in an algebraic way. The proof employs tools from real algebraic geometry including the Tarski-Seidenberg projection theorem and the Gromov-Yomdin algebraic lemma. On the other hand, the expected bound holds in the absence of algebraic structure, by polynomial partitioning. Balancing between the two extremes yields improved bounds for the Kakeya maximal conjecture in higher dimensions. This is joint work with J. Hickman, N. Katz and R. Zhang.

Pozivamo sve zainteresovane studente i profesore da prisustvuju predavanju.