Relevant Seminars

RSS

Seminar Talk Announcement

  • Luca Carai (ICS CAS):

    TBA

    04.11.2026 16:00Plenary room (room. 318, second floor) Institute of Computer Science Applied Mathematical Logic Seminar

  • Jan Vybíral (Department of Mathematics, FNSPE, CTU, Prague):

    On positive and positive-definite functions: The story of one conjecture in the times of AI.

    10.11.2026 13:30 CETPlenary room (room. 318, second floor) Institute of Computer Science (ZOOM 914 0834 4018, 668534)Hora Informaticae

    Motivated by a problem from numerical analysis, we consider the conjecture of Erich Novak. Its statement has an appealing simple form, which involves only elementary notions from analysis and linear algebra. In its original form, this conjecture was posed in 1997 and remained open for many years. In 2010, Aicke Hinrichs and the author of the talk reformulated and generalized this conjecture and - supported by large numerical evidence - asked if for any positive and positive definite function f:R^d -> R with f(0)=1, the matrix (f(x_j-x_k)-1/n)_{j,k=1,...,n} is positive semi- definite for all points x_1,...,x_n from R^d. A partial solution of this conjecture was given in 2020 by the author if g=f^2, where f is positive definite. The general form of the conjecture remained open until Friday September 11, 2026, where a counterexample to the original conjecture was found by ChatGPT. We report on the whole story and on the newly found solution.

    [LINK]

Past Talks