The UCF Mathematics and Applications Seminar, which takes place every Friday from 10:30-11:30 a.m. in MSB 318, provides a venue for researchers to present their current work, foster new collaborations, and showcase both foundational mathematics and its applications to graduate and undergraduate students.
Dr. Abey Lopez-Garcia will be speaking at this seminar about asymptotic properties of greedy energy sequences.
Abstract: In this talk I will discuss asymptotic properties of greedy energy sequences on compact subsets of a Euclidean space, with special emphasis in the case of the unit circle in the plane. Such infinite sequences are constructed by a greedy algorithm, in which the discrete potential generated by the first n points of the sequence is minimized at the (n+1)-st point, for each index n. The study of the asymptotic properties of such sequences was initiated by the Polish school of F. Leja in the 1950s and in the context of Newtonian potentials. In recent decades they have attracted an increasing interest due to several reasons: the relatively low cost for their construction, their good distribution properties and their nearly optimal properties in interpolation and energy minimization problems. In this talk I will mainly focus on the asymptotic properties of the optimal values of potentials generated by these sequences on the unit circle in the case of the logarithmic and Riesz potentials, describing some recent results obtained with E. Miña-Díaz.
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