SEMINAR:Energy Bounds For Weighted Spherical Codes And Designs Via...
Guest: Peter Boyvalenkov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
Title: Energy Bounds For Weighted Spherical Codes And Designs Via Linear Programming (MATH, CS)
Date/Time: February 5, 2025, 13:40
Location: FENS G032
Abstract:Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar every attaining code is optimal with respect to a large class of potential functions (absolutely monotone), in the sense of Levenshtein there is a bound for every weighted code, and in the sense of parameters (nodes and weights) they are independent of the potential function. We derive a necessary condition for optimality (in the linear programming framework) of our lower bounds which is also shown to be su cient when the potential is strictly absolutely monotone. Bounds are also obtained for the weighted energy of weighted spherical designs. We explore our bounds for several previously studied weighted spherical codes.
Joint work with S. Borodachov (Towson University, Towson, MD, USA), P. Dragnev (Purdue University Fort Wayne, IN, USA), D. Hardin and E. Sa (Vanderbilt University, Nashville, TN, USA), M. Stoyanova (So a University, Bulgaria).
Bio: PhD (1993), DrSci (2003), Professor (2010) in Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences. His research interests are in coding theory, combinatorics, and numerical analysis. He works on bounds for different parameters of codes and designs in polynomial metric spaces. During his research and participation in projects, Boyvalenkov has gained experience in applications of mathematics and informatics in different areas such as communications, data protection, and modeling processes. He has published more than 100 papers in journals, conference proceedings, and books, and has research visits in institutions in Germany, the Netherlands, Sweden, Russia, US (Purdue University Fort Wayne, Vanderbilt University, ICERM Providence), and Hungary. Boyvalenkov was visiting professor at Purdue University Fort Wayne for the 2018 and 2020 Fall semesters. He is currently Director of the Institute of Mathematics and Informatics of Bulgarian Academy of Sciences.