This National Science Foundation award provides support for the CBMS Conference: Additive Combinatorics from a Geometric Viewpoint, to be held at the University of South Carolina during May 21-25, 2018. The main speaker at this conference is Dr. Jozsef Solymosi from the University of British Columbia, one of the leading researchers in this area. The interaction at this event is expected to establish new partnerships and strengthen existing connections between researchers at other southeastern universities and those at the University of South Carolina. Moreover, a focused lecture series summing up current research in additive combinatorics in an accessible way substantially contributes to the professional development of the participants who will include Ph.D. students and junior researchers, as well as faculty from small colleges and teaching institutions, offering them valuable opportunities to enter collaborative networks. Recruitment from groups that are underrepresented in the mathematical sciences is a priority for the PIs.
The impact of additive combinatorics in general mathematics and theoretical computer science is enormous. The geometric viewpoint involves turning arithmetic problems into geometric problems, which can then be solved by geometric means - including discrete geometry, convex geometry, and some algebraic geometry. An archetypal example of this approach is Elekes' bound on the sum-product problem using the Szemeredi-Trotter theorem on the number of incidences between points and lines. Participants will see that arithmetic, algebra, combinatorics and geometry are intimately connected in unexpected ways. Dr. Solymosi's lectures will culminate in a monograph that will provide an accessible reference to graduate students, and fill a literature gap in an area where many results are found only in highly technical journal publications. The conference webpage is at http://imi.cas.sc.edu/events/nsf-cbms/
