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Additive combinatorics is a very active area of mathematics. It is the crossing point of number theory, harmonic analysis, ergodic theory, and combinatorics. Beyond the numerous conferences and workshops, special semester-long programs have been organized on the subject at Princeton (IAS), Cambridge (Newton Institute), UCLA (IPAM), and UC Berkeley (MSRI). In this series of lectures, Dr. Jozsef Solymosi (University of British Columbia) provides an elementary introduction to additive combinatorics using discrete geometry, algebra, extremal combinatorics, and a bit of algebraic geometry. He also shows how to apply these techniques in order to attack Erdos type problems in discrete geometry. The lectures and the monograph to be written are intended for graduate students and researchers working on related areas, and to help those who intend to enter the field.

Dr. Solymosi will give 10 lectures on the topic of the conference, which will be complemented by 4 one-hour lectures (by Gyula Karolyi, Giorgis Petridis, Orit Raz, and Joshua Zahl). Problems to be solved will be distributed and discussed. Open problem sessions will provide opportunity for collaboration among the participants. This program is designed for graduate students and early-career researchers. As seating is limited, prospective participants not affiliated with the University of South Carolina must submit an application before January 31, 2018 at: http://mathprograms.org/db/programs/622

The application must include a CV with date or expected date of Ph.D., an email address, a letter of reference, a statement of research interests, a publication list, and a statement on how participation is expected to enhance the applicants career.

Selection of participants will take place in the first two weeks of February. Acceptance letters will be sent out as soon as final selections have been made. Selection will focus on the background of the participants in relevant areas and the expected effect of the program on their career. In particular, we encourage young mathematicians from the Southeast and members of underrepresented groups in the mathematical sciences to apply. Approved applicants will be provided dorm accommodation and partial reimbursement of other expenses.

Arrival to the conference should be scheduled for May 20, 2018. The scientific program is scheduled for May 21-25, 2018.