Conference on Unexpected and Asymptotic Properties of Projective Varieties

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This National Science Foundation award supports the Conference on Unexpected and Asymptotic Properties of Projective Varieties that will take place on May 15-17, 2020 in Lincoln, Nebraska. In the intervening fifteen years since the previous conference on varieties with unexpected properties took place in Sienna, Italy, the state of the art in this area of research has undergone tremendous developments. Despite numerous foundational advances, there are many classically studied problems that still do not have a satisfactory resolution. The conference will highlight the transformative developments undergone by this area of research in recent years and formulate new directions for future research. Towards this end, we will bring together experts in the field and carefully select participants to ensure involvement of students and junior investigators and of individuals from groups under-represented in the mathematical sciences. Further details can be found at the conference website http://www.math.unl.edu/~aseceleanu2/BrianFest2020.htmlThe topic of the conference is anchored broadly in commutative algebra and algebraic geometry, with a focus on interpolation problems in algebraic geometry and asymptotic invariants of homogeneous ideals. The overall objective of this conference is to bring together experts in commutative algebra and algebraic geometry to confer on three topics of common interest: symbolic powers of ideals, asymptotic invariants of linear systems, and unexpected varieties. Despite the diverse contexts in which these notions arise and the many areas they exhibit connections to, each of these topics is closely related to the others. Communication among mathematicians working on these topics is vital and has already led to significant progress. The relatively small size of the meeting and its disciplinary focus will be particularly effective at enabling participants to establish productive collaborative relationships.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.