Workshop: Real Enumerative Geometry and Beyond; Nashville, TN; March 6-7, 2020

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This award supports the Shanks workshop “Real Enumerative Geometry and Beyond” that will take place on March 6-7, 2020, at Vanderbilt University, Nashville, TN. The workshop will address the latest advances in the field of mathematics known as the real enumerative geometry, with senior and junior researchers of different expertise reporting on topics of common interests. The main goal of the meeting is to facilitate discussions and collaborations in a focused setting. The small size of the workshop provides an ideal environment for graduate students and early career researchers to interact with experts in the field. A diverse group of researchers will report on new advances in the field, assuring that a vast amount of techniques are shared among its participants. The intensive and substantial exchange of a broad spectrum of ideas during the workshop is expected to stimulate further research with the aim of pushing the boundaries of this field. Real enumerative geometry is an area of research with a long history, which has been rapidly evolving in the recent years. The main impetus in present-day developments comes from ideas of J.-Y. Welschinger, who proposed a signed counting in the enumerative geometry of curves defined over the field of real numbers. These ideas were used to answer many long-standing questions in the enumerative geometry of real algebraic varieties through their implementation in the symplectic, tropical or algebraic geometry framework. Very recently, these ideas were adapted in the A1-homotopy theory in an attempt to answer questions in enumerative geometry over arbitrary fields. The workshop is expected to lift the barriers between the seemingly unrelated fields of real enumerative geometry and A1-homotopy theory and build bridges between these fields. Classical aspects of real enumerative geometry will be addressed by V. Kharlamov, tropical aspects by O. Viro, a symplectic geometry approach will be discussed by X. Chen and S. Tukachinsky, while recent results in A1-enumerative geometry will be presented by J. Kass, S. Pauli and I. Vogt. For more details, see the webpage of the workshop: https://my.vanderbilt.edu/rag2020/ .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.