for this workshop

## Foundations of tropical schemes

at the

American Institute of Mathematics, San Jose, California

organized by

Noah Giansiracusa, David Jensen, Diane Maclagan, and Steffen Marcus

This workshop, sponsored by AIM and the NSF, will focus on the continuing development of scheme-theoretic techniques in tropical geometry and their applications to broad questions in tropical geometry and algebraic geometry. Tropical scheme theory seeks to generalize the standard constructions in scheme theory to semirings, with the aim of providing algebraic and geometric foundations for tropical geometry. The goals of this workshop are to develop a common language and shared understanding of this developing theory and to explore applications. The main aims are:

- Develop computational techniques for working with tropical schemes.
- Develop standard algebraic techniques for tropical schemes such as primary decomposition, smoothness, free resolutions, and also geometric constructions such as a tropical Hilbert scheme.
- Apply the ideas developed to problems in algebraic geometry.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*