In recent years, tools from tropical geometry have been used to study fundamental problems in linear and semidefinite programming. The team is investigating how tropical techniques can be used to provide new insights about other problems from polynomial optimization. Two examples of such problems are the tropicalization of the hyperbolic programming and of the Moment-SOS hierarchy.

Another research direction consists in studying the connections between tropical geometry and alternative positivity certificates such as SONC/SAGE.

The team is also interested in using tropical tools to develop new noncommutative analogues of the positivity certificates.