Check websites of some of the former students/postdocs of Bernd Sturmfels: Pablo Parillo at MIT and Rekha Thomas at Washington University. They tackle real (meaning relatively big) problems with their algebraic geometry insight. This is mostly related to semidefinite programming and related problems. You can check Pablo's MIT course to get some idea: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-972-algebraic-techniques-and-semidefinite-optimization-spring-2006/

There is also a huge line of research on computational algebraic geometry. You can start visiting the website of Jon Hauenstein http://www3.nd.edu/~jhauenst/ They work with big industrial projects.

Algebraic geometry is also used in the topological data analysis which is now becoming a big thing in the data science.

Check websites of some of the former students/postdocs of Bernd Sturmfels: Pablo Parillo at MIT and Rekha Thomas at University of Washington. They tackle real (meaning relatively big) problems with their algebraic geometry insight. This is mostly related to semidefinite programming and related problems. You can check Pablo's MIT course to get some idea: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-972-algebraic-techniques-and-semidefinite-optimization-spring-2006/

There is also a huge line of research on computational algebraic geometry. You can start visiting the website of Jon Hauenstein http://www3.nd.edu/~jhauenst/ They work with big industrial projects.

Algebraic geometry is also used in the topological data analysis which is now becoming a big thing in the data science.