“I am a mathematician. More specifically, I am an algebraic geometer with interests in the geometry of moduli spaces. Algebraic geometry is the study of varieties - the zero sets of polynomial equations in several variables. The subject has a central role in mathematics with connections to number theory, representation theory, and topology. Moduli questions in algebraic geometry concern the behavior of varieties as the coefficients of the defining polynomials vary. At the end of the 20th century, several fundamental links between the algebraic geometry of moduli spaces and path integrals in quantum field theory were made. I work on several questions concerning the cohomology and the cycle theory of moduli spaces.
My Einstein project in Berlin is at Humboldt-Universität. I will study the moduli of curves, sheaves, and K3 surfaces. I have a natural collaboration with the group of Gavril Farkas in the mathematics department. For the first event of the project, a conference in February at the Humboldt-Universität, I spent two weeks in Berlin. I also have hired a post-doc to support the project who started in January.“ (March 2015)