Michael Schultz

• PhD Mathematics
• Visiting Assistant Professor at Virginia Tech

A fundamental object of study in mirror symmetry of n-dimensional Fano varieties is the Aside connection on small quantum cohomology. When the Picard rank is 1, the Borel transform relates the quantum differential operator of the Fano to the Picard-Fuchs operator of the mirror to the associated pencil of anticanonical Calabi-Yau (n − 1)-folds on th...

We discuss the connection between Picard-Fuchs equations for certain families of lattice polarized K3 surfaces and the construction of integrable holomorphic conformal structures on their period domains. We then compute an explicit example of a locally conformally flat holomorphic metric associated with generic Jacobian Kummer surfaces, which allow...

We use the mixed-twist construction of Doran and Malmendier to obtain a multi-parameter family of K3 surfaces of Picard-rank $\rho \ge 16$. Upon identifying a particular Jacobian elliptic fibration on its general member, we determine the lattice polarization, the moduli space, and the Picard-Fuchs system for the family. We construct a sequence of r...

We survey the Hirzebruch signature theorem as a special case of the Atiyah-Singer index theorem. The family version of the Atiyah-Singer index theorem in the form of the Riemann-Roch-Grothendieck-Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of elliptic curves. The RRGQ formula all...