This thesis is divided into two chapters. In the first, given symmetric monoidal oc-categories C and D, subject to mild hypotheses on D, we define an oc-categorical analog of the Day convolution symmetric monoidal structure ...

Recently, unexpected connections have been discovered between characters of representations and lattice models in statistical mechanics. The bridge was first formed from Kuperberg's solution to the alternating sign matrix ...

Delzant's theorem for symplectic toric manifolds says that there is a one-to-one correspondence between certain convex polytopes in ... and symplectic toric 2n-manifolds, realized by the image of the moment map. I present ...

We develop a theory of less commutative algebraic geometry where the role of commutative rings is assumed by En-rings, that is, rings with multiplication parametrized by configuration spaces of points in Rn. As n increases, ...

This work focuses on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The work is divided into ...

We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by Fomin- Greene-Reiner-Shimozono, and we extend this notion to ...