Dr.Sungyoon Cho，University of Arizona

The Kudla-Rapoport conjecture predicts a relation between the arithmetic intersection numbers of special cycles on the unitary Shimura variety with hyperspecial level structure and the derivative of representation densities for hermitian forms. In this talk, we will give conjectural formulas that relate the arithmetic intersection numbers of special cycles on the unitary Shimura varieties with minuscule parahoric level structure and weighted representation densities.