Abstract：

For a del Pezzo surface of degree ≥ 3, we compute the oscillatory integral for its mirror Landau Ginzburg model in the sense of the Gross-Siebert program. We explicitly construct the mirror cycle of a line bundle and show that the leading order of the integral on this cycle involves the twisted Chern character and the Gamma class. It proves a mirror symmetric version of the Gamma conjecture for non-toric Fano surfaces with an arbitrary K-group insertion. This is joint work with Bohan Fang and Yan Zhou.