Study of geometric and analytic monodromies and local zeta functions

利用运动Milnor纤维理论，得到了多项式映射无穷远点单值性的Jordan正规形的一些表达式。并将这一结果推广到完全交簇的多项式映射的情形。利用快速衰减同调理论，我们还得到了合流A-超几何函数的积分表示。利用这个结果计算了它们在无穷远处的渐近展开式和Stokes乘子。

By using the theory of motivic Milnor fibers, we obtained some formulas which express the Jordan normal forms of monodromies at infinity of polynomial maps. Moreover we generalized this result to the case of polynomial maps from complete intersection varieties. By using the theory of rapid decay homologies we also obtained the integral representations of confluent A-hypergeometric functions. By this result we calculated their asymptotic expansions and Stokes multipliers at infinity.