Time：15:00-16:00, Wednesday, October 29 2025
Venue：E10-212
Host： Xujia Wang, ITS
Speaker: Neil Trudinger, Australian National University
Biography：Professor Neil Trudinger's distinguished career began with a PhD from Stanford in 1966, and has spanned renowned institutions worldwide, culminating in his long-standing professorship at the Australian National University. He is celebrated for a series of groundbreaking discoveries in partial differential equations, including the famous Moser-Trudinger inequality, pioneering work on the Yamabe problem, and profound insights into fully nonlinear elliptic equations. His exceptional contributions have earned him the highest honours, including the first Medal of the Australian Mathematical Society and a Fellowship in the Royal Society. The enduring impact of his work is perhaps best embodied by his co-authored book with David Gilbarg, a definitive text that received the AMS Steele Prize after being the most-cited mathematics book for a decade.
Title：Oblique boundary value problems for augmented Hessian equations under degenerate boundary conditions
Abstract：In this talk, we consider boundary regularity and classical existence for oblique boundary value problems for augmented Hessian equations under degenerate versions of the boundary curvature conditions, introduced in previous research with Feida Jiang. The key structural assumption is a quadratic gap between the maximum and minimum eigenvalues of the principal coefficients of the linearized operators. We also consider the application to conformal geometry. As well as building upon our earlier work, we also adapt a crucial idea from recent work of Xuezhang Chen and Wei Wei on the sigma_2 curvature equation in conformal geometry.
