activity
20232026
collaborators

5 papers

math.OC2026

Convergence of Riemannian Stochastic Gradient Descents: Varying Batch Sizes And Nonstandard Batch Forming

Hao Wu

We establish convergence theorems for Riemannian stochastic gradient descents in which the underlying probability spaces vary from iteration to iteration. As applications, we deduc…

math.DG2026

Bauer-Furuta invariants

Hao Wu

Adapting Bauer and Furuta's constructions of the refinement of the Seiberg-Witten invariants, we establish the analogous stable cohomotopy refinement of the monopole i…

math.CV2025

Asymptotics of hole probability regarding open balls for random sections on compact Riemann surfaces

Hao Wu

We obtain the asymptotic behavior of hole probability for random holomorphic sections on a compact Riemann surface with respect to the hole size.

math.CV2024

Hole probabilities of random zeros on compact Riemann surfaces

Hao Wu, Song-Yan Xie

We establish a convergence speed estimate for hole probabilities of zeros of random holomorphic sections on compact Riemann surfaces.

math.CV2023

Entire curves generating all shapes of Nevanlinna currents

Hao Wu, Song-Yan Xie

First, we show that every complex torus contains some entire curve such that the concentric holomorphic discs $\{g\restriction_{\…