Date/Time : 27 Aug 2025 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Sun Hongpeng, Renmin University of China

This paper introduces a preconditioned convex splitting algorithm enhanced with line search techniques for nonconvex optimization problems. The algorithm utilizes second-order backward differentiation formulas (BDF) for the implicit and linear components and the Adams-Bashforth scheme for the nonlinear and explicit parts of the gradient flow in variational functions. The proposed algorithm, resembling a generalized difference-of-convex function approach, involves a changing set of convex functions in each iteration. It integrates the Armijo line search strategy to improve performance. The study also discusses classical preconditioners such as symmetric Gauss-Seidel, Jacobi, and Richardson within this context. The global convergence of the algorithm is established through the Kurdyka-Łojasiewicz properties, ensuring convergence within a finite number of preconditioned iterations. Numerical experiments demonstrate its high efficiency. This is a joint work with Xinhua Shen and Zaijiu Shang.

Add to calendar :

Date/Time : 27 Aug 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Guolei Zhong, Institute for Basic Science, Korea

Let X be a smooth projective variety and G an abelian subgroup of automorphisms of X over the field of algebraic numbers. Suppose that G is of positive entropy. It was proved by Dinh and Sibony that the group is then free abelian of rank no more than dim(X)-1. In the past decade, from algebraic dynamics, the geometry of the extremal case when the rank achieves the maximal has been well-understood by Zhang. In this talk, we study the maximal rank case in the aspect of arithmetic dynamics. More precisely, we construct a canonical height function associated with the group, corresponding to a nef and big divisor, satisfying the Northcott property. By characterizing its null locus, we prove the Kawaguchi–Silverman conjecture for each group element. Some further discussion towards its application and the existence of Zariski dense orbits will also be presented. This is based on a joint work with Fei Hu.

Add to calendar :