Abstract: Let k be a non-Archimedean field of residue characteristic zero. We prove a non-Archimedean rigidity theorem for Julia sets: if two polynomials of degree at least 2 over k have the same Julia set, and this Julia set is not a singleton, then the two polynomials are dynamically related. As a consequence, we show that for any two complex polynomials f and g of degree at least 2, either their sets of preperiodic points coincide, or the number of their common preperiodic points is uniformly bounded above by a constant depending only on the degrees, thereby confirming a conjecture of DeMarco–Krieger–Ye in the polynomial setting. This is joint work with Jit Wu Yap.

Abstract: For an n-dimensional variety X, its degree of irrationality irr(X) is defined to be the minimal degree of a dominant rational map from X to P^n. In this talk, we completely determine the degree of irrationality of complex abelian surfaces. More precisely, a complex abelian surface A has degree of irrationality 3 if and only if it admits a polarization of type (1, 1), (1, 2), (1, 3), or (1, 6); in all other cases, irr(A) = 4. This talk is based on joint work with Zhi Jiang and Xin Yang.

Abstract: For a smooth projective 3-fold V of intermediate Kodaira dimension, we establish Noether-type inequalities relating the Iitaka volume Ivol(V) and the geometric genus p_g(V). In the Kodaira dimension 2 case, we prove that the equality holds only if the bicanonical system of V induces the Iitaka fibration and the canonical system of V is composed with a pencil of surfaces whose general member has Iitaka volume 1/2 provided that p_g(V) ≥ 4. This is a joint work with Meng Chen, Chen Jiang and Yang Liu.

Abstract: In this talk, I will introduce quantum cohomology and quantum K-theory from a physics perspective. I will then discuss my recent work on the quantum K-theory of partial flag manifolds, presented in arXiv:2606.15261.