Oscar Garcia-Prada Room: Lecture Hall

Richard Wentworth Room: Lecture Hall

Lynn Heller Room: Lecture Hall

Natsuo Miyatake: Equilibrium Metrics and Complete Harmonic Metrics Room: Lecture Hall Let $X$ be a compact Riemann surface. For a positive line bundle $L\to X$, a continuous Hermitian metric $e^{-\phi}h_\ast$ on $L$, and a nonpolar compact subset $K\subseteq X$, one can construct an equilibrium metric from the envelope of subharmonic weight functions bounded above by $\phi$ on $K$. The approximation of equilibrium metrics by sequences of singular metrics has been studied in a variety of contexts, including complex geometry, potential theory, dynamical systems, and probability theory. In this talk, I will introduce two functions, called entropy and free energy, associated with semipositive singular Hermitian metrics on the canonical bundle of a Riemann surface. These quantities are defined using an extension of the notion of complete harmonic metrics on cyclic Higgs bundles, whose existence and uniqueness were established by Li--Mochizuki, to complete Hermitian metrics associated with semipositive singular metrics on the canonical bundle that are not necessarily induced by holomorphic $r$-differentials. I will then discuss my ongoing research aimed at quantitatively establishing the principles of entropy increase and free energy decrease in various situations where an equilibrium metric is approximated by a sequence of singular metrics.

Bin Wang: Parabolic Hitchin Systems for Classical Groups Room: Lecture Hall We will discuss the geometry of strongly parabolic Hitchin systems for classical groups over smooth curves. We begin by relating the singularities of generic spectral curves to Kazhdan--Lusztig maps, and then explain how the generic Hitchin fibers can be identified with natural abelian varieties. If time permits, we will also discuss the structure of the Hitchin base for even special orthogonal groups. This talk is based on joint works with Xiaoyu Su, Xueqing Wen and Yaoxiong Wen.

Georgios Kydonakis Room: Lecture Hall

Andy Neitzke Room: Lecture Hall

Sukjoo Lee: Symplectic leaves of meromorphic Hitchin systems Room: Lecture Hall I will discuss symplectic leaves in moduli spaces of meromorphic $GL_r$-Higgs bundles on a smooth projective curve. These moduli spaces carry natural Poisson structures, studied independently by Bottacin and Markman, and their symplectic leaves are expected to be governed by the adjoint orbits of the residues at the marked points. However, it has not been clear whether the corresponding loci of Higgs bundles are connected. The Hitchin map is also expected to restrict to a symplectic integrable system on each leaf. For general choices of residue orbits, especially non-maximal ones, this leads to the problem of describing the Hitchin base and the generic fibers. I will discuss these questions using $\xi$-parabolic Higgs bundles, which lift the condition of fixing residue orbits to compatible parabolic flag data. This is joint work with Jiachoon Lee.

Arya Yae Room: Lecture Hall

Enya Hsiao Room: Lecture Hall

Takashi Ono Room: Lecture Hall

Philsang Yoo Room: Lecture Hall

Yukinobu Toda Room: Lecture Hall