The Geometry and Physics of Higgs Bundles

22 Jun 2026, 08:00 → 24 Jun 2026, 17:00 Asia/Tokyo

Lecture Hall (Kavli IPMU)

Dates:  June 22 - 24, 2026

Overview:

The theory of Higgs bundles provides a unifying framework for problems in topology, representation theory, integrable systems, and quantum field theory. Over the past decades, it has formalized our understanding of non-abelian Hodge theory and the geometric aspects of physical dualities.

This meeting addresses recent progress in the moduli spaces of Higgs bundles and their physical applications. We will explore the intersection of algebraic, differential, and symplectic geometry with mathematical physics. Specific themes of the workshop include Hitchin systems, parabolic and singular structures, spectral and cameral methods, geometric Langlands duality, and their relation to supersymmetric gauge theories.

By bringing together researchers from these adjacent fields, the conference aims to clarify recent advancements and prompt new collaborative efforts at the interface of geometry and physics.

Invited speakers:

• Oscar Garcia-Prada
• Lynn Heller
• Enya Hsiao
• Georgios Kydonakis
• Sukjoo Lee
• Natsuo Miyatake
• Andy Neitzke
• Takashi Ono
• Yukinobu Toda
• Bin Wang
• Philsang Yoo
• Richard Wentworth
• Arya Yae

Organizing Committee:

• Hisashi Kasuya
• Hiraku Nakajima
• Laura Schaposnik
• Mengxue Yang
• Lutian Zhao

Registration:
Please note that, unfortunately, we cannot offer funding or assist with visa applications for general attendees. If you need a visa to travel to Japan, we strongly recommend arranging a tourist visa. The deadline to register is June 15 at 0:00 JST.

Venue:

Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU),

the University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa City, Chiba 277-8583, Japan

Monday 22 June

09:30 Registration and Safety Training

1 Oscar Garcia-Prada

2 Richard Wentworth

12:00 Lunch Break

3 Lynn Heller

4 Natsuo Miyatake: Equilibrium Metrics and Complete Harmonic Metrics

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.

15:00 Coffee Break (3rd floor)

5 Bin Wang: Parabolic Hitchin Systems for Classical Groups

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.

Tuesday 23 June

6 Georgios Kydonakis

7 Andy Neitzke

Group Photo

12:00 Lunch Break

8 Sukjoo Lee: Symplectic leaves of meromorphic Hitchin systems

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.

9 Arya Yae

15:00 Coffee Break (3rd floor)

10 Enya Hsiao

16:15 Free Time

18:00 Conference Dinner

Wednesday 24 June

11 Takashi Ono

12 Philsang Yoo

11:45 Lunch Break

13 Yukinobu Toda

15:00 Coffee Break (3rd floor)