GAUGE THEORY AND STRING GEOMETRY (Mini Courses + Conference) -- GAUGE THEORY AND STRING GEOMETRY (Mini Courses + Conference) MSI ANU

GAUGE THEORY AND STRING GEOMETRY (Mini Courses + Conference) 

Monday, 24 Nov 2025, 9am - Friday, 5 Dec 2025, 5pm 

Description This two-week program aims to explore the intersection of gauge theory and
string geometry, two of the most profound and rapidly developing areas of modern
mathematics and theoretical physics.  The first week will feature a series of five
mini-courses taught by internationally acclaimed leaders in the field, while the second
week will be an international conference bringing together experts and early-career
researchers to foster discussions and new collaborations.  

Gauge theory and string geometry have been at the forefront of mathematical and physical
research for decades.  Gauge theory, originating from physics, provides a framework for
understanding fundamental forces and has inspired a range of mathematical advances.
Notably, Donaldson’s work using gauge theory has led to significant progress in
4-manifold topology, and the development of Seiberg-Witten theory further refined our
understanding of smooth 4-manifolds.  

In parallel, string theory emerged as a candidate for unifying all known fundamental
forces, leading to a deep interaction with mathematics.  It inspired the concept of
mirror symmetry, which reveals a duality between seemingly distinct Calabi- Yau
manifolds and has motivated many developments in symplectic geometry and enumerative
geometry.  

The program will provide ample opportunities for participants to interact with experts,
discuss open problems, and potentially initiate collaborations.  We aim to foster an
inclusive and interactive environment that encourages the exchange of ideas between
researchers at different stages of their careers.  

More information can be found on our webpage
(https://url.au.m.mimecastprotect.com/s/oCYhCnx1jni3lwjJquJhvuJbkJB?domain=maths.anu.edu.au).  

- Mini Courses (24-29 Nov 2025): 

Daemi Aliakbar (Washington University in St.  Louis) Title and abstract TBC.  Speaker
information
(https://url.au.m.mimecastprotect.com/s/wTYECoV1kpfPl9Z7LHVivupXdj4?domain=math.wustl.edu) 

Siqi He (Chinese Academy of Sciences) Title: Z/2 Harmonic 1-Forms and Related Problems
in Geometry 

Abstract: This mini-course will focus on Z/2 harmonic 1-forms and their connections to
gauge theory, topology, and compactification problems.  The lectures will be divided
into four parts: 

Gauge Theory with SL(2,C) structure group: Gauge-theoretic equations with SL(2,C)
structure group, including flat connection equations and the Kapustin–Witten
equations.  We will discuss their basic properties and related geometric and topological
problems.  

Compactness of Flat SL(2,C) Connections: Taubes’ compactness theorem and the role of
Z/2 harmonic 1-forms in describing the ideal boundary.  Basic properties of Z/2 harmonic
1-forms will also be introduced.  

Deformation of Z/2 Harmonic 1-Forms: Donaldson’s work on the deformation of Z/2
harmonic 1-forms, along with possible geometric applications of these deformations.  

Relations to Low-Dimensional Topology: Connections between Z/2 harmonic 1-forms and
classical objects in low-dimensional topology, including Thurston’s compactification
of Teichmüller space, measured foliations, and the Morgan–Shalen compactification.  

The lectures are intended for PhD students and early-career researchers with a
background in differential geometry or gauge theory.  

Speaker information
(https://url.au.m.mimecastprotect.com/s/dwusCp81lrtOQkKjNuGs0uG-Oio?domain=mcm.ac.cn/) 

Johanna Knapp (University of Melbourne) Title: The Physical Mathematics of Gauged Linear
Sigma Models 

Abstract: Gauged linear sigma models (GLSMs), first introduced by Witten in 1993, are
supersymmetric gauge theories in two dimensions.  They provide a powerful tool to study
properties of extra dimensions in string theory and the mathematical structures behind
them.  The aim of these lectures is to show how a physics analysis of GLSMs (vacuum
configurations, low-energy effective theories, D-branes, path integrals etc.)  leads to
advanced mathematics (GIT quotients, categorical equivalences, enumerative invariants
etc.).  The main focus will be on GLSMs that are related to Calabi-Yau compactifications
of string theory.  

A rough outline of the lectures is as follows (we may not cover all of it): 

1.  GLSMs: physics definition and phases 

• Field content and symmetries • Phases of GLSMs • Higgs vs Coulomb branches •
Examples 

2.  (B-type) D-branes in GLSMs 

• B-branes in GLSMs • D-brane transport and categorical equivalences (physics
perspective) 

3.  GLSM partition functions and what they compute 

• (Hemi-)sphere partition function • B-brane central charges and enumerative
invariants 

Speaker information
(https://url.au.m.mimecastprotect.com/s/6RtzCq71mwfkLBlpPFNt6uEHegR?domain=findanexpert.unimelb.edu.au) 

Yixuan Li (Australian National University) Title: Mirror Symmetry of Type A Affine
Grassmannian Slices 

Abstract: This mini-course is about a mirror symmetry result central to Mina
Aganagic’s ICM 2022 talk [1] on two categorifications of Jones polynomials.  Recall
that the Jones polynomial of a knot can be calculated via the fundamental representation
V of the quantum group U_q(sl_2) roughly in the following way: First present the knot as
the closure of a braid with n strands by Alexander’s theorem.  Then associated to the
n strands, we have the weight spaces of the tensor product of n copies of V.  Associated
to the braid, we have a product of R-matrices acting on each weight space.  Jones
polynomial is related to the trace of this product of R-matrices on the weight spaces of
this tensor product.  Thus to category this picture, we need to upgrade the weight
spaces to categories and the R matrices to certain braid group actions on these
categories.  Taking trace would be interpreted as taking a homomorphism between certain
objects in the category.  

Via the geometric Satake equivalence[2][3], weight spaces of tensor products of
fundamental representations of gl(m) are related to the geometry of certain slices in
the affine grassmannian of Gl(m).  These slices are conical symplectic singularities.
There are two ways to smoothen this singularity: One can consider the semi-universal
symplectic deformation or the symplectic resolution.  Hence the weight spaces will be
categorified into certain Fukaya categories of deformed affine grassmannian slices or
the category of coherent sheaves on the symplectic resolution of these slices.  The
braid group action will in fact be provided by the monodromy action of the
semi-universal symplectic deformation.  

Mirror symmetry is a relation between Fukaya category of a symplectic manifold X and the
derived category of coherent sheaves on a complex manifold X^.  In fact these two
categorifications will be related to each other by a conjectural homological mirror
symmetry.  In [4] we proved a partial result saying that the coherent side embeds into
the symplectic side.  In fact, as another evidence, we can show manually that both the
quantum connection on X^ and a Gauss-Manin connection on X can be identified with
certain Knizhnik-Zamolodchikov connections, following the work [5] of Danilenko.  

These talks are prepared for PhD students and early career researchers with a background
in representation theory or geometry/topology.  Time permitting, I will mention the
connection of these slices with certain monopole moduli spaces as predicted by [6].
What we need in order to prove these predictions is some control over Kapustin-Witten
equations.  

Speaker information
(https://url.au.m.mimecastprotect.com/s/L6sSCr81nytnwMo50cNu8u4oQCa?domain=maths.anu.edu.au) 

Emanuel Scheidegger (BICMR, Peking University) Title and abstract TBC.  Speaker
information
(https://url.au.m.mimecastprotect.com/s/k9Q1Cvl1rKiLO1KDjFyCRuQm9_K?domain=bicmr.pku.edu.cn) 

- Conference 01-05 Dec 2025 Invited speakers: 

Bohui Chen (Sichuan University) 

Cheol-Hyun Cho (Postech) 

Cheng-Yong Du ( Sichuan Normal University) 

Michele Galli (University of Queensland) 

Huijun Fan (Wuhan University) 

Fuquan Fang (Capital Normal University) 

Kenji Fukaya (Tsinghua University, Beijing) 

Fei Han (National University of Singapore) 

Siqi He (Chinese Academy of Science) 

Weiqiang He (Sun Yat-sen University) 

Hai-Long Her (Jinan University) 

Jianxun Hu (Sun Yat-sen University) 

Tsuyoshi Kato (Kyoto University) 

Ctirad Klimcik (Université Aix-Marseille, France) 

Xiaobo Liu (Peking University) 

Jock McOrist (University of New England) 

Ruben Minasian (CEA-Saclay, France) 

Yong-Geun Oh (POSTECH) 

Hiroshi Ohta (Nagoya University) 

Kaoru Ono (Kyoto University) 

Jongil Park (Seoul National University) 

Shuaige Qiao (Capital Normal University, Beijing) 

Hirofumi Sasahira (Kyushu university, Japan) 

Emanuel Scheidegger (BICMR, Peking University) 

Shanzhong Sun (Capital Normal University, Beijing, China) 

Meng-Chwan Tan (National University of Singapore) 

Gabriele Tartaglino-Mazzucchelli (University of Queensland) 

Gang Tian (Peking University) 

Mathai Varghese (University of Adelaide) 

Yaoxiong Wen (Korea Institute for Advanced Study, Seoul) 

Hang Wang (East China Normal University, China) 

Longting Wu (Southern University of Science and Technology, China) 

Siye Wu (National Tsing Hua University, Hsinchu) 

Chenglang Yang (Wuhan University) 

Jun Zhang (University of Science and Technology of China) 

Ruibin Zhang (University of Sydney) 

Yingchun Zhang (Shanghai Jiaotong University) 

Organising Committee Peter Bouwknegt (Australian National University) 

Brett Parker (Australian National University) 

Bryan Wang (Australian National University) 

Scientific Committee Kenji Fukaya (Tsinghua University) 

Kaoru Ono (RIMS, Kyoto University) 

Yongbin Ruan (Zhejiang University) 

Gang Tian (Peking University) 

Venue 

Seminar rooms 1.33 & 1.37 Mathematical Sciences Institute ANU College of Science Hanna
Neumann Building #145, Science Road The Australian National University Canberra ACT 2600 

Register at
https://url.au.m.mimecastprotect.com/s/ch1fCoV1kpfPl9Z7LH1Vtvup2l_t?domain=payments.anu.edu.au