The goal of this workshop is to bring together both senior and junior specialists in the fields of almost complex and non-Kähler geometry to present their latest achievements in research. Key topics will include cohomological properties of complex and symplectic manifolds, analytical techniques in non-Kähler geometry, special structures on complex manifolds, deformations of complex objects, topological aspects of complex and symplectic manifolds, and Hodge theory on almost Hermitian manifolds. Registration to open soon. This is event is part of a special semester on complex geometry at the Renyi Institute.

Speakers:

Yakov Eliashberg (TBC) Richard Hind Tom Holt Uros Kuzman Lorenzo Sillary Nicoletta Tardini Scott Wilson Weiyi Zhang Daniele Angella Gueo Grantcharov Nicolina Istrati Slawomir Kolodziej Alexandra Otiman Tat Dat To Valentino Tosatti Misha Verbitsky Vestislav Apostolov Gil Cavalcanti

Aim of the School is to bring together young students and researchers with experts in the research areas of global analysis, spectral theory, mathematical physics and their interplay. The school consists of four mini-courses leading towards a broad understanding of current research topics from different perspectives. The mini-courses will be aimed at a broad audience.

Speakers of the mini-courses: * Nelia Charalambous on "The spectrum of geometric operators on noncompact manifolds" * Jeffrez Galkowski on "The high energy behavior of Laplace eigenfunctions: applications of geodesic beams" * Frédéric Rochon on "L2-cohomology of complete hyperKähler metrics" * Alexander Strohmaier on "Spectral Theory on Spacetimes"

This three-day conference celebrates the 60th birthday and influential career of Igor Kriz, whose groundbreaking contributions have shaped modern perspectives in homotopy theory and its interactions with physics. This special event will gather leading researchers and early-career mathematicians from around the world for a series of stimulating lectures, discussions, and collaborations.

The conference will spotlight cutting-edge developments in equivariant and motivic homotopy theory, as well as their deep connections to mathematical physics and symplectic topology. Invited talks by prominent experts will explore recent advances and open problems at the rich interface of these fields, honoring the wide-ranging impact of Kriz’s work.

We warmly invite you to be part of this celebration of mathematics, community, and visionary research. If you plan to attend, please complete the registration form below. We have some funding available for graduate students and junior researcher participants. If you wish to apply for travel funding, you may do so on the registration form.

Holomorphic-topological (HT) field theories form a fascinating class of quantum field theories. These theories combine features of topological quantum field theories (TQFT) and conformal field theories (CFT).

Due to the mixed holomorphic-topological nature of such theories, they create interactions between TQFT data (e.g., algbras, monoidal categories, etc) and CFT data (e.g., chiral algebras and chiral categories). This leads to exciting new mathematical structures, and connections to integrable systems, quantum topology and many other areas of mathematics. Recently. much progress has been made on the representation-theoretic aspects of HT theories. Examples include:

1. (Shifted) Poisson vertex algebras and their quantizations are constructed from local operators in HT theories.

2. Dimensional reduction of 4d HT theories lead to integrable systems and solutions of quantum Yang-Baxter equations.

3. 4d N=2 theories are linked to representation theory of K-theoretic Coulomb branches, cluster algebra categorifications, wall crossings and elliptic stable envelops.

4. New examples of chiral algebras and their dualities are derived from boundary conditions and dualities of 3d HT theories.

Moreover, many interesting TQFTs are given by deformations of holomorphic-topological theories. Examples include topological twists of 3d N=4 and 4d N=2 theories. These theories have attracted considerable attention in recent years for their connections to 3d mirror symmetry and the Langlands program. Some of these TQFTs only admit Lagrangian descriptions as HT QFTs, and therefore studying HT theories offers a possible approach for understanding these non-Lagrangian TQFTs.

This conference will focus on the representation-theoretic aspects of HT theories, particularly:

1. Chiral algebras arising from observables of HT QFT.

2. Quantum algebras, including Yangians and quantum affine algebras, and their relation to HT theories.

3. Chiral categories and OPE of line operators in HT theories.

4. Deformation of HT theories and their relation to chiral algebra deformations.

5. Relation between various HT theories under dimensional-reduction.

We aim to bring together leading mathematicians and physicists, to inform each other about the recent progress made in this area.

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Limited funding is available to support travel and lodging of early-career researchers. Due to space constraints, all participants must register and we may not be able to accept all applicants. For fullest consideration for funding and participation, please as soon as possible. For more information, please refer to the In Person Registration option on the Registration page of this website.

A workshop introducing researchers with some background in harmonic analysis and dispersive partial differential equations to some open problems in general relativity and quantum information.

About: Recently, there have been some remarkable breakthroughs of harmonic analysis techniques in general relativity and quantum information. As some featured examples, we refer to a result in 2021 of Hintz and Vasy and now in 2025 of Hintz, Petersen, and Vasy, in proving global nonlinear stability of Kerr-de Sitter spacetimes, extending Fourier-harmonic analytic methods into nonlinear geometric PDES, and the solution of the L2 curvature conjecture for the Einstein Equations by Klainerman, Rodnianski, and Szeftel.

Some main themes of this workshop will be to explore:

How harmonic analysis can be used in General Relativity settings, which often involve obstacles like a lack of global Fourier transforms, noncompactness of Lorentzian manifolds and the associated scattering theory, and nonlinear and geometric structure of PDEs.

The analysis of Schrodinger operators that arise in quantum computing (including themes such as Lieb-Robinson bounds).

One of the main goals of the workshop will be to introduce researchers with some background in harmonic analysis and dispersive PDE to some open and accessible problems in general relativity and quantum information. The structure of the workshop will accommodate time for plenary talks, problem sessions, and discussion and collaboration time. Thus the workshop is ideal for researchers in harmonic analysis or dispersive PDE seeking an introduction to how these techniques may be applied in a general relativity or quantum information setting, and to be acquainted with some accessible open problems in those fields, or conversely researchers in General Relativity or Quantum Information seeking to incorporate more harmonic analysis techniques into their research.

Participation is in person only. There will be talks that are delivered by video link.

Speakers:

Di Fang (Duke University) - online talk

Jesse Gell-Redman (University of Melbourne)

Zihua Guo (Monash University)

Andrew Hassell (Australian National University)

Xiao Ma (University of Michigan) - online talk

Todd Oliynyk (Monash University)

David Ou Yang (Ludwig-Maximilians-Universität München)

Volker Schlue (University of Melbourne)

Andras Vasy (Stanford University) - online talk

Jingxuan Zhang (Tsinghua University)

Scientific and Organising Committee:

Alexandria Rose (Australian National University)

Pierre Portal (Australian National University)

Xiaoxu Wu (Australian National University)

Tony Martin (Australian National University)

This is the 2nd conference organized by the International Society of Nonlinear Mathematical Physics (ISNMP) which is located in Bad Ems, Germany. The conference aims to provide a platform for experts to report and discuss their research progress on all aspects of nonlinear mathematical physics, with a focus on integrable and exactly solvable systems. This time the conference will be held in memory of Wilhelm I. Fushchich on his 90th anniversary and in honour of Jarmo Hietarinta on the occasion of his 80th birthday.