会议摘要（Abstract）

This week-long research workshop will bring together the researchers working at the forefront of numerical methods for frequency-domain wave equations and the corresponding applications. The workshop will have the following three themes.

Theme A: New discretization methods for frequency-domain wave problems and their analysis.

Theme B: Fast solvers for linear systems arising from frequency-domain wave problems - formulation, implementation, and analysis.

Theme C: Applications of the fast solvers, including inverse problems, geophysical imaging, and electromagnetics.

Theme B is the central theme of the workshop, but a key component of the programme will be synergetic interactions of Theme B with Themes A and C.

The workshop aims at 

1. To disseminate recent advances in each of Themes A, B, and C to the collective audience. 

2. To exploit recent advances in Theme A in the development of fast solvers in Theme B.

3. To explore how the demands of the applications in Theme C can inform the development of fast solvers in Theme B.

4. To initiate new research projects via the interactions described above. 

举办意义(Description of the aim)

The efficient computation of wave propagation and scattering problems at high frequency on modern multiprocessor computers (i.e., the goal of Theme B) has long been considered one of the ‘hard problems’ in numerical PDEs/scientific computing and is also of huge importance in applications - e.g., in seismic imaging and electromagnetics.

These wave problems are difficult to solve numerically because (a) the solutions are often highly oscillatory and very fine discretisations are needed to resolve them, leading to large system matrices; (b) the large system matrices are also highly indefinite and non-normal, meaning that standard iterative methods are not reliable; (c) the propagative nature of these problems means that the presence of a source at any point can have considerable effect far away, thus inhibiting the performance of parallel algorithms which rely on localization techniques. Each of these essential difficulties gets worse as the frequency increases.

Despite the difficulties above, in the last decade there has been huge progress in the development of fast solvers for wave problems (i.e., Theme B) informed by progress in Helmholtz theory and discretization methods (Theme A). There are many groups active in this area, including the organizers and the invitees of this workshop. Many successful algorithms are not yet rigorously understood, and instead are justified empirically by computational experiments and partial theory, combined with intuitive physical arguments.

We hope that the following questions will be answered during the week. 

1. Given that new methods are proposed, tested and implemented on a much faster timescale than that on which their rigorous analysis can proceed, what is the appropriate role of the numerical analyst in supporting the development and application of new methods? Conversely, what is the role of the practitioner in instigating and supporting theoretical investigations?

2. Spectral coarse spaces have proved effective in solvers for high frequency wave problems in practice (Themes B,C), but a full understanding of their properties is missing. Is it possible to make progress by harnessing the growing knowledge of non-polynomial discretization techniques for wave problems (Theme A)?　

3. Much progress has been made in the last 20 years on multiscale methods for coercive elliptic problems, and in recent years this has been partly extended to obtain new results for Helmholtz problems (Theme A). There is thus great potential for synergetic interaction between Themes A and B.

4. Perfectly-matched layers (PML) are used in some of the state-of-the-art fast solvers (Theme B), and recently there has been considerable progress in understanding their properties, but their rigorous understanding in the wide context of general geometries and variable coefficients is generally an open question. Is it possible to making progress on this question by using some new tools in semiclassical analysis?

5. Practitioners in the geophysics community (Theme C) use optimized finite-difference methods for solving the wave equation, whereas much of the rigorous theory for fast solvers is set in a finite element context. What tools are needed to ensure that emerging methods are discretisation agnostic and readily available for use in applications?

Introduction

The Asian Winter School (AWS) on Strings, Particles and Cosmology is a pan-Asian collaborative effort of high energy theorists from China, India, Japan and Korea to give young researchers in Asia an opportunity to come together and learn about the latest developments in high energy theory from leading experts on the subject.

This school is aimed towards advanced graduate students, postdoctoral fellows and active researchers in the field. This is the 19th in a series of Asian Winter Schools that have been organized on a rotating basis among China, Japan, India and Korea. We welcome students from all of these participating countries as well as students from outside.

The previous Asian Winter Schools in this series have provided young researchers with opportunities for discussions with leading experts in different areas and also for initiating collaboration with other young researchers belonging to the different participating countries. We hope the 2025 School will continue this tradition.

Invited Speakers

Jonathan J. Heckman (University of Pennsylvania):

Jonathan Sorce (Massachusetts Institute of Technology): 

Sameer Murthy (King's College London): 

Micha Berkooz (Weizmann Institute of Science): 

Victor A. Rodriguez (Princeton University): 

Washington Taylor (Massachusetts Institute of Technology):

Miguel Montero (Institute of Theoretical Physics in Madrid): 

Pasterski (Perimeter Institute):

Vladimir Kazakov (École normale supérieure): 

Local Organization Committee

Bin Chen (Peking University)

Ling-Yan Hung (Tsinghua University)

Jianxin Lu (University of Science and Technology of China)

Wei Song (Tsinghua University)

Yinan Wang (Peking University)

Zhenbin Yang (Tsinghua University)

Steering Committee

Agnese Bissi (ICTP, Italy)

Bin Chen (Peking, China)

Atish Dabholkar (ICTP, Italy)

Rajesh Gopakumar (ICTS, India)

Koji Hashimoto (Kyoto, Japan)

Seok Kim (SNU, Korea)

Kimyeong Lee (KIAS, Korea)

Miao Li (ITP, CAS & Sun Yat-Sen, China)

Jian-Xin Lu (USTC, China)

Jun Nishimura (KEK, Japan)

Hirosi Ooguri (Caltech, USA & Kavli IPMU, Japan)

Ashoke Sen (ICTS, India)

Sang-Jin Sin (Hanyang, Korea)

Wei Song (Yau MSC, Tsinghua, China)

Tadashi Takayanagi (Yukawa ITP, Japan)

Spenta R. Wadia (ICTS, India)

Piljin Yi (KIAS, Korea)

Advisory Board

David Gross (Kavli Institute for Theoretical Physics)

Andrew Strominger (Harvard University)

Hirotaka Sugawara (OIST)

Shing-Tung Yau (Harvard University)

Course Organizers

Nabamita Banerjee (Indian Institute of Science Education and Research)

Seung-Joo Lee (IBS Center for Theoretical Physics of the Universe)

Honda Masazumi (RIKEN • Advanced Science Institute )

Onkar Parrikar (Tata institute of fundamental research)

Yinan Wang (Peking University)

Junggi Yoon (Asia Pacific Center for Theoretical Physics)

Masahito Yamazaki (Kavli Institute for the Physics and Mathematics of the Universe)

Zhenbin Yang (Tsinghua University)

Past Asian Winter Schools

KAWS 2024, Kyoto, Japan

KAWS 2023, Daejeon, Korea

KAWS 2022, online, India

KAWS 2021, online, China

KAWS 2020, Sendai, Japan

KAWS 2019, Seoul, Korea

KAWS 2018, Bangalore, India

AWS 2017, Zhuhai, China

AWS 2016, Okinawa, Japan

AWS 2015, Busan, Korea

AWS 2013, Puri, India

AWS 2013, Beijing, China

AWS 2012, Gunma, Japan

AWS 2011, Jeju, Korea

AWS 2010, Mahabaleshwar, India

AWS 2009, Beijing, China

AWS 2008, Gunma, Japan

AWS 2007, Pheonix Park, Korea

Supporting Organizations

Website: https://asianwinterschool.github.io/index.html

举办意义(Description of the aim)

In the past few decades, there have been remarkable advances in both observational and theoretical aspects of cosmology. However, significant challenges remain in understanding the fully nonlinear features of cosmological dynamics. This conference aims to facilitate interactions between the mathematical and physical cosmology communities, and to identify important future directions in the field. Some topics that will be discussed include: N-body simulations, structure formation, averaging, post-Newtonian cosmological expansions, quiescent big bang singularities, mixmaster and chaotic dynamics.

Talks Link: https://bimsa.net/activity/strdyncos/

Theme

A hundred years ago, matrix mechanics brought revolutionary progress to modern physics, leading the scientific community into a deep exploration of the microscopic world. To celebrate this significant milestone, we plan to invite scholars and researchers from around the world to participate in the “100 Years of Matrix Mechanics” International Symposium on January 13-17, 2025 at the Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China. This conference aims to gather the world’s top scholars to discuss frontier research and applications based on matrix mechanics, covering multiple fields of mathematics, physics, and computer science.

The “100 Years of Matrix Mechanics” International Symposium aims to review and celebrate the outstanding achievements of matrix mechanics over the past century, while also exploring its potential applications in future science. This conference hopes to achieve breakthroughs in the following areas:

● Delving into the latest research advances in matrix mechanics in information processing and computational methods.

● Sharing innovative methods and outcomes of applying matrix mechanics in various disciplines.

● Promoting interdisciplinary exchange and collaboration, inspiring new research ideas and cooperative projects.

Conference Topics

Topics include, but are not limited to:

● Mathematics related to Matrix Mechanics

● Coding and Error Correction Theory

● Computational Methods

● Symmetry and Algebra

● Tensor Categories and Topological Structures

Hosts

Tsinghua University

Physical Society of Hong Kong (PSHK)

Beijing Institute of Mathematical Sciences and Applications (BIMSA)

Tsinghua Sanya International Mathematical Forum (TSIMF)

Organizers

Zhengwei Liu (刘正伟), Tsinghua University

Ziwen Liu (刘子文), Tsinghua University

David Ding (丁大威), Tsinghua University

Jinpeng Liu (刘锦鹏), Tsinghua University

Bei Zeng (曾蓓), Physical Society of Hong Kong (PSHK)

Xin Wang (王欣), Physical Society of Hong Kong (PSHK)

Jinsong Wu (吴劲松), BIMSA

Song Cheng (程嵩), BIMSA

Ching-Ray Chang (张庆瑞), Taiwan University

Supporting Organizations

Link

https://qlab.bimsa.cn/events/matrix/2025/

Acknowledgement

致谢北京市自然科学基金（重点资助项目Z220002）经费支持

Expressing thanks supported by the Beijing Natural Science Foundation (Project Z220002)

会议摘要（Abstract）

The proposed conference will gather leading experts on numerical approaches to the study of the Einstein equations. Recent developments in observations as well as in numerical and computational techniques and perturbation theory motivate a conference that gathers researchers from different communities.

The Einstein equations of general relativity play a central role in modern physics. Due to the highly nonlinear nature of the equations, numerical methods provide an essential tool to explore strong field dynamics. Gravitational wave forms constructed using numerical and perturbative techniques are an essential component in the success of gravitational wave observatories. The planned space based gravitational wave observatories poses new challenges in the analysis of gravitational wave emissions. The large scale dynamics of cosmological models beyond the Newtonian regime is another major challenge at present.

举办意义(Description of the aim)

Our goal is to foster interactions between the different communities doing research on these topics and to stimulate research for attacking major open problems in the field.

Talks Link: https://bimsa.net/activity/newoldnumrel/