ZOOM

Meeting ID: 832 8778 9283

Passcode: TSIMF

会议摘要（Abstract）

Data analysis has a wide range of applications in science and engineering. Topological computational analysis has become an important analytical tool. As an emerging branch of algebraic topology, persistent homology integrates certain geometric features into topological invariants, thereby bridging the gap between traditional topology and geometry. Computational topology, particularly topological deep learning, holds the promise of providing potentially revolutionary approaches to scientific research. For example, persistent homology has achieved significant success in the extraction, simplification, and drug discovery of complex macromolecular structures. The topological descriptions serve as an excellent foundation for machine learning applied to large-scale complex datasets and images. In computational science, algebraic topology is also applied in concurrent computing, distributed computing, sequential computation, and networks. In summary, computational topology has found many valuable applications in fields such as physics, chemistry, biology, materials science, fluid dynamics, computer graphics, control theory, geometric design, shape analysis, and computational science. This success has greatly advanced the development of related mathematical fields, including computational geometry, differential geometry, spectral geometry, geometric topology, geometric algebra, combinatorial mathematics, partial differential equations, optimization theory, inverse problems, and statistics.

The upcoming seminar on Data Analytics and Topology will bring together researchers from mathematics, physics, chemistry, biology, and computational science to explore new methods for connecting different disciplines and to promote the application of topology in both mathematics and various applied fields.

The primary goals of the proposed seminar are as follows:

● To promote the development of mathematical analysis and topological tools that can effectively utilize current computational capabilities to advance our understanding of the complexities of chemical, biological, and computational systems.

● To inspire a flow of information from "experiment to mathematics," similar to how quantum physics in the last century contributed to the establishment of heuristic new mathematics.

● To foster new connections, interactions, and collaborations between mathematicians and data scientists.

● To provide a platform for exchanging ideas and sharing topological results related to data science and computational science research.

● To introduce graduate students, postdoctoral researchers, and junior faculty members to this field and related disciplines, helping to train the next generation of researchers in computational topology.

● To enhance the participation of women, underrepresented minorities, and individuals with disabilities in research related to computational topology and its applications.

举办意义(Description of the aim)

Currently, a significant obstacle for mathematicians in the fields of computational topology and its applications is the lack of knowledge in data science and/or computational science. Conversely, for data scientists and computer scientists, the primary barrier is the absence of knowledge in the newly developed mathematical tools and topological techniques. The upcoming seminar aims to help bridge the gap between scientists and mathematicians and to foster collaboration between these two communities.

Quantum algebra has become an important direction in mathematical research in recent years. It is a natural combination and extension of theories such as representation theory, Hopf algebra theory, tensor category theory, and Lie theory. It has also gained widespread attention due to its profound connections with low-dimensional topology, rational conformal field theory, and topological field theory. In recent years, the field of quantum algebra has developed rapidly, with a series of outstanding works and progress emerging.

To enhance communication and discussions among experts in quantum algebra, showcase cutting-edge work from various directions within the field, and promote cross-disciplinary collaborations, we organize the Advances in Quantum Algebra conference in February 2025. The conference focuses on several core directions of quantum algebra, including tensor categories, Hopf algebras, vertex operator algebras, subfactor theory, topological order, topological quantum field theory, and low-dimensional topology, among others.

The conference aims to gather experts’ views and suggestions on core issues in the field, providing valuable references for young scholars in this area. Through the display of cutting-edge work across various directions of quantum algebra, this conference seeks to stimulate intellectual exchange among the experts, providing an excellent platform for cross-disciplinary and cross-field collaboration, while further advancing the development of quantum algebra.

We are delighted to annouce the “The Lotus and the Swampland” School and conference, to be held in TSIMF, Tanya, China, from Feb. 10 to Feb. 13, 2025, hosted by the BIMSA (Beijing Institute of Mathematical Sciences and Applications). This event is proposed by Prof. Cumrun Vafa, who will also be attending it.

This unique event will consist of a two-day School, followed by a two-day conference. It brings together experts in the Swampland program and its application to the universe. Each distinguished speaker is expected to deliver a lecture during the School and present a talk in the conference, providing participants with a comprehensive learning experience.
Event Details:
• Location: TSIMF, Sanya, China (http://www.tsimf.cn/)
• School: [Feb. 10-11, 2025] (two days)
• Workshop: [Feb. 12-13, 2025] (two days)
The School aims to summarize lessons we have learned from string theory about quantum gravity with a focus on the Swampland program equipping attendees with new insights and practical tools.

Date

2025-02-10 ~ 2025-02-13

Location

Organizers

• Babak Haghighat ( YMSC & BIMSA )

• Fengjun Xu ( 徐锋军, BIMSA )

• Shing-Tung Yau ( Tsinghua University&BIMSA )

• Cumrun Vafa ( Harvard University )

Special Guest

• Cumrun Vafa ( Harvard University )

Speakers

• Alek Bedroya ( Princeton University )

• Hector Parra de Freitas ( Harvard University )

• Severin Luest ( U. Montpellier )

• Jacob McNamara ( Caltech )

• Georges Obied ( Oxford )

• Gary Shiu ( University of Wisconsin-Madison )

• Houri Tarazi ( Chicago University )

• Tim Wrase ( Lehigh University )

• Kai Xu ( Harvard )

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