会议摘要（Abstract）

The stable homotopy groups of spheres have been a central and enduring topic in algebraic topology, playing a key role in our understanding of the deep structure of spaces. Over the decades, substantial progress has been made in both theoretical and computational aspects of these groups. Classical tools such as spectral sequences, especially the Adams and Adams-Novikov spectral sequences have provided a robust framework for advancing the theoretical understanding of stable homotopy groups. However, many questions remain unanswered.

This workshop will focus on the problem of computing stable homotopy groups, including both history and the recent advances in this subject. We will begin by providing an overview of the history and foundational concepts underlying the study of stable homotopy groups of spheres. We will also explore how these groups are connected to broader areas in algebraic topology and mathematics, such as cobordism theory, K-theory, and motivic homotopy theory.

The computational aspect has seen recent breakthroughs, particularly through the use of modern tools like motivic and equivariant homotopy theory, for example, the recent result by Lin, Wang and Xu. We will survey some of the latest results in these areas, highlighting the role of computational techniques, including the use of motivic tools, higher chromatic tools and spectral sequences, which have pushed the boundaries of what can be computed.

Despite these advancements, significant challenges remain in understanding the full structure of the stable homotopy groups of spheres. We will address some open problems in the field. Finally, we will outline possible future directions: where does the future of stable homotopy theory lie, and how might we move closer to a complete understanding?

举办意义(Description of the aim)

This workshop aims to gather leading experts and early-career researchers to explore the latest advances in the field of stable homotopy theory, with a particular focus on the calculation and structure of stable homotopy groups of spheres. As one of the most fundamental problems in algebraic topology, understanding these groups has led to deep insights across multiple areas of mathematics, including cobordism theory and K-theory.

Thematic Focus:

The workshop will revolve around the following thematic areas:

1. Computational Techniques and theoretical developments: Recent progress in computational methods, particularly the use of motivic and equivariant homotopy theory, has led to new insights into the stable homotopy groups of spheres. Sessions will focus on motivic homotopy theory, computation-assisted spectral sequences computation, and other advances in computational tools, offering a comprehensive overview of the current state of the art.

2. Interactions with Other Fields and Open Problems: The workshop will emphasize the intersections of stable homotopy theory with other mathematical areas. We will address some open problems in the field and outline possible future directions.

Distinguished Lectures (tentative):

The workshop will feature special lectures by Weinan Lin, Guozhen Wang and Zhouli Xu. whose pioneering work on Adams spectral sequence computation has largely extend our understanding of the stable homotopy groups.

In addition to these distinguished lectures, the workshop will include interactive problem-solving sessions, collaborative working groups, and open discussions on new computational challenges and conceptual developments. The goal is to foster collaboration, encourage the exchange of ideas, and inspire further research in stable homotopy theory and its related fields.