C. T. C. Wall

2.1. Birth and Early Life

Charles Terence Clegg Wall was born on December 14, 1936, in Britain. His early education took place at Marlborough College, a prestigious independent boarding school in Marlborough, Wiltshire.

2.2. Education

Following his time at Marlborough College, Wall pursued higher education at Trinity College, Cambridge, part of the esteemed University of Cambridge. He completed his PhD at Cambridge in 1959. His doctoral thesis, titled "Algebraic aspects of cobordism," was a significant early contribution to algebraic topology and was supervised by prominent mathematicians Frank Adams and Christopher Zeeman.

3.1. Topology and Cobordism Theory

Wall's early research focused on cobordism theory within the field of algebraic topology. His 1959 University of Cambridge PhD thesis, "Algebraic aspects of cobordism," laid important groundwork in this area.

3.2. Manifolds, Geometric Topology, and Surgery Theory

His research then primarily shifted to manifolds, with a particular emphasis on geometric topology and the related abstract algebra involved in surgery theory. Wall is recognized as one of the founders of surgery theory, a powerful technique for classifying manifolds. In 1964, he introduced the Brauer-Wall group of a field, a concept that has found applications in various areas of algebra. His 1970 research monograph, "Surgery on Compact Manifolds," stands as a major reference work in geometric topology, widely cited for its comprehensive treatment of the subject.

3.3. Contributions to Group Theory

In 1971, Wall put forth a significant conjecture stating that every finitely generated group is accessible. This conjecture greatly stimulated progress in understanding the splittings of groups. While Martin Dunwoody proved the conjecture for the class of finitely presented groups in 1985, the full resolution of the conjecture took until 1991. To the surprise of many mathematicians at the time, Dunwoody discovered a finitely generated group that is not accessible, thereby demonstrating that Wall's conjecture was not correct in its general formulation.

3.4. Research in Singularity Theory

Since the mid-1970s, Wall's work has largely concentrated on singularity theory, a field developed by mathematicians such as R. Thom, J. Milnor, and V. Arnold. His contributions in this area particularly concern the classification of isolated singularities of differentiable maps and of algebraic varieties. He has authored two influential research monographs on singularity theory.

3.5. Major Publications

Wall's contributions to mathematics are documented in several influential research monographs:

• "Surgery on Compact Manifolds" (1970): A seminal work in geometric topology, providing a comprehensive framework for surgery theory.
• "The Geometry of Topological Stability" (1995): Co-authored with Andrew du Plessis, this book contains a substantial amount of original research in singularity theory.
• "Singular Points of Plane Curves" (2004): Another significant monograph detailing his work in singularity theory, specifically on the classification of singularities of plane curves.

3.6. Notable Students

Charles Terence Clegg Wall has supervised numerous students who have gone on to make their own significant contributions to mathematics. His notable students include:

• Michael Boardman
• Bill Bruce
• Andrew Casson
• Francis E. A. Johnson
• David Mond
• Andrew du Plessis
• David Trotman

4.1. Professor at the University of Liverpool

In 1965, Charles Terence Clegg Wall was appointed professor at the University of Liverpool. He later became an emeritus professor at the same institution, maintaining a long-standing association with the university.

4.2. President of the London Mathematical Society

From 1978 to 1980, Wall served as the president of the London Mathematical Society, a prestigious role within the British mathematical community.

6.1. Family

Charles Terence Clegg Wall married Sandra Hearnshaw in 1959. Together, they have four children. As of 2024, they also have seven grandchildren and four great-grandchildren, named Rory, Felix, Valentina, and Leo.

6.2. Political Activities

Reflecting his engagement in center-left political discourse, Wall was actively involved with the Social Democratic Party (SDP). He served as the treasurer for the Wirral area SDP from 1985 until its merger with the then Liberal Party in 1988. Following the merger, Wall continued his political involvement as the treasurer for the newly formed Wirral West Liberal Democrats. However, as of May 2020, he no longer holds this position.

6.3. Other Social Activities

Wall has also contributed to his local community through various social roles. He served as an LEA-appointed governor of West Kirby Grammar School starting in 1987, a position he has since relinquished. Additionally, he held the post of treasurer at the Hoylake Chamber Concert Society.

7.1. Reception in the Mathematical Community

Wall's research and contributions are highly regarded within the mathematical community. His foundational work in surgery theory, particularly his monograph "Surgery on Compact Manifolds," is considered a cornerstone in geometric topology. While his conjecture on group accessibility was ultimately disproven in its general form, it significantly stimulated research and understanding within group theory, demonstrating the profound impact of even unproven conjectures in driving mathematical progress. His later work in singularity theory further solidified his reputation as a versatile and deep mathematician.

7.2. Impact on Future Generations

The theories and methodologies developed by Wall, especially in surgery theory and singularity theory, have provided essential tools and frameworks for subsequent mathematicians. His work on the classification of manifolds and singularities continues to be a fundamental reference for researchers. Furthermore, his role as a supervisor to numerous notable students, many of whom became prominent mathematicians themselves, highlights his significant mentorship and influence on the development of future generations in the field.

• [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Wall.html Biography at MacTutor History of Mathematics Archive]
• [https://mathgenealogy.org/id.php?id=24418 Academic genealogy at Mathematics Genealogy Project]
• [http://www.liv.ac.uk/~ctcw/homepage.html Contact details and list of recent publications]
• [http://www.maths.ed.ac.uk/~aar/wall70.htm Information on his 70th birthday conference, Edinburgh, 2006]
• [http://www.maths.ed.ac.uk/~aar/surgery Resources on surgery theory]