George A. Willis
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George A. Willis | |
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| Born | November 10, 1954 Adelaide, South Australia |
| Nationality | Australian |
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| Occupation | Australian Mathematician |
George A. Willis FAA (born 10 November 1954, Adelaide, South Australia) is an Australian mathematician. Willis received BSc (1976) and BSc (Hons) degrees in mathematics from the University of Adelaide (1977), and a doctorate from the University of Newcastle upon Tyne (1981) under the supervision of Professor B. E. Johnson. He has published widely and has advised 14 PhD students (as of April 2023). He is currently Emeritus Professor of Mathematics at the University of Newcastle (Australia). He is best known for his works in https://en.wikipedia.org/wiki/Group_theory group theory, particularly https://en.wikipedia.org/wiki/Totally_disconnected_group totally disconnected groups.
Career
Willis' career has been largely spent at the University of Newcastle (Australia). He was appointed full Professor as well as ARC Professorial Fellow in 2009, and ARC Laureate Fellow in 2018.
After the conferral of his doctorate degree from the University of Newcastle upon Tyne in 1981, he returned to Australia and took up a position as the Rothman's Postdoctoral Fellow at the University of New South Wales. From 1983-1985 he worked at the University of Halifax, Nova Scotia, as the Killam Postdoctoral Fellow, and then returned again to Australia as a Queen Elizabeth II Fellow at the University of Adelaide, before beginning a lectureship at Flinders University of South Australia in 1987. Willis then moved to the Australian National University as a research fellow in 1989, before finally moving to the University of Newcastle (Australia) to take up a lectureship where he steadily moved through the academic ranks, before reaching Emeritus Professor in 2023.
Research
Early in his career George Willis brought new life to the field of totally disconnected locally compact groups, and followed this up with a life-long career fostering collaborations resulting in game-changing concepts reaching into many areas of mathematics.
Willis’s key insight was the discovery of an integer-valued function defined on the groups which he named "the scale"[1].
Building from this breakthrough, he demonstrated that for any totally disconnected group, each scale value has an associated tree with branching number equal to the scale, and thus implemented a fundamental strategy of mathematics by showing that abstract totally disconnected locally compact groups have concretely describable features that are transferrable to different applications[2].
On the quest for a complete theory of locally compact groups, Willis pioneered the creation of a local theory. Alongside the many researchers who have built upon his advances[3], Willis uncovered the further features of flatness[4], flat rank and contraction[5] subgroups. These methods meet the challenges of a relatively weak interaction between topology and algebra in this subject.
Awards, Honours & Memberships
- Humboldt Research Award, 2023
- Invited plenary speaker, International Congress of Mathematicians, 2022
- Laureate Professorship (Australian Research Council) 2018
- Fellow (Royal Society of New South Wales) 2018
- Gavin Brown Prize (Australian Mathematical Society) 2016
- Fellow (Australian Academy of Science) 2014
- Invited plenary speaker, Australian Mathematical Society Annual Meeting 2011
- Professorial Fellow (Australian Research Council) 2009
- Invited plenary speaker, British Mathematical Colloquium 2003
References
- ↑ Willis, George (1994). "The structure of totally disconnected, locally compact groups". Mathematische Annalen. 300: 341–363. doi:10.1007/BF01450491.
- ↑ Willis, George (2015). "The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups". Mathematische Annalen. 361: 403–442. doi:10.1007/s00208-014-1074-y.
- ↑ Bywaters, Timothy P.; Tornier, Stefan (2019). "Willis theory via graphs". Groups Geom. Dyn. 13: 1335–1372. doi:10.4171/GGD/525.
- ↑ Shalom, Yehuda; Willis, George (2013). "Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity". Geometric and Functional Analysis. 23: 1631–1683. doi:10.1007/s00039-013-0236-5.
- ↑ Glöckner, Helge; Willis, George (2021). "Locally pro-𝑝 contraction groups are nilpotent". Reine Angew. Math. 781: 85–103. doi:10.1515/crelle-2021-0050.
External links
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