astronomy

George A. Willis

George A. Willis is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand George A. Willis rather than just read about it. In short: George A. Willis FAA (born 10 November 1954) is an Australian mathematician.

Key takeaways

George A. Willis belongs to astronomy; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect George A. Willis to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of George A. Willis from memory before moving on to harder problems.

Reference excerpt

George A. Willis FAA (born 10 November 1954) 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 is currently emeritus Professor of Mathematics at the University of Newcastle (Australia). He is best known for his works in group theory, particularly totally disconnected groups.

Career Willis' career has been largely spent in regional Australia 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 to 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 is now emeritus Professor. During his career he has published widely and has advised 14 PhD students (as of April 2023). He was Editor-in-Chief of the Journal of the Australian Mathematical Society (Cambridge University Press) from 2012 to 2019.

Research Willis' first research paper was published in 1982 based on his research for his doctoral thesis. Willis' early research was centered around functional analysis and harmonic analysis, before shifting into group theory, particularly totally disconnected locally compact (TDLC) groups and the interaction between algebra and topology. Major areas and results include:

Willis' general structural results for totally disconnected locally compact groups paved the way to an understanding of these groups that had remained intractable for 60 years. Out of this body of work came what is now known as "Willis' Theory", a "whole new insight" into the structure and classification of totally disconnected locally compact groups. In October 2014 an Arbeitsgemeinschaft was held in Oberwolfach dedicated to research on totally disconnected groups. Willis showed that factorisation in Banach and group algebra is possible in cases when the Cohen factorisation theorem does not apply, and decisively closed the argument using negative counterexamples. Willis and Yehuda Shalom co-authored a paper that answered the conjecture of Margulis and Zimmer for a broad class of groups, and provided a unified framework for considering a number of results and conjectures in the rigidity theory of arithmetic groups. This paper won Willis the 2016 Gavin Brown Prize. Willis and Udo Baumgartner began describing contraction groups in 2004, by proving the theorem that if the scale is not 1 then the contraction subgroup is not trivial. Willis and Helge Glöckner, in the culmination of almost 20 years of work, arrived at a complete description of the closed contraction groups.

Awards, honours, and memberships Willis is a Fellow of the Australian Academy of Science, and a member of the Australian Mathematical Society, American Mathematical Society, and the London Mathematical Society.

Thomas Ranken Lyle Medal, 2025 George Szekeres Medal, 2023 Humboldt Research Award, 2023 Invited plenary speaker, International Congress of Mathematicians, 2022 Australian Laureate Fellowship (Australian Research Council) 2017 Fellow of the Royal Society of New South Wales 2018 Gavin Brown Prize (Australian Mathematical Society) 2016 Fellow of the Australian Academy of Science 2014 Invited plenary speaker, Australian Mathematical Society Annual Meeting 2011 Professorial Fellow (Australian Research Council) 2009 Invited speaker, British Mathematical Colloquium 2003

Notable publications Willis, G. (1994). "The structure of totally disconnected locally compact groups". Mathematische Annalen. 300: 341–363. doi:10.1007/BF01450491. S2CID 120442216. Shalom, Yehuda; Willis, George A. (2013). "Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity". Geometric and Functional Analysis. 23 (5): 1631–1683. arXiv:0911.1966. doi:10.1007/s00039-013-0236-5. S2CID 253644791. Praeger, Cheryl E.; Ramagge, Jacqui; Willis, George A. (2020). "A graph-theoretic description of scale-multiplicative semigroups of automorphisms". Israel Journal of Mathematics. 237: 221–265. arXiv:1710.00439. doi:10.1007/s11856-020-2005-0. S2CID 255434569. Glöckner, Helge; Willis, George A. (2021). "Locally pro-p contraction groups are nilpotent". Journal für die reine und angewandte Mathematik. 2021 (781): 85–103. arXiv:2006.10999. doi:10.1515/crelle-2021-0050. S2CID 219956769.

References

Illustrations

Worked examples

Example 1 — a first encounter with George A. Willis

Start with the simplest possible case. Write down what George A. Willis claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to George A. Willis before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about George A. Willis ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of George A. Willis

In research: George A. Willis appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses George A. Willis in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: George A. Willis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1954 births, 20th-century Australian mathematicians, Academic staff of the University of Newcastle (Australia), so understanding it makes those chapters shorter.
In everyday life: Look for George A. Willis outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study George A. Willis in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what George A. Willis means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain George A. Willis out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is George A. Willis in simple terms?

George A. Willis FAA (born 10 November 1954) is an Australian mathematician.

Why does George A. Willis matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study George A. Willis?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on George A. Willis.