Condensed concepts

The picture below is of Godel's rotating universe . It represents an exact solution to Einstein's gravitational field equations and has the strange property of closed timelike curves (i.e. one can travel into the past!). This mathematical solution was found by Kurt Godel while he was employed by the Institute for Advanced Study at Princeton. I think I first encountered this picture in my final undergraduate year in the classic book, The Large Scale Structure of Space-Time by Hawking and Ellis, while working on a research project in general relativity. Godel's universe is just one example of the fascinating science and stories recounted in the book Who Got Einstein's Office? Eccentricity and Genius at the Institute for Advanced Study by Ed Regis , first published 30 years ago. I only read the book this past week and loved it. It is a captivating blend of science, mathematics, personalities, history, philosophy, humorous anecdotes, gossip, eccentricities ...

This is not about managing university endowments! On a recent flight I watched the fascinating HBO documentary, Becoming Warren Buffett. He may be one of the richest people in the world, and perhaps the most successful investor of all time. However, what is much more striking than his success is how he got there: in a completely counter-cultural (or iconoclastic) way. Here a few lessons that I think are particularly relevant to universities as they struggle with their identity, purpose, and management. Focus. Several times Buffett and some of his admirers emphasised this. Good research of companies and understanding the market requires considerable focus. You can't be doing lots of different things or jumping into the latest fad. Universities need to focus on teaching and research. Faculty need to focus on just a few things they can do well. The long view. Buffett does not "play" the market. He finds companies that are undervalued or have enduring market share

Last week at UQ we had a very nice mathematics colloquium , "Crowdsourcing mathematics problems" by Timothy Gowers. He first talked about the Polymath project , including its successes and marginal contributions. He then talked about a specific example of a project currently underway on his own blog , concerning transitive dice. This was pretty accessible to the general audience. This is where a well defined important problem is defined on a blog and then anyone is free to contribute to the discussion and solution. A strength of this approach is that it makes use of the complementary strengths, experience, and expertise of the participants. Specifically, solving problems includes: selecting a problem that is important, interesting, and potentially ripe for solution defining the problem clearly breaking the problem down into smaller parts including conjectures sketching a possible heuristic argument for the truth of the conjecture giving a rigorous proof of the conje

Some of my UQ colleagues and Jaime Merino have written a series of nice papers inspired by an organometallic molecular material Mo3S7(dmit)3. They have considered possible model effective Hamiltonians to describe it and the different ground states that arise depending on the model parameters. There is a rich interplay of strong correlations, Hund's rule coupling, spin frustration, spin-orbit coupling, flat bands, and Dirac cone physics. Possible ground states include some sort of Mott insulator, a Haldane phase, semi-metal, ... A good place to start is the following paper Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice  C. Janani, J. Merino, Ian P. McCulloch, and B. J. Powell The figure below (taken from this paper ) shows some of the molecular structure and some of the hopping integrals that are associated with an underlying decorated honeycomb lattice. This model could be called  kagomene,  because it interpol