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H. C. Chan, in terms of : Some Recent Developments, *Proceedings of the Twelfth International Conference in Fibonacci Numbers*, (2010): 17-25. Read Pi in terms of Phi (Fib Conf 2006).

H. C. Chan, in terms of , *Fibonacci Quart.* **44** (2006): 141–144. Read Pi in terms of phi.

H. C. Chan, More Formulas for , *Amer. Math. Monthly* **113**: 452-455. Read More formulas for Pi.

H. C. Chan, Machin-type formulas expressing in terms of , *Fibonacci Quart.* **46/47** (2008/2009): 32–37 Read Pi via Machin.

Two quick updates with regards to polymath projects. Firstly, given the poll on starting the mini-polymath4 project, I will start the project at Thu July 12 2012 UTC 22:00. As usual, the main research thread on this project will be held at the polymath blog, with the discussion thread hosted separately on this blog.

Second, the Polymath7 project, which seeks to establish the “hot spots conjecture” for acute-angled triangles, has made a fair amount of progress so far; for instance, the first part of the conjecture (asserting that the second Neumann eigenfunction of an acute non-equilateral triangle is simple) is now solved, and the second part (asserting that the “hot spots” (i.e. extrema) of that second eigenfunction lie on the boundary of the triangle) has been solved in a number of special cases (such as the isosceles case). It’s been quite an active discussion…

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Chris Evans has proposed a new polymath project, namely to attack the “Hot Spots conjecture” for acute-angled triangles. The details and motivation of this project can be found at the above link, but this blog post can serve as a place to discuss the problem (and, if the discussion takes off, to start organising a more formal polymath project around it).

Auburn University’s College of Sciences and Mathematics Colloquia are held on Fridays in Parker Hall, Room 250, from 4:00-4:50 (unless otherwise advised).

Refreshments are served in Parker Hall, Room 244, beginning at 3:30.

March 23, 2012

Speaker: Fuzhen Zhang (Nova Southeastern University, Fort Lauderdale, FL)

Title: The Schur Complement

Abstract: Auburn is the birthplace of the mathematical term “Schur complement.” This talk will present the historical connection of Auburn and the term, review classical results, and show some new results on the topic.

Faculty host: T. Y. Tam

A brief bio: Fuzhen Zhang has about 50 research articles. He authored two books (Linear Algebra: Challenging Problems for Students, Johns Hopkins University Press, 1996; 2nd edition 2009. Matrix Theory: Basic Results and Techniques, Springer, 1999; 2nd edition 2011) and edited the book The Schur Complement and Its Applications, Springer 2005). He is an associate editor of several journals, including Linear and Multilinear Algebra, International Journal of Information and Systems Sciences, Banach Journal of Mathematical Analysis (BJMA). He is also a collaborating editor for the American Mathematical Monthly.

Dr. Emilie Haynsworth was the first to call it the Schur complement. She directed the work of 18 students who earned doctorates, all at Auburn University.