A Scorching Summer School in Shanghai

November 1, 2013

Jing Leng, Charles Puelz, and Leo Taslaman

The 2013 Gene Golub SIAM Summer School, in conjunction with the third International Summer School on Numerical Linear Algebra and the 10th Shanghai Summer School on Analysis and Numerics in Modern Sciences, took place July 22 to August 2 in a hot Shanghai, with record-breaking temperatures, close to 40C/104F. We were well prepared; the organizers equipped each of us with a flask for water and an umbrella for the sun---both very much appreciated! Our schedule was more or less the same every day: four hours of lectures in the morning, starting at eight, followed by lunch and a bit of rest before the afternoon tutorials. Several students used an impressive cafe on the 15th floor of the mathematics building as a venue for digging into our assigned problems. Coffee and a view of downtown Shanghai accompanied our discussions of matrix functions, model reduction, eigenvalues, and high-performance computing.

Nick Higham and Marlis Hochbruck gave the lectures during the first week. Higham focused on functions of matrices, beginning with the history of the subject and ending with recently developed algorithms for computing matrix exponentials. Hochbruck discussed exponential integrators and explained how matrix functions (exponential and phi-functions in particular) can be used to solve differential equations. During the tutorials we cut our teeth on plenty of problems, some of them open, so no one was left unchallenged.

The second week of the summer school saw lectures by Peter Benner, Ren-Cang Li, and Sherry Li. Benner followed a thorough presentation of the basic notions and common algorithms used in model reduction with some state-of-the-art results. Ren-Cang Li lectured on Rayleigh quotient-based methods for eigenvalue computations, providing detailed explanations of various algorithms. Offering a refreshingly computational/HPC component to the summer school, Sherry Li explained how combinatorial arguments are useful in quantifying fill-in for particular factorizations of matrices. She complemented the theory with several lectures on parallel computing. The tutorials for this part of the school consisted of both theoretical exercises and computational problems in OpenMP and MPI.

In addition to the presentations of cutting-edge material, we took advantage of the phenomenal opportunity to converse with new acquaintances from all over the world. The organizers seem to have put a lot of thought into this aspect of the summer school: The students' home institutions represented 15 countries. In addition, the lecturers allocated part of the tutorial time to ten-minute presentations by students of their current work---an opportunity that a majority took. Interactions among students occurred not only on a mathematical level: Randomly assigned seats for every lunch and dinner facilitated further dialogue, allowing us to chat about everything from hobbies to favorite foods, with fellow students as well as with lecturers and local organizers. We feel confident that these contacts will lead to connections and future collaborations. Given our new networks of friends, conferences will surely be more fun in the future!

On the weekends some ambitious students studied, but most chose to enjoy the vivid night life of Shanghai. We spent the first week sightseeing, visiting museums, and exploring several local bars, but in the end we all converged on an obscure club known as "Perry's." The local organizers also made sure that we experienced a fair amount of Chinese culture. In particular, the array of local dishes offered at each lunch and dinner left no one bored; to mention only a few, we tried jellyfish, frog, duck feet, and pig intestine and stomach. The organizers also arranged an excursion to a beautiful old village outside Shanghai. There, we walked around in ancient gardens, smelled stinky tofu, enjoyed boat taxis, and haggled in the local market.

The Gene Golub SIAM Summer School provided us with many things: exposure to important material in numerical linear algebra, networking with other students and professors, and incredible cultural experiences. In addition to what we learned in the daily lectures and exercises on leading-edge research topics, we now know scholars---junior and senior---from all over the world, both personally and professionally. And the ten-minute student presentations gave us an understanding of the types of mathematical problems of interest to our newly made friends. Thanks to Gene Golub, we experienced all these things and had a great deal of fun while doing it. For this we are very grateful. Surely the summer of 2013 in Shanghai will be unforgettable for all of us.

The U.S. National Science Foundation, the National Science Foundation of China, and several local institutions, such as the Shanghai Center for Mathematical Sciences and the Sino-French Institute for Applied Mathematics, also provided financial support.

Selected photos of the 2013 school can be found at http://www.cs.ucdavis.edu/~bai/g2s3/Photos/. Also worth a visit is Nick Higham's blog post on the school at http://nickhigham.wordpress.com/2013/08/09/gene-golub-siam-summer-school-2013/.

Jing Leng of Fudan University, China, Charles Puelz of Rice University, USA, and Leo Taslaman of the University of Manchester, UK, were students in the 2013 Gene Golub SIAM Summer School.


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