Helmut Pottmann of King Abdullah University of Science and Technology, Saudi Arabia, led the lineup of exciting talks Thursday with his discussion of Freeform Architecture and Discrete Differential Geometry. With the emergence of freeform structures, come interesting mathematical problems related to actual fabrication in contemporary architecture. Dr. Pottmann spoke about recent advances in geometric computing for such freeform architecture, with special emphasis on discrete differential geometry. Taking the audience through interesting structures such as meshes with planar quadrilateral faces and single curved panels, he discussed the many architectural applications of geometry.

Michael Heroux on Computing Essentials: What SIAM Members Should Know about Emerging Architectures

Michael Heroux of Sandia National Laboratories gave a very engaging and relevant lecture: Computing Essentials: What SIAM Members Should Know about Emerging Architectures. “This is a time of disruptive change in the computing architecture field,” he began, explaining that the commodity curve had changed. Multicore and GPU processors today with terascale laptop, petascale deskside and exascale center systems have moved the computing industry beyond increased clock speed and instruction level parallelism even while memory per core and consistency of performance has been going down. He explained that all of these changes are happening because of lack of energy efficiency. Meanwhile, we see more heterogeneity with performance variability and core specializations. These are trends that those in the field should be aware of in order to make their algorithms and applications more efficient, Heroux said. “If you care about performance, parallel computing is your future,” he said. “If you don’t care about performance, there’s another talk down the hall,” he added jokingly, prompting laughter, but no exits.  He also stressed the importance of locality, resilience, and reliability. Since these systems are built with many parts, the overall reliability tends to be lower than that of each part. In addition, algorithms should be designed in such a way that they can adapt to future changes, as they were in the past. Improving performance now necessitates parallel execution, Heroux concluded. Thinking in parallel patterns provides opportunities for fine-grained dynamic parallelism. “Parallelism is the new commodity curve,” he said.

Complex Adaptive Systems and the Challenge of Sustainability- by Simon Levin

Pierre-Louis Lions of Collège de France gave an engaging talk On Mean Field Games. Mathematical modeling that aims to describe the behavior of a very large number of “agents”, Mean Field Games (MFG) are a new class of models where an agent optimizes decisions by taking into account and interacting with other agents. Explaining with simple examples how MFG models are derived, the theory behind them and their connections with other fields, Dr. Lions went on to describe a range of classical systems that present specific cases of MFG, such as, compressible Euler equations, Hartree equations, porous media equations, semilinear elliptic equations, Hamilton-Jacobi-Bellman equations, and Vlasov-Boltzmann models.

In an engrossing—yet slightly unnerving—talk on Complex Adaptive Systems and the Challenge of Sustainability, Simon Levin of Princeton University reinforced the many tests that face us today on account of Earth’s limited resources. The growing human population and increasing per capita demand emphasize the need to study patterns of sustainability. The question of whether we are consuming too much is similar to an ecological problem, such as how much a plant should invest in growth vs. reproduction, he explained. Hence, many lessons can be derived from ecological systems in order to make decisions regarding sustainability. Ecological and socioeconomic systems both organize as complex adaptive systems, which are made up of individual agents that interact locally and evolve based on these interactions.

Simon Levin on Complex Adaptive Systems and the Challenge of Sustainability (Photo courtesy of Nick Higham)

Levin went on to explain the influence of social norms, role of leadership and management systems in tackling such a global problem. Drawing a comparison between animal groups and human society, he pointed out that both are led by a small number of opinionated individuals where consensus relies on a large number of non-opinionated individuals who promote democratic decisions. A simple mathematical model such as a gradient system can measure the level of synchrony in a group, thus giving its average direction.  This can be further modified with adaptive network models with induced and spontaneous opinion changes. The mathematical challenges would involve scaling: crossing scales of space and time, and scaling from individuals to collectives. Thus reinforcing parallels with evolutionary biology, the lecture elucidated on lessons we can take from ecology and evolution to move toward a sustainable future.

Richard Tapia of Rice University, in his invited lecture, The Isoperimetric Problem Revisited: Exposing Euler’s 1744 Proof of Necessity as a Proof of Sufficiency, as Such the First and Shortest in History, did exactly what the title indicates: argue that Euler’s original proof should be viewed as the first and shortest solution to the isoperimetric problem in history. After outlining the history of the isoperimetric problem, Dr. Tapia went on to demonstrate that Euler’s proof was just one observation away from establishing sufficiency. Euler constructed multiplier theory to solve the isoperimetric problem in 1744, concluding that while his theory was necessary, it wasn’t sufficient to prove that the circle was the solution. More than a century later, Weierstrass constructed an elegant sufficiency theory for problems in the calculus of variations, giving the first complete proof that the circle solved the isoperimetric problem. However, Dr. Tapia sought to demonstrate that Euler’s original proof was merely an observation away from establishing sufficiency and should be viewed as the first and shortest solution to the isoperimetric problem in history.

The SIAM book giveaway last evening saw eager students line up in the Exhibit Hall for freebies from SIAM’s comprehensive collection of high-quality books delivered by experts in mathematics, computational science, and engineering.

This was followed by the Professional Development session later in the evening, where students were able to interact with academics and professionals from universities, government labs and industry. The focus was on verbal communication, and panelists shared their experiences on professional networking and interactions, the importance of delivering good presentations, and job interview skills.

Photo of the day:

Richard Tapia as bullfighter! (Photo courtesy of Nick Higham)

Tweets of the day:

12 Jul Sven Leyffer ‏@SvenLeyffer

Heroux #SIAMAN12: With C++ as hammer everything looks like a thumb

12 Jul Nick Higham ‏@nhigham

Good example to all speakers: Simon Levin looks at the audience not the screen! ‪#SIAMAN12‬ http://ow.ly/i/LuOt

What to look for on Friday:

Invited Lectures:

8:30 AM – 9:15 AM

IC9 Overcoming the Tyranny of Scales in Subsurface Flow and Reactive Transport Simulation

Timothy D. Scheibe, Pacific Northwest National Laboratory, USA

Nicollet ABC – Level 1

8:30 AM – 9:15 AM

IC10 Network Formation and Ion Conduction in Ionomer Membranes

Keith Promislow, Michigan State University, USA

Nicollet D – Level 1

9:15 AM – 10:00 AM

IP4 Complex Networks. A Tour d’ Horizon

Ernesto Estrada, University of Strathclyde, United Kingdom

Nicollet ABC – Level 1

2:00 PM – 2:45 PM

IP5 Linear Algebra Methods for Data Mining with Applications to Materials Science

Yousef Saad, University of Minnesota, USA

Nicollet ABC – Level 1

2:45 PM – 3:30 PM

IP6 Multifidelity Modeling for Identification, Prediction and Optimization of Large-scale Complex Systems

Karen E. Willcox, Massachusetts Institute of Technology, USA

Nicollet ABC – Level 1