Considered the nation´s most prestigious award for new faculty members, these awards honor the most promising young researchers in science and engineering fields who have translated their work into significant education activities. For their leadership role they also receive monetary awards, ranging from $400,000 to nearly $1 million over five years to support their career research and education goals.

This year´s awards, announced September 9th, bring to 160 the number of PECASE recipients since 1996.

LEADER IN MATHEMATICS

Vakil, a theoretical mathematician at Stanford University, is at the forefront of modern algebraic geometry. He is a leading figure in the study of the moduli space of curves, to deepen a growing understanding of the “universal facts� of these objects. This is adding much to core mathematics theory as well as applications such as String Theory and physics.

Originally from Toronto, Vakil received his undergraduate degree at the University of Toronto, where he was a four-time Putnam Competition winner. After completing a PhD at Harvard, he taught at Princeton and MIT before moving to Stanford in 2001. His field of research is algebraic geometry, with connections to nearby fields, including combinatorics, topology, number theory, and physics. He has long been interested in teaching mathematics through problem solving; he coached the Canadian team to the International Mathematical Olympiad from1989 to 1996, and has written two books related to problem-solving (one on the Putnam competition, and one titled "A Mathematical Mosaic:Patterns and Problem Solving").

Vakil has established significant educational outreach to Bay-Area groups devoted to stimulating mathematics learning among high-school students, and he has established a journal introducing high-school students to mathematics through hands-on problem solving. A three-time medalist (including two golds) in the International Mathematical Olympiad, he has worked extensively with gifted high school students. He is author of A Mathematical Mosaic: Patterns and Problem Solving where he tries to encourage curiosity, a sense of beauty, and the love of knowledge.

The book which is a collection of puzzles, mathematical explanations and historical tidbits, speaks in an interesting and understandable way about number theory, combinatorics, game theory, geometry, and calculus to say nothing about magic tricks, and other digressions, weaving them into a mosaic that reveals their interconnections. It is a must for teachers seeking to challenge their best students and for students preparing for mathematics competitions.

In his public seminars Vakil likes to show that lurking behind even the most trivial-looking doodles can be mathematics of surprising beauty and power. According to Vakil, doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, he says, there is often some sophisticated and fun mathematics buried inside common doodles.

Vakil is interested in attracting talented high school and undergraduate students into the mathematical sciences, by exposing them to exciting and advanced yet accessible ideas, for example through problem solving; this will be done primarily through the Stanford University Math Camp, a problem solving seminar at Stanford, the Berkeley Math Circle, and various writings. In particular, his goal is to attract students from previously untapped pools of talent. In addition he hopes to build a center for algebraic geometry at Stanford, by providing resources for graduate students and postdoctoral students, developing new courses, inviting visitors, and sponsoring seminars and conferences, often jointly with other institutions. Finally he hopes to continue to bring sophisticated mathematical ideas (of all levels) to a wider audience through expository writing.

LEADING COMPUTER SCIENTIST

Sandeep Shukla, at the Virginia Polytechnic Institute and State University, is a leading researcher in designing, analyzing and predicting performance of electronic systems embedded on a chip. The award citation reads: ‘He has integrated several innovative techniques and theories into novel approaches to solve problems in microelectronic systems design. He applies research concepts into new courses in computer engineering and mentors minority and women students in processor design as well as in computer science and engineering overall.’

A gold medalist and first rank holder from Jadavpur university (1991), Shukla earned his MS and Ph.D degrees from the State University of New York.

Shukla, who joined the Virginia Tech electrical and computer engineering faculty in August 2002, will use his Award to devise a strategy for achieving the optimal balance of power and performance in embedded computer systems. "The computing world is moving from the desktop and workstation to an arena of embedded and wearable computers," says Sandeep Shukla, who plans to help solve one of the major problems in this transition.

Embedded computers, he explained, are used in every sphere of modern life. More and more, embedded computers are becoming the brains behind mechanisms that we rely on throughout our everyday lives -- wireless devices, cars, automated elevators, climate control systems, traffic signals, and washing machines, to name a few.

"Some experts estimate that each individual in a developed nation may unknowingly use more than 100 embedded computers daily," Shukla noted. "Embedded computers also constitute the backbone of our complex systems, such as space mission controls, avionics, and weapons systems."

Most embedded computers are powered by rechargeable batteries. Because space is limited in their host devices, they typically operate on small, low-power batteries. "These computers must function on low power and at the same time offer a level of performance guaranteed by a Quality of Service (QoS) agreement that serves as an industry standard," Shukla noted. "In certain situations, as in the case of pace-makers, the batteries must last a long time without replacement."

There are two performance factors critical to embedded computers -- speed and quality of service. "If the power supplied by the battery is too low, the computer´s performance is reduced," Shukla said. "That might affect the speed of a palm pilot, for example, or the sound quality in a hearing device. The question is whether a compromise between performance and power is reasonable for a particular device or application."

The trend toward arranging embedded computers in a network also has created a need for research into the optimal balance of power and performance. Shukla´s goal is to support the current and future uses of embedded computers by developing a power usage strategy that can guarantee maximum performance. This entails analyzing the complex probabilities of when computers will require power and how much power they will use.

"It´s similar to designing a network of traffic lights for a particular traffic pattern," he explained. "The highway engineer has to study the probabilities of when and where traffic is the heaviest and then set up a network of lights that will allow a maximum flow of traffic."

To consider a minor example, a usage strategy could be devised for a cell phone that would put the system in the "sleep" mode during times when the probability of usage is low and keep the system in a "ready" mode when incoming and outgoing calls are expected and fast action is required. Such a strategy would reduce power use and increase the life of the battery while optimizing the cell phone´s performance.

Using a probability analysis modeling tool called PRISM, which he worked with at the University of Birmingham in England during the summer of 2002, Shukla will devise usage strategies for a network of wireless computers. Based on analyses of the usage frequencies and probabilities of all the computers in a networked embedded system, he will attempt to create a strategy that will reduce power use while increasing performance. "Eventually, companies will use probability design in developing embedded computers for everything from small wireless devices to large-scale computer networks," Shukla said.

Shukla also plans to develop graduate and undergraduate courses in embedded computer systems and to support the work of student assistants in FERMAT (Formal Engineering Research with Modeling, Abstraction and Transformation), the new research laboratory he has founded. He is working on two textbooks and is planning an outreach program for the local public schools.

Shukla began studying embedded computers while working as an engineer with Verizon and, later, Intel. Before coming to Virginia Tech, he was a member of the research faculty of the Center for Embedded Computer Systems at the University of California at Irvine.

In addition to research and development, Shukla´s work will involve the development of an embedded systems specialization for computer engineers. He acknowledges that there is is a dire shortage of engineers experienced in designing and implementing embedded systems and only a handful of universities around the world currently have specialization programs.