# Michael Aschbacher

Wolf Prize Laureate in Mathematics 2012

The Prize Committee for Mathematics has unanimously decided that the 2012 Wolf Prize be awarded to: Luis Caffarelli and Michael Aschbacher.

**Michael Aschbacher** And John Thompson (wolf prize Laureate of 1992) are the two great modern masters of the theory of finite groups, in an era that brought to fruition a line of research going back to Galois in the 1830s. The breadth and depth of Aschbacher’s understanding of finite groups in general, and finite simple groups in particular, and the power he brought to bear on their analysis, are astonishing.

Aschbacher astounded the finite group theory community with a series of papers that raised the classification project for finite simple groups from a distant dream to the reality it is today.

In a series of papers in the 1970’s Aschbacher developed the theory of standard components and tightly embedded subgroups, and brought the theory of groups of odd characteristic type close to the completion.

Turning next to groups of characteristic type, Aschbacher handled all of the most difficult cases, notably the Thin Group case, the p-Uniqueness Case, and finally the Quasithin Case. This last result, contained in two massive monographs written jointly with S.D Smith, completed the classification of finite simple groups. In the process, he significantly advanced the theories of GF(2) representations, Thompson factorization, and pushing- up.

Also worthy of mention are Aschbacher’s work on maximal subgroups of finite simple groups, his joint work with Y.Segev on the uniqueness of the sporadic groups, and his joint work with S.D. Smith on the Quillen conjecture.

Prof. Lieber has introduced new paradigms in the growth of a broad range of nanometer diameter wires and heterostructures. His contributions have provided a comprehensive tool box for systematic growth of materials heterostructures and devices, with the demonstrated potential for contributions to areas ranging from computing and

Communications to biology and medicine.

The most significant breakthrough made by Lieber was his creation of a general method for the synthesis of single crystal semiconductor nanowires based on the nanocluster-catalyzed growth model. This work provided the intellectual underpinnings for the predictable growth of nanowires of virtually all main group materials in the periodic table, and enabled Lieber to demonstrate control of electronic properties through doping and size limits with molecular-scale nanowires. He proposed and demonstrated a general concept for the growth of nanoscale axial heterostructures, nanowire-nanotube heterojunctions and the growth nanowire superlattices with novel photonic and electronic properties. In addition, Lieber pioneer the concept of both radial core-shell structures, and three-dimensionally-branched nanowires.

In addition to his rich contributions to the characterization of carbon nanotubes with STM and AFM, Lieber has made pioneering contributions illuminating the electrical, optical and optoelectronic properties of semiconductor nanowires, and has demonstrated unique ballistic and quantum transport in specifically designed core/shell nanowires.

By combining his advances in controlled synthesis and understanding physical properties of nanowires Lieber has provided seminal examples of nanotechnologies. He has exploited semiconductor nanowire building blocks to fashion an array of nanoscale functional electronic and optoelectronic devices, including the first p-n diode junctions, active bipolar transistors, field-effect transistor, complementary inverters, point-like nanoscale light-emitting diodes, and electrically-driven single nanowire lasers.

Prof.Lieber has made seminal advances at the interface between nanoelectronics and biological systems. He recognized the duality of chemical/biological and electronic signaling at the nanoscale to demonstrate the first direct electrical detection of proteins, and pushed this concept to the level with selective electrical sensing of individual viruses, and ultrahigh sensitivity detection of cancer markers.

He has pioneered the usage of nanodevices to record electrical activity from cultured neurons and cardiac cells as well as tissue samples, demonstrating unprecedented spatial and temporal resolution for fundamental neurobiology and medicine.