2013 AMS Levi L. Conant Prize Recipient
SYMMETRY IN MATHEMATICS AND PHYSICS
Abstrace: Deep at the heart of any discipline lies the idea of “symmetry.” We will explore the fascinating tale of symmetry, from its codification into a powerful tool called group theory by mathematicians in the 19th century, to its rise to the center of fundamental physics in the 20th century, and its evolution and influence today. Group theory begins with intuitive, pictorial ideas of what it means to have symmetry. In the 1830s, the 20 year old genius Evariste Galois invented group theory and turned it into a powerful tool in pure mathematics, but one devoid of apparent practical use. Much later, after decades of mathematical development, Albert Einstein introduced symmetry to physics with his theory of relativity. Yet it was only in the latter half of the 20th century that we discovered the true importance of symmetry in physics: particle physicists discovered it at the heart of the laws of nature, essentially giving our most basic laws their form. It has continued to have a central place ever since, and today, new mathematical ideas about symmetry, with exotic names like “quantum groups” and “higher categories,” may be poised to revolutionize the physics of the 21st century.
John Huerta earned his PhD in 2011 in mathematics from the University of California, Riverside. Huerta is a mathematical physicist, currently a postdoctoral fellow at Centre for Mathematical Analysis, Geometry, and Dynamical Systems in Lisbon. In 2013 he shared the Levi L. Conant Prize with his advisor, John Baez, at University of California, Riverside, for the paper “The Algebra of Grand Unified Theories.”Bulletin of the American Mathematical Society 47:483-552, 2010.