Michael Larsen | |
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| Nationality | American |
| Alma mater | Princeton University Harvard University |
| Awards | Putnam Fellow (1981, 1983) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Pennsylvania University of Missouri Indiana University Bloomington |
| Thesis | Unitary groups and L-adic representations (1988) |
| Doctoral advisor | Gerd Faltings |
Michael Jeffrey Larsen is an American mathematician, a distinguished professor of mathematics at Indiana University Bloomington. [1] [2]
In high school, Larsen tied with four other competitors for the top score in the 1977 International Mathematical Olympiad in Belgrade, winning a gold medal. [3] [4] As an undergraduate mathematics student at Harvard University, Larsen became a Putnam Fellow in 1981 and 1983. [5] He graduated from Harvard in 1984, [6] and earned his Ph.D. from Princeton University in 1988, under the supervision of Gerd Faltings. [7] After working at the Institute for Advanced Study he joined the faculty of the University of Pennsylvania in 1990, and then moved to the University of Missouri in 1997. [6] He joined the Indiana University faculty in 2001. [1]
His wife Ayelet Lindenstrauss is also a mathematician and Indiana University professor. [8] Their son Daniel at age 13 became the youngest person to publish a crossword in the New York Times. [9]
Larsen is known for his research in arithmetic algebraic geometry, combinatorial group theory, combinatorics, and number theory. [1] [2] He has written highly cited papers on domino tiling of Aztec diamonds, [10] topological quantum computing, [11] [12] and on the representation theory of braid groups. [13]
In 2013 he became a fellow of the American Mathematical Society, for "contributions to group theory, number theory, topology, and algebraic geometry". [14] He received the E. H. Moore Research Article Prize of the AMS in 2013 (jointly with Richard Pink).
John Carlos Baez is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California. He has worked on spin foams in loop quantum gravity, applications of higher categories to physics, and applied category theory. Additionally, Baez is known on the World Wide Web as the author of the crackpot index.
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions, possibly in some generalized sense. A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which does not always equal ; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions.
In physics, an anyon is a type of quasiparticle so far observed only in two-dimensional systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical properties intermediate between fermions and bosons. In general, the operation of exchanging two identical particles, although it may cause a global phase shift, cannot affect observables. Anyons are generally classified as abelian or non-abelian. Abelian anyons, detected by two experiments in 2020, play a major role in the fractional quantum Hall effect.
The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and James Harris Simons, who introduced the Chern–Simons 3-form. In the Chern–Simons theory, the action is proportional to the integral of the Chern–Simons 3-form.
In physics, topological order is a kind of order in the zero-temperature phase of matter. Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders cannot change into each other without a phase transition.
A topological quantum computer is a theoretical quantum computer proposed by Russian-American physicist Alexei Kitaev in 1997. It employs quasiparticles in two-dimensional systems, called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime. These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable. Small, cumulative perturbations can cause quantum states to decohere and introduce errors in the computation, but such small perturbations do not change the braids' topological properties. This is like the effort required to cut a string and reattach the ends to form a different braid, as opposed to a ball bumping into a wall.
Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.
Jürg Martin Fröhlich is a Swiss mathematician and theoretical physicist. He is best known for introducing rigorous techniques for the analysis of statistical mechanics models, in particular continuous symmetry breaking, and for pioneering the study of topological phases of matter using low-energy effective field theories.
Matilde Marcolli is an Italian and American mathematical physicist. She has conducted research work in areas of mathematics and theoretical physics; obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft, and the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation. Marcolli has authored and edited numerous books in the field. She is currently the Robert F. Christy Professor of Mathematics and Computing and Mathematical Sciences at the California Institute of Technology.
Lawrence David Guth is a professor of mathematics at the Massachusetts Institute of Technology.
Georgia McClure Benkart was an American mathematician who was known for her work in the structure and representation theory of Lie algebras and related algebraic structures. She published over 130 journal articles and co-authored three American Mathematical Society memoirs in four broad categories: modular Lie algebras; combinatorics of Lie algebra representations; graded algebras and superalgebras; and quantum groups and related structures.
Urs Schreiber is a mathematician specializing in the connection between mathematics and theoretical physics and currently working as a researcher at New York University Abu Dhabi. He was previously a researcher at the Czech Academy of Sciences, Institute of Mathematics, Department for Algebra, Geometry and Mathematical Physics.
Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
Vladimir Georgievich Turaev is a Russian mathematician, specializing in topology.
Kyōji Saitō is a Japanese mathematician, specializing in algebraic geometry and complex analytic geometry.
Kari Kaleva Vilonen is a Finnish mathematician, specializing in geometric representation theory. He is currently a professor at the University of Melbourne.
Sergio Doplicher is an Italian mathematical physicist, who mainly dealt with the mathematical foundations of quantum field theory and quantum gravity.
Yongbin Ruan is a Chinese mathematician, specializing in algebraic geometry, differential geometry, and symplectic geometry with applications to string theory.
Zhenghan Wang is a Chinese-American mathematician. He is a principal researcher at Microsoft Station Q, as well as a professor of mathematics at the University of California, Santa Barbara.
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