Matilde Marcolli | |
---|---|
Born | |
Nationality | Italy, United States |
Alma mater | University of Milan, University of Chicago |
Scientific career | |
Fields | Mathematics |
Institutions | University of Bonn, Florida State University, Max Planck Institute for Mathematics, Caltech, University of Toronto, Perimeter Institute |
Doctoral advisor | Melvin Rothenberg |
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.
Marcolli obtained her Laurea in Physics in 1993 summa cum laude from the University of Milan under the supervision of Renzo Piccinini, with a thesis on Classes of self equivalences of fibre bundles. [1] She moved to the USA in 1994, where she obtained a master's degree (1994) and a PhD (1997) in Mathematics from the University of Chicago, under the supervision of Melvin Rothenberg, with a thesis on Three dimensional aspects of Seiberg-Witten Gauge Theory. Between 1997 and 2000 she worked at the Massachusetts Institute of Technology (MIT) as a C.L.E. Moore instructor in the Department of Mathematics. [2]
Between 2000 and 2010 she held a C3 position (German equivalent of associate professor) at the Max Planck Institute for Mathematics in Bonn and held an associate professor position (courtesy) at Florida State University in Tallahassee. She also held an honorary professorship at the University of Bonn. From 2008 to 2017 she was a full professor of Mathematics in the Division of Physics, Mathematics and Astronomy of the California Institute of Technology. Between 2018 and 2020 she was a professor in the mathematics department of the University of Toronto and a member of the Perimeter Institute. [3] She is currently the Robert F. Christy Professor of Mathematics and Computing and Mathematical Sciences at the California Institute of Technology.
She held visiting positions at the Tata Institute of Fundamental Research in Mumbai, the Kavli Institute for Theoretical Physics in Santa Barbara, the Mittag-Leffler Institute in Stockholm, the Isaac Newton Institute in Cambridge, and the Mathematical Sciences Research Institute in Berkeley, California. [4]
Marcolli's research work has covered different areas of mathematics and theoretical physics: gauge theory and low-dimensional topology, [5] [6] algebraic-geometric structures in quantum field theory, [7] [8] noncommutative geometry with applications to number theory [9] [10] and to physics models, especially related to particle physics, [11] quantum gravity [12] and cosmology, [13] [14] and to the quantum Hall effect. [15] [16] She also worked in linguistics.
She has collaborated with several other mathematicians, physicists, and linguists, [17] among them Yuri I. Manin, Alain Connes, Michael Atiyah, Roger Penrose, Noam Chomsky. Twenty six graduate students obtained their PhD under her supervision between 2006 and 2022. [18]
In 2001 she obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft (DFG) [19] and in 2002 the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation. [20] She was a plenary speaker in the 2008 European Congress of Mathematics in Amsterdam (with a talk on Renormalization, Galois symmetries and motives) [21] and an invited speaker of the 2010 International Congress of Mathematicians in Hyderabad (with a talk on Noncommutative Geometry and Arithmetic). [22]
Alain Connes is a French mathematician, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the Collège de France, Institut des Hautes Études Scientifiques, Ohio State University and Vanderbilt University. He was awarded the Fields Medal in 1982.
Edward Witten is an American mathematical and theoretical physicist. He is a professor emeritus in the school of natural sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics. In 1990, he became the first physicist to be awarded a Fields Medal by the International Mathematical Union, for his mathematical insights in physics, such as his 1981 proof of the positive energy theorem in general relativity, and his interpretation of the Jones invariants of knots as Feynman integrals. He is considered the practical founder of M-theory.
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 theoretical physics, the matrix theory is a quantum mechanical model proposed in 1997 by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind; it is also known as BFSS matrix model, after the authors' initials.
In mathematics, noncommutative topology is a term used for the relationship between topological and C*-algebraic concepts. The term has its origins in the Gelfand–Naimark theorem, which implies the duality of the category of locally compact Hausdorff spaces and the category of commutative C*-algebras. Noncommutative topology is related to analytic noncommutative geometry.
In mathematical physics, noncommutative quantum field theory is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions are noncommutative. One commonly studied version of such theories has the "canonical" commutation relation:
Yuri Ivanovich Manin was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
In theoretical particle physics, the non-commutative Standard Model, is a model based on noncommutative geometry that unifies a modified form of general relativity with the Standard Model.
In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. This object is denoted F1, or, in a French–English pun, Fun. The name "field with one element" and the notation F1 are only suggestive, as there is no field with one element in classical abstract algebra. Instead, F1 refers to the idea that there should be a way to replace sets and operations, the traditional building blocks for abstract algebra, with other, more flexible objects. Many theories of F1 have been proposed, but it is not clear which, if any, of them give F1 all the desired properties. While there is still no field with a single element in these theories, there is a field-like object whose characteristic is one.
In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The definition typically involves a Hilbert space, an algebra of operators on it and an unbounded self-adjoint operator, endowed with supplemental structures. It was conceived by Alain Connes who was motivated by the Atiyah-Singer index theorem and sought its extension to 'noncommutative' spaces. Some authors refer to this notion as unbounded K-cycles or as unbounded Fredholm modules.
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory. As a result of this change some variables that are usually continuous may become discrete. Often only such discrete variables are called "quantized"; usage varies.
Nikita Alexandrovich Nekrasov is a Russian mathematical and theoretical physicist at the Simons Center for Geometry and Physics and C.N.Yang Institute for Theoretical Physics at Stony Brook University in New York, and a Professor of the Russian Academy of Sciences.
In mathematics, a Bost–Connes system is a quantum statistical dynamical system related to an algebraic number field, whose partition function is related to the Dedekind zeta function of the number field. Bost & Connes (1995) introduced Bost–Connes systems by constructing one for the rational numbers. Connes, Marcolli & Ramachandran (2005) extended the construction to imaginary quadratic fields.
Ali H. Chamseddine is a Lebanese physicist known for his contributions to particle physics, general relativity and mathematical physics. As of 2013, Chamseddine is a physics Professor at the American University of Beirut and the Institut des hautes études scientifiques.
Ralph Martin Kaufmann is a German mathematician working in the United States.
Supersymmetric localization is a method to exactly compute correlation functions of supersymmetric operators in certain supersymmetric quantum field theories such as the partition function, supersymmetric Wilson loops, etc. The method can be seen as an extension of the Berline–Vergne– Atiyah– Bott formula for equivariant integration to path integrals of certain supersymmetric quantum field theories. Although the method cannot be applied to general local operators, it does provide the full nonperturbative answer for the restricted class of supersymmetric operators. It is a powerful tool which is currently extensively used in the study of supersymmetric quantum field theory. The method, built on the previous works by E.Witten, in its modern form involves subjecting the theory to a nontrivial supergravity background, such that the fermionic symmetry preserved by the latter can be used to perform the localization computation, as in.
Caterina (Katia) Consani is an Italian mathematician specializing in arithmetic geometry. She is a professor of mathematics at Johns Hopkins University.
Serguei Barannikov is a mathematician, known for his works in algebraic topology, algebraic geometry and mathematical physics.
Don Malcolm Blasius is an American mathematician.
Henri Moscovici is a Romanian-American mathematician, specializing in non-commutative geometry and global analysis.
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