![]() ![]() We demonstrate, indeed, that noncommutative effects of the kind considered here, can be those responsible for the present speed up of the cosmic expansion. e., the minisuperspace variables are promoted to operators, and the WDW equation is written in terms of these variables, iii) noncommutativity in the minisuperspace is achieved through the replacement of the standard product of functions by the Moyal star product in the WDW equation, and, finally, iv) semi-classical cosmological equations are obtained by means of the WKB approximation applied to the (equivalent) modified Hamilton-Jacobi equation. Our recipe to build noncommutativity into our model is based in the approach of reference, and can be summarized in the following steps: i) the Hamiltonian is derived from the Einstein-Hilbert action (plus a self-interacting scalar field action) for a Friedmann-Robertson-Walker spacetime with flat spatial sections, ii) canonical quantization recipe is applied, i. To our purpose it will be enough to explore the asymptotic properties of the cosmological model in the phase space. Quantum groups and noncommutative spaces (with Deepak Parashar), Vieweg Verlag, 2010.In this paper we investigate to which extent noncommutativity, a intrinsically quantum property, may influence the Friedmann-Robertson-Walker cosmological dynamics at late times/large scales.Deformation spaces (with Hossein Abbaspour and Thomas Tradler), Vieweg Verlag, 2010.Arithmetic and Geometry around Quantization (with Ozgur Ceyhan and Yuri Manin) Birkhauser, 2010.An invitation to Noncommutative Geometry (with Masoud Khalkhali) World Scientific, 2008.Traces in Geometry, Number Theory, and Quantum Fields (with Sergio Albeverio, Sylvie Paycha, Jorge Plazas), Vieweg Verlag, 2008.Noncommutative geometry and Number Theory (with Caterina Consani) Vieweg Verlag, 2005.Frobenius manifolds (with Claus Hertling), Vieweg Verlag, 2003.Feynman Motives, World Scientific, Singapore, 2009.(with Alain Connes), American Mathematical Society, Colloquium Publications, 2008. Noncommutative geometry, quantum fields and motives.American Mathematical Society, University Lectures Series, 2005. We show that this produces a multiplicative shift of the amplitude of the power. We consider then the coupling of gravity to matter determined by an almost-commutative geometry over the spherical space form. She was a plenary speaker in the 2008 European Congress of Mathematics in Amsterdam (with a talk on Renormalization, Galois symmetries and motives) and an invited speaker of the 2010 International Congress of Mathematicians in Hyderabad (with a talk on Noncommutative Geometry and Arithmetic). We consider a model of modified gravity based on the spectral action functional, for a cosmic topology given by a spherical space form, and the associated slow-roll inflation scenario. ![]() In 2001 she obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft (DFG) and in 2002 the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation. Ten graduate students obtained their PhD under her supervision between 20. She has collaborated with several other mathematicians and physicists, among them Yuri I. Marcolli's research work has covered different areas of mathematics and theoretical physics: gauge theory and low-dimensional topology, algebraic-geometric structures in quantum field theory, noncommutative geometry with applications to number theory and to physics models, especially related to particle physics, quantum gravity and cosmology, and to the quantum Hall effect. 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. Since 2008 she is full professor of Mathematics in the Division of Physics, Mathematics and Astronomy of the California Institute of Technology in Pasadena. She also held an honorary professorship at the University of Bonn. Between 20 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. Moore instructor in the Department of Mathematics. Between 19 she worked at the Massachusetts Institute of Technology (MIT) as a C.L.E. 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. 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.
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