![]() ![]() As such, it is especially suitable for describing quantum phenomena and has been applied to various problems in physics, from condensed matter physics to elementary particle physics. ![]() Noncommutative Geometry is a field of geometry that incorporates quantum effect, such as the Heiserberg uncertainty principle, into the structure of geometry itself. Their policies may differ from this site. Some links on this page may take you to non-federal websites. Some full text articles may not yet be available without a charge during the embargo (administrative interval). When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH In addition to these publications and to frequent lectures at workshops and conferences, the PI also delivered five general audience lectures on her research over the past three years. For outreach the PI has authored four research monographs and has edited eight volumes arising from conferences, workshops and special programs that she co-organized over the past few years. The PI is also mentoring two postdocs (one from an underrepresented group). In the past two years, seven papers were coauthored by the PI with Caltech undergraduates. The PI has also supervised eleven undergraduates at Caltech (four belonging to underrepresented groups) on summer research projects. The PI graduated twelve PhD students over the past five years (eight belonging to ethnic minorities) and is currently supervising seven other graduate students. Broader impact: The PI was invited speaker in the Mathematical Physics session of the International Congress of Mathematicians, Hyderabad 2010, and plenary speaker in the European Congress of Mathematics, Amsterdam 2008. The last part proposes a new point of view, based on the correspondence between BPS states counting and statistical physics model of crystal melting recently developed in String Theory. A third part of the proposal deals with extending models of particle physics and cosmology based on NCG, and to connect these models of low energy limits of String Theory. A second part of the research deals with the use of NCG techniques in spin foams models, as developed in recent work of the PI, with the aim of combining this method with the almost commutative geometries used in the NCG approach to particle physics models. For quasicrystal structures, the aim is to combine algebro-geometric techniques and NCG methods. The goal is to extend the NCG approach to fractional Hall effects. One part focuses on applications to quantum Hall systems and quasicrystals. This grant is for research in applications of Noncommutative Geometry (NCG) to models in theoretical physics. Particle Physics/Theory, MATHEMATICAL PHYSICSĠ1001213DB NSF RESEARCH & RELATED ACTIVIT 01001314DB NSF RESEARCH & RELATED ACTIVIT 01001415DB NSF RESEARCH & RELATED ACTIVIT Primary Place of Performance Congressional District:Įlem. Matilde Marcolli (Principal Investigator) Sponsored Research Office:.We then show that, while the slow-roll parameters differ between the spherical and flat manifolds but do not distinguish different topologies within each class, the power spectra detect the different scalings of the slow-roll potential and therefore distinguish between the various topologies, both in the spherical and in the flat case.Noncommutative Geometry Models in Physics NSF Org:īogdan Mihaila (703)292-8235 PHY Division Of Physics MPS Direct For Mathematical & Physical ScienįY 2012 = $61,000.00 FY 2013 = $62,500.00 FY 2014 = $64,000.00 We show this by explicitly computing the nonperturbative spectral action for some candidate flat cosmic topologies given by Bieberbach manifolds and showing that the resulting inflation potential differs from that of the flat torus by a multiplicative factor, similarly to what happens in the case of the spectral action of the spherical forms in relation to the case of the 3-sphere. Download a PDF of the paper titled The coupling of topology and inflation in Noncommutative Cosmology, by Matilde Marcolli and 2 other authors Download PDF Abstract:We show that, in a model of modified gravity based on the spectral action functional, there is a nontrivial coupling between cosmic topology and inflation, in the sense that the shape of the possible slow-roll inflation potentials obtained in the model from the nonperturbative form of the spectral action are sensitive not only to the geometry (flat or positively curved) of the universe, but also to the different possible non-simply connected topologies.
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