Matilde Marcolli

Bio: Matilde Marcolli is an academic researcher from California Institute of Technology. The author has contributed to research in topics: Noncommutative geometry & Renormalization. The author has an hindex of 34, co-authored 303 publications receiving 5503 citations. Previous affiliations of Matilde Marcolli include Max Planck Society & University of Toronto.

Noncommutative Geometry, Quantum Fields and Motives

Abstract: Quantum fields, noncommutative spaces, and motives The Riemann zeta function and noncommutative geometry Quantum statistical mechanics and Galois symmetries Endomotives, thermodynamics, and the Weil explicit formula Appendix Bibliography Index.

Gravity and the standard model with neutrino mixing

Abstract: We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral action. It yields all the detailed structure of the standard model with several predictions at unification scale. Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings. From these relations, one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value. The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector.

Gravity and the standard model with neutrino mixing

Abstract: ARASON H, 1992, PHYS REV D, V46, P3945, DOI 10.1103-PhysRevD.46.3945; Atiyah M.F., 1967, K THEORY; Avramidi I. G., 1986, THESIS MOSCOW U; BARRETT JW, HEPTH0608221; Carminati L, 1999, EUR PHYS J C, V8, P697; Casas JA, 2000, NUCL PHYS B, V573, P652, DOI 10.1016-S0550-3213(99)00781-6; Chamseddine AH, 1996, PHYS REV LETT, V77, P4868, DOI 10.1103-PhysRevLett.77.4868; CHAMSEDDINE AH, 1992, PHYS LETT B, V296, P109, DOI 10.1016-0370-2693(92)90810-Q; Chamseddine AH, 2006, J MATH PHYS, V47, DOI 10.1063-1.2196748; Chamseddine AH, 1997, COMMUN MATH PHYS, V186, P731, DOI 10.1007-s002200050126; CHANG D, 1985, PHYS REV D, V31, P1718, DOI 10.1103-PhysRevD.31.1718; CODELLO A, HEPTH0607128; Coleman S., 1985, ASPECTS SYMMETRY; CONNES A, HEPTH0608226; Connes A, 1996, COMMUN MATH PHYS, V182, P155, DOI 10.1007-BF02506388; Connes A., 1994, NONCOMMUTATIVE GEOME; CONNES A, 1995, J MATH PHYS, V36, P6194, DOI 10.1063-1.531241; Dabrowski L., 2003, BANACH CTR PUBLICATI, V61, P49; DONOGHUE JF, 1994, PHYS REV D, V50, P3874, DOI 10.1103-PhysRevD.50.3874; EINHORN MB, 1992, PHYS REV D, V46, P5206, DOI 10.1103-PhysRevD.46.5206; Feynman R.P., 1995, FEYNMAN LECT GRAVITA; FIGUEROA H, 2000, ELEMENTS NONCOMMUTAT; Frohlich J., 1994, CRM P LECT NOTES, V7, P57; GILKEY P, 1984, INVARIANCE THEORY EQ; Gracia-Bondia JM, 1998, PHYS LETT B, V416, P123, DOI 10.1016-S0370-2693(97)01310-5; HOLMAN R, 1991, PHYS REV D, V43, P3833, DOI 10.1103-PhysRevD.43.3833; Inagaki T, 2004, J HIGH ENERGY PHYS; Knecht M, 2006, PHYS LETT B, V640, P272, DOI 10.1016-j.physletb.2006.06.052; Kolda C, 2000, J HIGH ENERGY PHYS, DOI 10.1088-1126-6708-2000-07-035; Lawson H.B., 1989, PRINCETON MATH SERIE, V38; Lazzarini S, 2001, PHYS LETT B, V510, P277, DOI 10.1016-S0370-2693(01)00595-0; Lizzi F, 1997, PHYS REV D, V55, P6357, DOI 10.1103-PhysRevD.55.6357; Mohapatra R. N., 2004, MASSIVE NEUTRINOS PH; vanNieuwenhuizen P, 1996, PHYS LETT B, V389, P29, DOI 10.1016-S0370-2693(96)01251-8; PARKER L, 1984, PHYS REV D, V29, P1584, DOI 10.1103-PhysRevD.29.1584; PERCACCI R, HEPTH0409199; PILAFTSIS A, 2002, PHYS REV D, V29; Ramond P., 1990, FIELD THEORY MODERN; REINA L, HEPTH0512377; ROSS G, 1985, FRONTIERS PHYS SERIE, V60; SHER M, 1989, PHYS REP, V179, P273, DOI 10.1016-0370-1573(89)90061-6; Veltman M., 1994, DIAGRAMMATICA PATH F; Weinberg S., 1972, GRAVITATION COSMOLOG

Continued fractions, modular symbols, and noncommutative geometry

Abstract: Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss-Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take into account some congruence properties of successive convergents. This result has an application to the Mixmaster Universe model in general relativity. We then study some averages involving modular symbols and show that Dirichlet series related to modular forms of weight 2 can be obtained by integrating certain functions on real axis defined in terms of continued fractions. We argue that the quotient PGL(2, Z) \ P 1(R) should be considered as noncommutative modular curve, and show that the modular complex can be seen as a sequence of K 0-groups of the related crossed-product C *-algebras.

Locality of Gravitational Systems from Entanglement of Conformal Field Theories

Abstract: The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory are guaranteed by positivity conditions on the bulk matter energy density. As positivity and monotonicity of the relative entropy are general properties of quantum systems, this can be interpreted as a derivation of bulk energy conditions in any holographic system for which the Ryu-Takayanagi prescription applies. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.

Phd by thesis

Abstract: Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Convergence of probability measures

Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

The Quantum Theory of Light

Abstract: (b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>