Combe, Noémie C.; Manin, Yuri I.; Marcolli, Matilde Birational maps and Nori motives. (English) Zbl 07814249 Papadopoulos, Athanase (ed.), Essays in geometry. Dedicated to Norbert A’Campo. Berlin: European Mathematical Society. IRMA Lect. Math. Theor. Phys. 34, 761-780 (2023). MSC: 14A20 14H10 PDFBibTeX XMLCite \textit{N. C. Combe} et al., IRMA Lect. Math. Theor. Phys. 34, 761--780 (2023; Zbl 07814249) Full Text: DOI arXiv
Gakkhar, Sita; Marcolli, Matilde Dynamical geometry and a persistence \(K\)-theory in noisy point clouds. (English) Zbl 07789224 Nielsen, Frank (ed.) et al., Geometric science of information. 6th international conference, GSI 2023, St. Malo, France, August 30 – September 1, 2023. Proceedings. Part I. Cham: Springer. Lect. Notes Comput. Sci. 14071, 474-483 (2023). MSC: 58B34 PDFBibTeX XMLCite \textit{S. Gakkhar} and \textit{M. Marcolli}, Lect. Notes Comput. Sci. 14071, 474--483 (2023; Zbl 07789224) Full Text: DOI
Manin, Yuri I.; Marcolli, Matilde Cohn-Elkies functions from Gabor frames. (English) Zbl 07724022 Complex Anal. Oper. Theory 17, No. 6, Paper No. 93, 32 p. (2023). MSC: 42C15 42C40 52C17 94A12 PDFBibTeX XMLCite \textit{Y. I. Manin} and \textit{M. Marcolli}, Complex Anal. Oper. Theory 17, No. 6, Paper No. 93, 32 p. (2023; Zbl 07724022) Full Text: DOI arXiv
Lieber, Joshua F.; Manin, Yuri I.; Marcolli, Matilde Bost-Connes systems and \(\mathbb{F}_1\)-structures in Grothendieck rings, spectra, and Nori motives. (English) Zbl 1489.14005 Aluffi, Paolo (ed.) et al., Facets of algebraic geometry. A collection in honor of William Fulton’s 80th birthday. Volume 2. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 473, 147-227 (2022). MSC: 14A23 14G10 14C25 PDFBibTeX XMLCite \textit{J. F. Lieber} et al., Lond. Math. Soc. Lect. Note Ser. 473, 147--227 (2022; Zbl 1489.14005) Full Text: DOI arXiv Link
Combe, Noémie; Manin, Yuri I.; Marcolli, Matilde Geometry of information: classical and quantum aspects. (English) Zbl 1481.14001 Theor. Comput. Sci. 908, 2-27 (2022). MSC: 14-02 81-02 94-02 14G10 14C15 14C35 14E18 14A22 17B37 03C60 81P45 94A17 PDFBibTeX XMLCite \textit{N. Combe} et al., Theor. Comput. Sci. 908, 2--27 (2022; Zbl 1481.14001) Full Text: DOI arXiv Link
Manin, Yuri; Marcolli, Matilde Computability questions in the sphere packing problem. arXiv:2212.05119 Preprint, arXiv:2212.05119 [cs.IT] (2022). MSC: 03D78 94B60 52C17 BibTeX Cite \textit{Y. Manin} and \textit{M. Marcolli}, ``Computability questions in the sphere packing problem'', Preprint, arXiv:2212.05119 [cs.IT] (2022) Full Text: arXiv OA License
Shu, Kevin; Ortegaray, Andrew; Berwick, Robert C.; Marcolli, Matilde Phylogenetics of Indo-European language families via an algebro-geometric analysis of their syntactic structures. (English) Zbl 07465805 Math. Comput. Sci. 15, No. 4, 803-857 (2021). MSC: 91F20 92D15 05C85 60J10 PDFBibTeX XMLCite \textit{K. Shu} et al., Math. Comput. Sci. 15, No. 4, 803--857 (2021; Zbl 07465805) Full Text: DOI arXiv Link
Lima, Alicia; Marcolli, Matilde Functor of points and height functions for noncommutative Arakelov geometry. (English) Zbl 1479.14033 J. Geom. Phys. 169, Article ID 104337, 28 p. (2021). MSC: 14G40 14A22 PDFBibTeX XMLCite \textit{A. Lima} and \textit{M. Marcolli}, J. Geom. Phys. 169, Article ID 104337, 28 p. (2021; Zbl 1479.14033) Full Text: DOI arXiv Link
Atiyah, Michael; Marcolli, Matilde Anyon networks from geometric models of matter. (English) Zbl 1471.81107 Q. J. Math. 72, No. 1-2, 717-733 (2021). MSC: 81V27 57R18 18M15 93B27 68Q06 PDFBibTeX XMLCite \textit{M. Atiyah} and \textit{M. Marcolli}, Q. J. Math. 72, No. 1--2, 717--733 (2021; Zbl 1471.81107) Full Text: DOI
Marcolli, Matilde; Penrose, Roger Gluing non-commutative twistor spaces. (English) Zbl 1479.14004 Q. J. Math. 72, No. 1-2, 417-454 (2021). Reviewer: Helge Øystein Maakestad (Sætre i Hurum) MSC: 14A22 14D21 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{R. Penrose}, Q. J. Math. 72, No. 1--2, 417--454 (2021; Zbl 1479.14004) Full Text: DOI arXiv Link
Marcolli, Matilde Aspects of \(p\)-adic geometry related to entanglement entropy. (English) Zbl 1468.81084 Novikov, Sergey (ed.) et al., Integrability, quantization, and geometry II. Quantum theories and algebraic geometry. Dedicated to the memory of Boris Dubrovin 1950–2019. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 103, Part 2, 353-382 (2021). MSC: 81T30 83E50 14G20 11Z05 PDFBibTeX XMLCite \textit{M. Marcolli}, Proc. Symp. Pure Math. 103, 353--382 (2021; Zbl 1468.81084)
Ceyhan, Özgür; Marcolli, Matilde Feynman integrals and periods in configuration spaces. (English) Zbl 1456.81192 Ebrahimi-Fard, K. (ed.) et al., Amplitudes, Hodge theory and ramification. From periods and motives to Feynman amplitudes. Lectures presented at the Clay Mathematics Institute 2014 summer school, “Periods and Motives: Feynman amplitudes in the 21st century”, Madrid, Spain, June 30 – July 25, 2014. Providence, RI: American Mathematical Society (AMS); Cambridge, MA: Clay Mathematics Institute. Clay Math. Proc. 21, 35-102 (2020). Reviewer: Alexander Hock (Münster) MSC: 81Q30 81T18 35J08 42C05 11M32 14C15 PDFBibTeX XMLCite \textit{Ö. Ceyhan} and \textit{M. Marcolli}, Clay Math. Proc. 21, 35--102 (2020; Zbl 1456.81192) Full Text: arXiv
Manin, Yuri I.; Marcolli, Matilde Homotopy types and geometries below \(\mathrm{Spec}(\mathbb{Z})\). (English) Zbl 1504.14007 Moree, Pieter (ed.) et al., Dynamics: topology and numbers. Conference, Max Planck Institute for Mathematics, Bonn, Germany, July 2–6, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 744, 27-56 (2020). MSC: 14A23 14-02 14G40 14G15 14G10 37P35 14C15 14A22 11M41 55P43 82B10 PDFBibTeX XMLCite \textit{Y. I. Manin} and \textit{M. Marcolli}, Contemp. Math. 744, 27--56 (2020; Zbl 1504.14007) Full Text: DOI arXiv
Manin, Yuri I.; Marcolli, Matilde Quantum statistical mechanics of the absolute Galois group. (English) Zbl 1505.11095 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 038, 52 p. (2020). MSC: 11G32 11M55 11R32 82B10 82C10 58B34 PDFBibTeX XMLCite \textit{Y. I. Manin} and \textit{M. Marcolli}, SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 038, 52 p. (2020; Zbl 1505.11095) Full Text: DOI arXiv
Manin, Yuri I.; Marcolli, Matilde Nori diagrams and persistent homology. (English) Zbl 1464.18002 Math. Comput. Sci. 14, No. 1, 77-102 (2020). Reviewer: Tobias Fritz (Innsbruck) MSC: 18-02 55-02 14-02 55N31 14C15 18M25 18N40 PDFBibTeX XMLCite \textit{Y. I. Manin} and \textit{M. Marcolli}, Math. Comput. Sci. 14, No. 1, 77--102 (2020; Zbl 1464.18002) Full Text: DOI arXiv Link
Fathizadeh, Farzad; Kafkoulis, Yeorgia; Marcolli, Matilde Bell polynomials and Brownian bridge in spectral gravity models on multifractal Robertson-Walker cosmologies. (English) Zbl 1435.83210 Ann. Henri Poincaré 21, No. 4, 1329-1382 (2020). MSC: 83F05 83D05 35K08 83C45 52C17 PDFBibTeX XMLCite \textit{F. Fathizadeh} et al., Ann. Henri Poincaré 21, No. 4, 1329--1382 (2020; Zbl 1435.83210) Full Text: DOI arXiv
Marcolli, Matilde Holographic codes on Bruhat-Tits buildings and Drinfeld symmetric spaces. (English) Zbl 1451.14085 Pure Appl. Math. Q. 16, No. 1, 1-33 (2020). Reviewer: Diana Maimut (Bucharest) MSC: 14G50 94A60 94A62 PDFBibTeX XMLCite \textit{M. Marcolli}, Pure Appl. Math. Q. 16, No. 1, 1--33 (2020; Zbl 1451.14085) Full Text: DOI arXiv
Marcolli, Matilde; Panangaden, Jane Quantum Statistical Mechanics and the Boundary of Modular Curves. arXiv:2006.16897 Preprint, arXiv:2006.16897 [math-ph] (2020). MSC: 82B10 11F67 11M55 58B34 BibTeX Cite \textit{M. Marcolli} and \textit{J. Panangaden}, ``Quantum Statistical Mechanics and the Boundary of Modular Curves'', Preprint, arXiv:2006.16897 [math-ph] (2020) Full Text: arXiv OA License
Marcolli, Matilde Motivic information. (English) Zbl 1420.14013 Boll. Unione Mat. Ital. 12, No. 1-2, 19-41 (2019). Reviewer: Nikolai L. Manev (Sofia) MSC: 14C15 94A17 14E18 14G10 PDFBibTeX XMLCite \textit{M. Marcolli}, Boll. Unione Mat. Ital. 12, No. 1--2, 19--41 (2019; Zbl 1420.14013) Full Text: DOI arXiv
Cornelissen, Gunther; Li, Xin; Marcolli, Matilde; Smit, Harry Reconstructing global fields from dynamics in the abelianized Galois group. (English) Zbl 1431.11110 Sel. Math., New Ser. 25, No. 2, Paper No. 24, 18 p. (2019). Reviewer: Thomas Schmidt (Corvallis) MSC: 11M55 11R37 11R42 11R56 14H30 46N55 58B34 82C10 PDFBibTeX XMLCite \textit{G. Cornelissen} et al., Sel. Math., New Ser. 25, No. 2, Paper No. 24, 18 p. (2019; Zbl 1431.11110) Full Text: DOI arXiv
Fan, Wentao; Fathizadeh, Farzad; Marcolli, Matilde Modular forms in the spectral action of Bianchi IX gravitational instantons. (English) Zbl 1409.83062 J. High Energy Phys. 2019, No. 1, Paper No. 234, 38 p. (2019). MSC: 83C45 83C65 35K08 83D05 PDFBibTeX XMLCite \textit{W. Fan} et al., J. High Energy Phys. 2019, No. 1, Paper No. 234, 38 p. (2019; Zbl 1409.83062) Full Text: DOI arXiv
Marcolli, Matilde; Tabuada, Gonçalo Feynman quadrics-motive of the massive sunset graph. (English) Zbl 1403.14017 J. Number Theory 195, 159-183 (2019). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 14C15 14H40 81Q30 81T18 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{G. Tabuada}, J. Number Theory 195, 159--183 (2019; Zbl 1403.14017) Full Text: DOI arXiv Link
Fan, Wentao; Fathizadeh, Farzad; Marcolli, Matilde Motives and periods in Bianchi IX gravity models. (English) Zbl 1404.58014 Lett. Math. Phys. 108, No. 12, 2729-2747 (2018). MSC: 58B34 14C15 83F05 PDFBibTeX XMLCite \textit{W. Fan} et al., Lett. Math. Phys. 108, No. 12, 2729--2747 (2018; Zbl 1404.58014) Full Text: DOI arXiv Link
Heydeman, Matthew; Marcolli, Matilde; Saberi, Ingmar A.; Stoica, Bogdan Tensor networks, \(p\)-adic fields, and algebraic curves: arithmetic and the \(\mathrm{AdS}_3 / \mathrm{CFT}_2\) correspondence. (English) Zbl 1414.81207 Adv. Theor. Math. Phys. 22, No. 1, 93-176 (2018). Reviewer: Farhang Loran (Isfahan) MSC: 81T40 81T20 14H45 11F85 14G20 22E50 81P70 94B27 81T17 81P40 83C57 PDFBibTeX XMLCite \textit{M. Heydeman} et al., Adv. Theor. Math. Phys. 22, No. 1, 93--176 (2018; Zbl 1414.81207) Full Text: DOI arXiv
Bernardara, Marcello; Marcolli, Matilde; Tabuada, Gonçalo Some remarks concerning Voevodsky’s nilpotence conjecture. (English) Zbl 1388.14017 J. Reine Angew. Math. 738, 299-312 (2018). Reviewer: Arvid Siqveland (Kongsberg) MSC: 14A22 14C35 18E30 PDFBibTeX XMLCite \textit{M. Bernardara} et al., J. Reine Angew. Math. 738, 299--312 (2018; Zbl 1388.14017) Full Text: DOI arXiv Link
Marcolli, Matilde Noncommutative cosmology. (English) Zbl 1401.81005 Hackensack, NJ: World Scientific (ISBN 978-981-3202-83-2/hbk; 978-981-3202-84-9/pbk; 978-981-3202-86-3/ebook). xv, 275 p. (2018). Reviewer: Hans-Jürgen Schmidt (Potsdam) MSC: 81-02 83F05 81T17 83C65 58B34 81R60 00A79 14A22 83D05 22D25 37F35 83C45 62P35 PDFBibTeX XMLCite \textit{M. Marcolli}, Noncommutative cosmology. Hackensack, NJ: World Scientific (2018; Zbl 1401.81005) Full Text: DOI
Marcolli, Matilde; Ren, Zhi \(q\)-deformations of statistical mechanical systems and motives over finite fields. (English) Zbl 1386.82006 \(p\)-Adic Numbers Ultrametric Anal. Appl. 9, No. 3, 204-227 (2017). MSC: 82B10 81T05 58B34 13F35 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{Z. Ren}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 9, No. 3, 204--227 (2017; Zbl 1386.82006) Full Text: DOI arXiv
Atiyah, Michael; Marcolli, Matilde Anyons in geometric models of matter. (English) Zbl 1380.83230 J. High Energy Phys. 2017, No. 7, Paper No. 76, 24 p. (2017). MSC: 83E05 53Z05 PDFBibTeX XMLCite \textit{M. Atiyah} and \textit{M. Marcolli}, J. High Energy Phys. 2017, No. 7, Paper No. 76, 24 p. (2017; Zbl 1380.83230) Full Text: DOI arXiv
Marcolli, Matilde; Seipp, Kyle Twisted index theory on orbifold symmetric products and the fractional quantum Hall effect. (English) Zbl 1388.81994 Adv. Theor. Math. Phys. 21, No. 2, 451-501 (2017). Reviewer: Eric Stachura (Haverford) MSC: 81V70 81R60 16S35 57R18 81Q35 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{K. Seipp}, Adv. Theor. Math. Phys. 21, No. 2, 451--501 (2017; Zbl 1388.81994) Full Text: DOI arXiv
Fathizadeh, Farzad; Marcolli, Matilde Periods and motives in the spectral action of Robertson-Walker spacetimes. (English) Zbl 1379.83026 Commun. Math. Phys. 356, No. 2, 641-671 (2017). MSC: 83F05 53Z05 35Q75 81Q10 PDFBibTeX XMLCite \textit{F. Fathizadeh} and \textit{M. Marcolli}, Commun. Math. Phys. 356, No. 2, 641--671 (2017; Zbl 1379.83026) Full Text: DOI arXiv
Marcolli, Matilde; Tabuada, Gonçalo Bost-Connes systems, categorification, quantum statistical mechanics, and Weil numbers. (English) Zbl 1429.14003 J. Noncommut. Geom. 11, No. 1, 1-49 (2017). MSC: 14A22 14C15 82B10 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{G. Tabuada}, J. Noncommut. Geom. 11, No. 1, 1--49 (2017; Zbl 1429.14003) Full Text: DOI arXiv
Marcolli, Matilde Book review of: W. D. van Suijlekom, Noncommutative geometry and particle physics. (English) Zbl 1352.00016 Bull. Am. Math. Soc., New Ser. 54, No. 1, 167-169 (2017). MSC: 00A17 81-02 81R60 81V22 81T13 81V10 81T75 58B34 PDFBibTeX XMLCite \textit{M. Marcolli}, Bull. Am. Math. Soc., New Ser. 54, No. 1, 167--169 (2017; Zbl 1352.00016) Full Text: DOI
Manin, Yuri I.; Marcolli, Matilde Semantic spaces. (English) Zbl 1409.68302 Math. Comput. Sci. 10, No. 4, 459-477 (2016). MSC: 68T50 14M15 PDFBibTeX XMLCite \textit{Y. I. Manin} and \textit{M. Marcolli}, Math. Comput. Sci. 10, No. 4, 459--477 (2016; Zbl 1409.68302) Full Text: DOI arXiv Link
Manin, Yuri I.; Marcolli, Matilde Moduli operad over \(\mathbb F_1\). (English) Zbl 1428.18035 Thas, Koen (ed.), Absolute arithmetic and \(\mathbb{F}_1\)-geometry. Zürich: European Mathematical Society (EMS). 331-361 (2016). MSC: 18M85 14A20 14H10 14C35 14A23 PDFBibTeX XMLCite \textit{Y. I. Manin} and \textit{M. Marcolli}, in: Absolute arithmetic and \(\mathbb{F}_1\)-geometry. Zürich: European Mathematical Society (EMS). 331--361 (2016; Zbl 1428.18035) Full Text: DOI arXiv
Marcolli, Matilde; Tabuada, Gonçalo Noncommutative numerical motives, Tannakian structures, and motivic Galois groups. (English) Zbl 1376.14004 J. Eur. Math. Soc. (JEMS) 18, No. 3, 623-655 (2016). Reviewer: Pieter Belmans (Bonn) MSC: 14A22 14C15 16E40 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{G. Tabuada}, J. Eur. Math. Soc. (JEMS) 18, No. 3, 623--655 (2016; Zbl 1376.14004) Full Text: DOI arXiv
Fan, Wentao; Fathizadeh, Farzad; Marcolli, Matilde Spectral action for Bianchi type-IX cosmological models. (English) Zbl 1388.83911 J. High Energy Phys. 2015, No. 10, Paper No. 85, 29 p. (2015). MSC: 83F05 83C65 PDFBibTeX XMLCite \textit{W. Fan} et al., J. High Energy Phys. 2015, No. 10, Paper No. 85, 29 p. (2015; Zbl 1388.83911) Full Text: DOI arXiv
Marcolli, Matilde; Tabuada, Gonçalo Unconditional noncommutative motivic Galois groups. (English) Zbl 1360.14009 Kennedy, Gary (ed.) et al., Hodge theory and classical algebraic geometry. Conference on Hodge theory and classical algebraic geometry, Ohio State University, Columbus, OH, USA, May 13–15, 2013. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-0990-6/pbk; 978-1-4704-2671-2/ebook). Contemporary Mathematics 647, 109-115 (2015). MSC: 14A22 14C15 14G32 14F40 18G55 19D55 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{G. Tabuada}, Contemp. Math. 647, 109--115 (2015; Zbl 1360.14009) Full Text: DOI arXiv Link
Marcolli, Matilde; Tabuada, Gonçalo Noncommutative motives and their applications. (English) Zbl 1359.14005 Eisenbud, David (ed.) et al., Commutative algebra and noncommutative algebraic geometry. Volume I: Expository articles. Cambridge: Cambridge University Press (ISBN 978-1-107-06562-8/hbk). Mathematical Sciences Research Institute Publications 67, 191-214 (2015). MSC: 14C15 14A22 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{G. Tabuada}, Math. Sci. Res. Inst. Publ. 67, 191--214 (2015; Zbl 1359.14005) Full Text: arXiv
Lo, Catharine Wing Kwan; Marcolli, Matilde \(\mathbb{F}_{\zeta}\)-geometry, Tate motives, and the Habiro ring. (English) Zbl 1327.14115 Int. J. Number Theory 11, No. 2, 311-339 (2015). Reviewer: Christodor-Paul Ionescu (Bucureşti) MSC: 14G15 11B25 13B25 PDFBibTeX XMLCite \textit{C. W. K. Lo} and \textit{M. Marcolli}, Int. J. Number Theory 11, No. 2, 311--339 (2015; Zbl 1327.14115) Full Text: DOI arXiv
Marcolli, Matilde; Napp, John Quantum computation and real multiplication. (English) Zbl 1395.81089 Math. Comput. Sci. 9, No. 1, 63-84 (2015). MSC: 81P68 58B34 11M55 68Q12 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{J. Napp}, Math. Comput. Sci. 9, No. 1, 63--84 (2015; Zbl 1395.81089) Full Text: DOI arXiv Link
Marcolli, Matilde; Ni, Xiang Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications. (English) Zbl 1346.81047 J. Singul. 15, 80-117 (2016). MSC: 81Q30 81T15 16T05 81T18 32A20 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{X. Ni}, J. Singul. 15, 80--117 (2014; Zbl 1346.81047) Full Text: DOI arXiv Link
Greenfield, M.; Marcolli, M.; Teh, K. Twisted spectral triples and quantum statistical mechanical systems. (English) Zbl 1315.58006 \(p\)-Adic Numbers Ultrametric Anal. Appl. 6, No. 2, 81-104 (2014). Reviewer: Yong Wang (Changchun) MSC: 58B34 81T75 82B10 PDFBibTeX XMLCite \textit{M. Greenfield} et al., \(p\)-Adic Numbers Ultrametric Anal. Appl. 6, No. 2, 81--104 (2014; Zbl 1315.58006) Full Text: DOI arXiv
Ceyhan, Özgür; Marcolli, Matilde Algebraic renormalization and Feynman integrals in configuration spaces. (English) Zbl 1309.81095 Adv. Theor. Math. Phys. 18, No. 2, 469-511 (2014). MSC: 81Q30 PDFBibTeX XMLCite \textit{Ö. Ceyhan} and \textit{M. Marcolli}, Adv. Theor. Math. Phys. 18, No. 2, 469--511 (2014; Zbl 1309.81095) Full Text: DOI arXiv Euclid
Marcolli, Matilde Noncommutative geometry models for particle physics. (English) Zbl 1447.81189 Cardona, Alexander (ed.) et al., Geometric, algebraic and topological methods for quantum field theory. Papers based on the presentations at the 7th summer school, Villa de Leyva, Colombia, July 4–22, 2011. Hackensack, NJ: World Scientific. 189-223 (2014). MSC: 81T75 81V25 81T13 81R40 81T17 PDFBibTeX XMLCite \textit{M. Marcolli}, in: Geometric, algebraic and topological methods for quantum field theory. Papers based on the presentations at the 7th summer school, Villa de Leyva, Colombia, July 4--22, 2011. Hackensack, NJ: World Scientific. 189--223 (2014; Zbl 1447.81189) Full Text: DOI
Ćaćić, Branimir; Marcolli, Matilde; Teh, Kevin Coupling of gravity to matter, spectral action and cosmic topology. (English) Zbl 1302.83036 J. Noncommut. Geom. 8, No. 2, 473-504 (2014). MSC: 83F05 83C65 58J42 PDFBibTeX XMLCite \textit{B. Ćaćić} et al., J. Noncommut. Geom. 8, No. 2, 473--504 (2014; Zbl 1302.83036) Full Text: DOI arXiv
Manin, Yuri I.; Marcolli, Matilde Big bang, blowup, and modular curves: algebraic geometry in cosmology. (English) Zbl 1296.85004 SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 073, 20 p. (2014). MSC: 85A40 14N05 14G35 83F05 83C75 PDFBibTeX XMLCite \textit{Y. I. Manin} and \textit{M. Marcolli}, SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 073, 20 p. (2014; Zbl 1296.85004) Full Text: DOI arXiv EMIS
Marcolli, Matilde; Tabuada, Gonçalo Noncommutative Artin motives. (English) Zbl 1296.14002 Sel. Math., New Ser. 20, No. 1, 315-358 (2014). Reviewer: Claudio Pedrini (Genova) MSC: 14C15 14F40 14G32 18G55 19D55 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{G. Tabuada}, Sel. Math., New Ser. 20, No. 1, 315--358 (2014; Zbl 1296.14002) Full Text: DOI arXiv Link
Jin, Zhaorong; Marcolli, Matilde Endomotives of toric varieties. (English) Zbl 1315.14010 J. Geom. Phys. 77, 48-71 (2014). MSC: 14C15 14M25 14G40 58B34 81R60 81S05 PDFBibTeX XMLCite \textit{Z. Jin} and \textit{M. Marcolli}, J. Geom. Phys. 77, 48--71 (2014; Zbl 1315.14010) Full Text: DOI arXiv
Marcolli, Matilde; Van Suijlekom, Walter D. Gauge networks in noncommutative geometry. (English) Zbl 1315.81098 J. Geom. Phys. 75, 71-91 (2014). MSC: 81T75 58J42 14A22 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{W. D. Van Suijlekom}, J. Geom. Phys. 75, 71--91 (2014; Zbl 1315.81098) Full Text: DOI arXiv
Cornelissen, Gunther; Marcolli, Matilde Graph reconstruction and quantum statistical mechanics. (English) Zbl 1278.05154 J. Geom. Phys. 72, 110-117 (2013). MSC: 05C60 05C90 37B10 46L55 53C24 81T75 82B10 PDFBibTeX XMLCite \textit{G. Cornelissen} and \textit{M. Marcolli}, J. Geom. Phys. 72, 110--117 (2013; Zbl 1278.05154) Full Text: DOI arXiv
Bejleri, Dori; Marcolli, Matilde Quantum field theory over \(\mathbb F_1\). (English) Zbl 1278.81130 J. Geom. Phys. 69, 40-59 (2013). MSC: 81T15 14D21 14H25 14C17 16E20 81T18 PDFBibTeX XMLCite \textit{D. Bejleri} and \textit{M. Marcolli}, J. Geom. Phys. 69, 40--59 (2013; Zbl 1278.81130) Full Text: DOI arXiv
Estrada, Christopher; Marcolli, Matilde Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models. (English) Zbl 1273.83119 Int. J. Geom. Methods Mod. Phys. 10, No. 7, Article ID 1350036, 30 p. (2013). MSC: 83C65 33C05 81T17 PDFBibTeX XMLCite \textit{C. Estrada} and \textit{M. Marcolli}, Int. J. Geom. Methods Mod. Phys. 10, No. 7, Article ID 1350036, 30 p. (2013; Zbl 1273.83119) Full Text: DOI arXiv
Estrada, Christopher; Marcolli, Matilde Noncommutative mixmaster cosmologies. (English) Zbl 1261.83044 Int. J. Geom. Methods Mod. Phys. 10, No. 1, Paper No. 1250086, 28 p. (2013). MSC: 83F05 83C65 46L87 58B34 85A40 83C25 PDFBibTeX XMLCite \textit{C. Estrada} and \textit{M. Marcolli}, Int. J. Geom. Methods Mod. Phys. 10, No. 1, Paper No. 1250086, 28 p. (2013; Zbl 1261.83044) Full Text: DOI arXiv
Aluffi, Paolo; Marcolli, Matilde A motivic approach to phase transitions in Potts models. (English) Zbl 1264.14006 J. Geom. Phys. 63, 6-31 (2013). Reviewer: Alexandru Dimca (Nice) MSC: 14C15 11G09 14C35 PDFBibTeX XMLCite \textit{P. Aluffi} and \textit{M. Marcolli}, J. Geom. Phys. 63, 6--31 (2013; Zbl 1264.14006) Full Text: DOI arXiv
Marcolli, Matilde; Perez, Christopher Codes as fractals and noncommutative spaces. (English) Zbl 1315.94139 Math. Comput. Sci. 6, No. 3, 199-215 (2012). MSC: 94B60 28A80 46L55 58B34 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{C. Perez}, Math. Comput. Sci. 6, No. 3, 199--215 (2012; Zbl 1315.94139) Full Text: DOI arXiv Link
Marcolli, Matilde; Tabuada, Gonçalo Kontsevich’s noncommutative numerical motives. (English) Zbl 1269.18004 Compos. Math. 148, No. 6, 1811-1820 (2012). Reviewer: Piotr Krasoń (Szczecin) MSC: 18D20 18F30 18G55 19A49 19D55 14A22 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{G. Tabuada}, Compos. Math. 148, No. 6, 1811--1820 (2012; Zbl 1269.18004) Full Text: DOI arXiv
Ceyhan, Özgür; Marcolli, Matilde Feynman integrals and motives of configuration spaces. (English) Zbl 1256.81051 Commun. Math. Phys. 313, No. 1, 35-70 (2012). MSC: 81Q30 PDFBibTeX XMLCite \textit{Ö. Ceyhan} and \textit{M. Marcolli}, Commun. Math. Phys. 313, No. 1, 35--70 (2012; Zbl 1256.81051) Full Text: DOI arXiv Link
Marcolli, Matilde; Pierpaoli, Elena; Teh, Kevin The coupling of topology and inflation in noncommutative cosmology. (English) Zbl 1242.83130 Commun. Math. Phys. 309, No. 2, 341-369 (2012). MSC: 83F05 83C65 83D05 54F65 81R60 53Z05 PDFBibTeX XMLCite \textit{M. Marcolli} et al., Commun. Math. Phys. 309, No. 2, 341--369 (2012; Zbl 1242.83130) Full Text: DOI arXiv Link
Marcolli, Matilde; Pierpaoli, Elena Early universe models from noncommutative geometry. (English) Zbl 1243.83005 Adv. Theor. Math. Phys. 14, No. 5, 1373-1432 (2010). MSC: 83-02 83C65 83F05 81T17 83C35 83D05 85A40 83C57 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{E. Pierpaoli}, Adv. Theor. Math. Phys. 14, No. 5, 1373--1432 (2011; Zbl 1243.83005) Full Text: DOI arXiv Euclid
Ramdorai, Sujatha; Plazas, Jorge [Marcolli, Matilde] Introduction to motives. With an appendix by Matilde Marcolli. (English) Zbl 1241.14006 Carey, Alan (ed.), Noncommutative geometry and physics: Renormalisation, motives, index theory. Based on the workshop “Number theory and physics”, Vienna, Austria, March 2009. Edited with the assistance of Harald Grosse and Steve Rosenberg. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-008-1/pbk). ESI Lectures in Mathematics and Physics, 41-87 (2011). Reviewer: Piotr Krasoń (Szczecin) MSC: 14C15 20G10 19D55 14A22 16S38 PDFBibTeX XMLCite \textit{S. Ramdorai} and \textit{J. Plazas}, in: Noncommutative geometry and physics: Renormalisation, motives, index theory. Based on the workshop ``Number theory and physics'', Vienna, Austria, March 2009. Edited with the assistance of Harald Grosse and Steve Rosenberg. Zürich: European Mathematical Society (EMS). 41--87 (2011; Zbl 1241.14006)
Marcolli, Matilde Seiberg-Witten gauge theory. Reprint of the 1999 hardback edition. (English) Zbl 1230.53003 Texts and Readings in Mathematics 17. New Delhi: Hindustan Book Agency (ISBN 978-93-80250-23-6/pbk; 978-93-86279-00-2/ebook). vii, 228 p. (2011). MSC: 53-02 57R57 53D40 53C07 53D45 57N10 81T13 PDFBibTeX XMLCite \textit{M. Marcolli}, Seiberg-Witten gauge theory. Reprint of the 1999 hardback edition. New Delhi: Hindustan Book Agency (2011; Zbl 1230.53003) Full Text: DOI
Marcolli, Matilde Building cosmological models via noncommutative geometry. (English) Zbl 1229.83057 Int. J. Geom. Methods Mod. Phys. 8, No. 5, 1131-1168 (2011). MSC: 83C65 83F05 85A40 54F65 83C60 83E50 PDFBibTeX XMLCite \textit{M. Marcolli}, Int. J. Geom. Methods Mod. Phys. 8, No. 5, 1131--1168 (2011; Zbl 1229.83057) Full Text: DOI
Marcolli, Matilde Noncommutative geometry and arithmetic. (English) Zbl 1234.46056 Bhatia, Rajendra (ed.) et al., Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19–27, 2010. Vol. III: Invited lectures. Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency (ISBN 978-981-4324-33-5/hbk; 978-81-85931-08-3/hbk; 978-981-4324-30-4/set; 978-981-4324-35-9/ebook). 2057-2077 (2011). Reviewer: Igor V. Nikolaev (Ottawa) MSC: 46L85 11M55 58B34 82C10 14A22 PDFBibTeX XMLCite \textit{M. Marcolli}, in: Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19--27, 2010. Vol. III: Invited lectures. Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency. 2057--2077 (2011; Zbl 1234.46056) Full Text: arXiv Link
Marcolli, Matilde (ed.); Parashar, Deepak (ed.) Quantum groups and noncommutative spaces. Perspectives on quantum geometry. Based on the presentations at the workshop, Bonn, Germany, August 6–8, 2007. (English) Zbl 1222.58002 Aspects of Mathematics E41. Wiesbaden: Vieweg+Teubner (ISBN 978-3-8348-1442-5/hbk; 978-3-8348-9831-9/ebook). viii, 240 p. (2011). MSC: 58-06 16-06 17-06 00B25 58B32 16T20 17B37 81R50 20G42 14M15 19D55 17B81 PDFBibTeX XMLCite \textit{M. Marcolli} (ed.) and \textit{D. Parashar} (ed.), Quantum groups and noncommutative spaces. Perspectives on quantum geometry. Based on the presentations at the workshop, Bonn, Germany, August 6--8, 2007. Wiesbaden: Vieweg+Teubner (2011; Zbl 1222.58002) Full Text: DOI
Marcolli, Matilde; Pierpaoli, Elena; Teh, Kevin The spectral action and cosmic topology. (English) Zbl 1216.83064 Commun. Math. Phys. 304, No. 1, 125-174 (2011). MSC: 83F05 85A40 81T20 11R52 53Z05 57M50 PDFBibTeX XMLCite \textit{M. Marcolli} et al., Commun. Math. Phys. 304, No. 1, 125--174 (2011; Zbl 1216.83064) Full Text: DOI arXiv Link
Aluffi, Paolo; Marcolli, Matilde Feynman motives and deletion-contraction relations. (English) Zbl 1221.81076 Cogolludo-Agustín, José Ignacio (ed.) et al., Topology of algebraic varieties and singularities. Invited papers of the conference in honor of Anatoly Libgober’s 60th birthday, Jaca, Spain, June 22–26, 2009. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matemática Española (ISBN 978-0-8218-4890-6/pbk). Contemporary Mathematics 538, 21-64 (2011). MSC: 81Q30 14C15 18E30 14F42 PDFBibTeX XMLCite \textit{P. Aluffi} and \textit{M. Marcolli}, Contemp. Math. 538, 21--64 (2011; Zbl 1221.81076) Full Text: arXiv
Ebrahimi-Fard, Kurusch (ed.); Marcolli, Matilde (ed.); van Suijlekom, Walter D. (ed.) Combinatorics and physics. Mini-workshop on renormalization, December 15–16, 2006, Conference on combinatorics and physics, March 19–23, 2007, Bonn, Germany. (English) Zbl 1214.81008 Contemporary Mathematics 539. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5329-0/pbk). ix, 465 p. (2011). MSC: 81-06 81T15 81R05 81R60 81Q30 05C90 65D30 00B25 PDFBibTeX XMLCite \textit{K. Ebrahimi-Fard} (ed.) et al., Combinatorics and physics. Mini-workshop on renormalization, December 15--16, 2006, Conference on combinatorics and physics, March 19--23, 2007, Bonn, Germany. Providence, RI: American Mathematical Society (AMS) (2011; Zbl 1214.81008) Full Text: DOI
Aluffi, Paolo; Marcolli, Matilde Graph hypersurfaces and a dichotomy in the Grothendieck ring. (English) Zbl 1211.14013 Lett. Math. Phys. 95, No. 3, 223-232 (2011). MSC: 14C15 14C35 14C30 81T15 14E08 16E20 PDFBibTeX XMLCite \textit{P. Aluffi} and \textit{M. Marcolli}, Lett. Math. Phys. 95, No. 3, 223--232 (2011; Zbl 1211.14013) Full Text: DOI arXiv Link
Aluffi, Paolo; Marcolli, Matilde Algebro-geometric Feynman rules. (English) Zbl 1225.81101 Int. J. Geom. Methods Mod. Phys. 8, No. 1, 203-237 (2011). Reviewer: Stefan Weinzierl (Mainz) MSC: 81T18 81Q30 58D30 18F30 13D15 16S34 PDFBibTeX XMLCite \textit{P. Aluffi} and \textit{M. Marcolli}, Int. J. Geom. Methods Mod. Phys. 8, No. 1, 203--237 (2011; Zbl 1225.81101) Full Text: DOI arXiv
Aluffi, Paolo; Marcolli, Matilde Parametric Feynman integrals and determinant hypersurfaces. (English) Zbl 1229.81099 Adv. Theor. Math. Phys. 14, No. 3, 911-963 (2010). MSC: 81Q30 81T18 PDFBibTeX XMLCite \textit{P. Aluffi} and \textit{M. Marcolli}, Adv. Theor. Math. Phys. 14, No. 3, 911--963 (2010; Zbl 1229.81099) Full Text: DOI arXiv Euclid
Marcolli, Matilde Motivic renormalization and singularities. (English) Zbl 1218.81081 Blanchard, Etienne (ed.) et al., Quanta of maths. Conference on non commutative geometry in honor of Alain Connes, Paris, France, March 29–April 6, 2007. Providence, RI: American Mathematical Society (AMS); Cambridge, MA: Clay Mathematics Institute (ISBN 978-0-8218-5203-3/pbk). Clay Mathematics Proceedings 11, 409-458 (2010). MSC: 81T15 81Q30 14C15 14C30 16T05 32S35 32S40 34M35 81T18 PDFBibTeX XMLCite \textit{M. Marcolli}, Clay Math. Proc. 11, 409--458 (2010; Zbl 1218.81081) Full Text: arXiv
Fleischhack, Christian (ed.); Marcolli, Matilde (ed.); Nest, Ryszard (ed.) Noncommutative geometry and loop quantum gravity: loops, algebras and spectral triples. Abstracts from the workshop held February 7th – February 13th, 2010. (English) Zbl 1209.00055 Oberwolfach Rep. 7, No. 1, 373-413 (2010). MSC: 00B05 58-06 81-06 58B34 46Lxx 58J42 81R15 83C45 PDFBibTeX XMLCite \textit{C. Fleischhack} (ed.) et al., Oberwolfach Rep. 7, No. 1, 373--413 (2010; Zbl 1209.00055) Full Text: DOI Link
Blanchard, Etienne (ed.); Ellwood, David (ed.); Khalkhali, Masoud (ed.); Marcolli, Matilde (ed.); Moscovici, Henri (ed.); Popa, Sorin (ed.) Quanta of maths. Conference on non commutative geometry in honor of Alain Connes, Paris, France, March 29–April 6, 2007. (English) Zbl 1206.00042 Clay Mathematics Proceedings 11. Providence, RI: American Mathematical Society (AMS); Cambridge, MA: Clay Mathematics Institute (ISBN 978-0-8218-5203-3/pbk). xvii, 675 p. (2010). MSC: 00B25 00B30 14-06 16-06 19-06 47-06 81-06 PDFBibTeX XMLCite \textit{E. Blanchard} (ed.) et al., Quanta of maths. Conference on non commutative geometry in honor of Alain Connes, Paris, France, March 29--April 6, 2007. Providence, RI: American Mathematical Society (AMS); Cambridge, MA: Clay Mathematics Institute (2010; Zbl 1206.00042)
Denicola, Domenic; Marcolli, Matilde; Al-Yasry, Ahmad Zainy Spin foams and noncommutative geometry. (English) Zbl 1202.83043 Classical Quantum Gravity 27, No. 20, Article ID 205025, 53 p. (2010). MSC: 83C45 83C60 83C65 81R60 57M50 53Z05 PDFBibTeX XMLCite \textit{D. Denicola} et al., Classical Quantum Gravity 27, No. 20, Article ID 205025, 53 p. (2010; Zbl 1202.83043) Full Text: DOI arXiv Link
Ceyhan, Özgür (ed.); Manin, Yuri I. (ed.); Marcolli, Matilde (ed.) Arithmetic and geometry around quantization. (English) Zbl 1190.00026 Progress in Mathematics 279. Basel: Birkhäuser (ISBN 978-0-8176-4830-5/hbk; 978-0-8176-4831-2/ebook). viii, 292 p. (2010). MSC: 00B25 14-06 11-06 81-06 53-06 PDFBibTeX XMLCite \textit{Ö. Ceyhan} (ed.) et al., Arithmetic and geometry around quantization. Basel: Birkhäuser (2010; Zbl 1190.00026) Full Text: DOI
Marcolli, Matilde Feynman motives. (English) Zbl 1192.14001 Hackensack, NJ: World Scientific (ISBN 978-981-4271-20-2/hbk; 978-981-4304-48-1/pbk; 978-981-4271-21-9/ebook). xiii, 220 p. (2010). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 14-02 81-02 14C15 81Q30 14A22 14J81 PDFBibTeX XMLCite \textit{M. Marcolli}, Feynman motives. Hackensack, NJ: World Scientific (2010; Zbl 1192.14001) Full Text: Link
Connes, Alain; Consani, Caterina; Marcolli, Matilde The Weil proof and the geometry of the adelès class space. (English) Zbl 1208.11108 Tschinkel, Yuri (ed.) et al., Algebra, arithmetic, and geometry. In honor of Yu. I. Manin on the occasion of his 70th birthday. Vol. I. Boston, MA: Birkhäuser (ISBN 978-0-8176-4744-5/hbk; 978-0-8176-4745-2/ebook). Progress in Mathematics 269, 339-405 (2009). Reviewer: Florin Nicolae (Berlin) MSC: 11M55 58B34 11M26 46L55 PDFBibTeX XMLCite \textit{A. Connes} et al., Prog. Math. 269, 339--405 (2009; Zbl 1208.11108) Full Text: DOI arXiv Link
Marcolli, Matilde Cyclotomy and endomotives. (English) Zbl 1236.46067 \(p\)-Adic Numbers Ultrametric Anal. Appl. 1, No. 3, 217-263 (2009). Reviewer: Igor V. Nikolaev (Ottawa) MSC: 46L89 11M55 46L55 57M27 82B10 81R60 PDFBibTeX XMLCite \textit{M. Marcolli}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 1, No. 3, 217--263 (2009; Zbl 1236.46067) Full Text: DOI arXiv
Aluffi, Paolo; Marcolli, Matilde Feynman motives of banana graphs. (English) Zbl 1171.81384 Commun. Number Theory Phys. 3, No. 1, 1-57 (2009). MSC: 81Q30 14C17 14C35 14E07 81T18 PDFBibTeX XMLCite \textit{P. Aluffi} and \textit{M. Marcolli}, Commun. Number Theory Phys. 3, No. 1, 1--57 (2009; Zbl 1171.81384) Full Text: DOI arXiv
Connes, Alain; Consani, Caterina; Marcolli, Matilde Fun with \(\mathbb F_1\). (English) Zbl 1228.11143 J. Number Theory 129, No. 6, 1532-1561 (2009). MSC: 11M55 14G15 11M26 46L55 PDFBibTeX XMLCite \textit{A. Connes} et al., J. Number Theory 129, No. 6, 1532--1561 (2009; Zbl 1228.11143) Full Text: DOI arXiv
Marcolli, Matilde Noncommutative geometry and number theory. (English) Zbl 1239.58003 Nieuw Arch. Wiskd. (5) 9, No. 2, 109-112 (2008). MSC: 58B34 11M26 11Z05 46L87 81R60 PDFBibTeX XMLCite \textit{M. Marcolli}, Nieuw Arch. Wiskd. (5) 9, No. 2, 109--112 (2008; Zbl 1239.58003)
Connes, Alain; Marcolli, Matilde Noncommutative geometry, quantum fields and motives. (English) Zbl 1159.58004 Texts and Readings in Mathematics 47. New Delhi: Hindustan Book Agency (ISBN 978-81-85931-80-7). xxii, 785 p. (2008). MSC: 58B34 58-02 11-02 81-02 11G35 PDFBibTeX XMLCite \textit{A. Connes} and \textit{M. Marcolli}, Noncommutative geometry, quantum fields and motives. New Delhi: Hindustan Book Agency (2008; Zbl 1159.58004)
Manin, Yuri I.; Marcolli, Matilde Modular shadows and the Lévy-Mellin \(\infty\)-adic transform. (English) Zbl 1228.11144 Edixhoven, Bas et al., Modular forms on Schiermonnikoog. Based on the conference on modular forms, Schiermonnikoog, Netherlands, October 2006. Cambridge: Cambridge University Press (ISBN 978-0-521-49354-3/hbk). 189-238 (2008). MSC: 11M55 11F85 58B34 PDFBibTeX XMLCite \textit{Y. I. Manin} and \textit{M. Marcolli}, in: Modular forms on Schiermonnikoog. Based on the conference on modular forms, Schiermonnikoog, Netherlands, October 2006. Cambridge: Cambridge University Press. 189--238 (2008; Zbl 1228.11144) Full Text: DOI arXiv
Marcolli, Matilde Solvmanifolds and noncommutative tori with real multiplication. (English) Zbl 1161.58005 Commun. Number Theory Phys. 2, No. 2, 421-476 (2008). Reviewer: Charlotte Wahl (Hannover) MSC: 58B34 11R42 11R80 19K56 PDFBibTeX XMLCite \textit{M. Marcolli}, Commun. Number Theory Phys. 2, No. 2, 421--476 (2008; Zbl 1161.58005) Full Text: DOI arXiv
Marcolli, Matilde; al-Yasry, Ahmad Zainy Coverings, correspondences, and noncommutative geometry. (English) Zbl 1157.58001 J. Geom. Phys. 58, No. 12, 1639-1661 (2008). MSC: 58B34 57M12 57Q20 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{A. Z. al-Yasry}, J. Geom. Phys. 58, No. 12, 1639--1661 (2008; Zbl 1157.58001) Full Text: DOI arXiv
Cornelissen, G.; Marcolli, M.; Reihani, K.; Vdovina, A. Noncommutative geometry on trees and buildings. (English) Zbl 1153.58002 Albeverio, Sergio (ed) et al., Traces in number theory, geometry and quantum fields. Wiesbaden: Vieweg (ISBN 978-3-8348-0371-9/hbk). Aspects of Mathematics E38, 73-98 (2008). Reviewer: Akira Asada (Takarazuka) MSC: 58B32 58B34 30F40 54F50 PDFBibTeX XMLCite \textit{G. Cornelissen} et al., in: Traces in number theory, geometry and quantum fields. Wiesbaden: Vieweg. 73--98 (2008; Zbl 1153.58002) Full Text: arXiv
Connes, Alain; Marcolli, Matilde A walk in the noncommutative garden. (English) Zbl 1145.14005 Khalkhali, Masoud (ed.) et al., An invitation to noncommutative geometry. Lectures of the international workshop on noncommutative geometry, Tehran, Iran, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-616-4/hbk; 978-981-270-779-6/pbk). 1-128 (2008). Reviewer: Arvid Siqveland (Kongsberg) MSC: 14A22 58B34 81T17 PDFBibTeX XMLCite \textit{A. Connes} and \textit{M. Marcolli}, in: An invitation to noncommutative geometry. Lectures of the international workshop on noncommutative geometry, Tehran, Iran, 2005. Hackensack, NJ: World Scientific. 1--128 (2008; Zbl 1145.14005) Full Text: arXiv
Cornelissen, Gunther; Marcolli, Matilde Zeta functions that hear the shape of a Riemann surface. (English) Zbl 1174.58004 J. Geom. Phys. 58, No. 5, 619-632 (2008). MSC: 58B34 58J42 30F10 58J52 58J53 PDFBibTeX XMLCite \textit{G. Cornelissen} and \textit{M. Marcolli}, J. Geom. Phys. 58, No. 5, 619--632 (2008; Zbl 1174.58004) Full Text: DOI arXiv
Connes, Alain; Marcolli, Matilde Noncommutative geometry, quantum fields and motives. (English) Zbl 1209.58007 Colloquium Publications. American Mathematical Society 55. Providence, RI: American Mathematical Society (AMS)/Hindustan Book Agency (ISBN 978-0-8218-4210-2/hbk). xxii, 785 p. (2008). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 58B34 58-02 11-02 81-02 11G35 PDFBibTeX XMLCite \textit{A. Connes} and \textit{M. Marcolli}, Noncommutative geometry, quantum fields and motives. Providence, RI: American Mathematical Society (AMS)/Hindustan Book Agency (2008; Zbl 1209.58007)
Khalkhali, Masoud (ed.); Marcolli, Matilde (ed.) An invitation to noncommutative geometry. Lectures of the international workshop on noncommutative geometry, Tehran, Iran, 2005. (English) Zbl 1135.14002 Hackensack, NJ: World Scientific (ISBN 978-981-270-616-4/hbk; 978-981-270-779-6/pbk). vii, 506 p. (2008). MSC: 14-06 46-06 81-06 58-06 00B25 PDFBibTeX XMLCite \textit{M. Khalkhali} (ed.) and \textit{M. Marcolli} (ed.), An invitation to noncommutative geometry. Lectures of the international workshop on noncommutative geometry, Tehran, Iran, 2005. Hackensack, NJ: World Scientific (2008; Zbl 1135.14002)
Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde Gravity and the standard model with neutrino mixing. (English) Zbl 1140.81022 Adv. Theor. Math. Phys. 11, No. 6, 991-1089 (2007). Reviewer: Paninjukunnath Achuthan (Madras) MSC: 81V22 81V17 83C65 PDFBibTeX XMLCite \textit{A. H. Chamseddine} et al., Adv. Theor. Math. Phys. 11, No. 6, 991--1089 (2007; Zbl 1140.81022) Full Text: DOI arXiv Euclid
Connes, Alain; Consani, Caterina; Marcolli, Matilde Noncommutative geometry and motives: the thermodynamics of endomotives. (English) Zbl 1125.14001 Adv. Math. 214, No. 2, 761-831 (2007). Reviewer: Werner Kleinert (Berlin) MSC: 14A22 14G10 14C35 14C25 14G25 14F43 11G40 81T15 PDFBibTeX XMLCite \textit{A. Connes} et al., Adv. Math. 214, No. 2, 761--831 (2007; Zbl 1125.14001) Full Text: DOI arXiv Link
Connes, Alain; Marcolli, Matilde Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory. (English) Zbl 1200.81113 Cartier, Pierre (ed.) et al., Frontiers in number theory, physics, and geometry II. On conformal field theories, discrete groups and renormalization. Papers from the meeting, Les Houches, France, March 9–21, 2003. Berlin: Springer (ISBN 978-3-540-30307-7/hbk). 617-713 (2007). MSC: 81T15 14L15 16T05 81Q30 81T18 PDFBibTeX XMLCite \textit{A. Connes} and \textit{M. Marcolli}, in: Frontiers in number theory, physics, and geometry II. On conformal field theories, discrete groups and renormalization. Papers from the meeting, Les Houches, France, March 9--21, 2003. Berlin: Springer. 617--713 (2007; Zbl 1200.81113) Full Text: DOI
Marcolli, Matilde Modular curves, \(C^*\)-algebras and chaotic cosmology. (English) Zbl 1176.83162 Cartier, Pierre (ed.) et al., Frontiers in number theory, physics, and geometry II. On conformal field theories, discrete groups and renormalization. Papers from the meeting, Les Houches, France, March 9–21, 2003. Berlin: Springer (ISBN 978-3-540-30307-7/hbk). 361-372 (2007). MSC: 83F05 11J70 14G35 81R60 83C65 PDFBibTeX XMLCite \textit{M. Marcolli}, in: Frontiers in number theory, physics, and geometry II. On conformal field theories, discrete groups and renormalization. Papers from the meeting, Les Houches, France, March 9--21, 2003. Berlin: Springer. 361--372 (2007; Zbl 1176.83162) Full Text: DOI arXiv
Connes, Alain; Marcolli, Matilde From physics to number theory via noncommutative geometry. 2nd printing. (English) Zbl 1126.58006 Cartier, Pierre (ed.) et al., Frontiers in number theory, physics, and geometry I. On random matrices, zeta functions, and dynamical systems. Papers from the meeting, Les Houches, France, March 9–21, 2003. Berlin: Springer (ISBN 978-3-540-23189-9/hbk). 269-347 (2006). Reviewer: Akira Asada (Takarazuka) MSC: 58B34 82C10 81R60 46L89 14Gxx 11M55 PDFBibTeX XMLCite \textit{A. Connes} and \textit{M. Marcolli}, in: Frontiers in number theory, physics, and geometry I. On random matrices, zeta functions, and dynamical systems. Papers from the meeting, Les Houches, France, March 9--21, 2003. Berlin: Springer. 269--347 (2006; Zbl 1126.58006)
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan KMS states and complex multiplication. II. (English) Zbl 1123.58004 Bratteli, Ola (ed.) et al., Operator algebras. The Abel symposium 2004. Proceedings of the first Abel symposium, Oslo, Norway, September 3–5, 2004. Berlin: Springer (ISBN 3-540-34196-X/hbk). Abel Symposia 1, 15-59 (2006). MSC: 58B34 46L89 11G15 PDFBibTeX XMLCite \textit{A. Connes} et al., Abel Symp. 1, 15--59 (2006; Zbl 1123.58004)
Marcolli, Matilde; Mathai, Varghese Towards the fractional quantum Hall effect: a noncommutative geometry perspective. (English) Zbl 1105.81068 Consani, Caterina (ed.) et al., Noncommutative geometry and number theory. Where arithmetic meets geometry and physics. Based on two workshops, Bonn, Germany, August 2003 and June 2004. Wiesbaden: Vieweg (ISBN 3-8348-0170-4/hbk). Aspects of Mathematics E 37, 235-261 (2006). MSC: 81V70 82D20 78A25 81R60 58B34 PDFBibTeX XMLCite \textit{M. Marcolli} and \textit{V. Mathai}, in: Noncommutative geometry and number theory. Where arithmetic meets geometry and physics. Based on two workshops, Bonn, Germany, August 2003 and June 2004. Wiesbaden: Vieweg. 235--261 (2006; Zbl 1105.81068) Full Text: arXiv
Consani, Caterina; Marcolli, Matilde Archimedean cohomology revisited. (English) Zbl 1101.14034 Consani, Caterina (ed.) et al., Noncommutative geometry and number theory. Where arithmetic meets geometry and physics. Based on two workshops, Bonn, Germany, August 2003 and June 2004. Wiesbaden: Vieweg (ISBN 3-8348-0170-4/hbk). Aspects of Mathematics E 37, 109-140 (2006). MSC: 14G40 14G10 11G35 58J42 14A22 PDFBibTeX XMLCite \textit{C. Consani} and \textit{M. Marcolli}, in: Noncommutative geometry and number theory. Where arithmetic meets geometry and physics. Based on two workshops, Bonn, Germany, August 2003 and June 2004. Wiesbaden: Vieweg. 109--140 (2006; Zbl 1101.14034) Full Text: arXiv
Connes, Alain; Marcolli, Matilde \(\mathbb Q\)-lattices: quantum statistical mechanics and Galois theory. (English) Zbl 1139.58003 J. Geom. Phys. 56, No. 1, 2-23 (2006). MSC: 58B34 46L60 11G18 14G35 82B26 PDFBibTeX XMLCite \textit{A. Connes} and \textit{M. Marcolli}, J. Geom. Phys. 56, No. 1, 2--23 (2006; Zbl 1139.58003) Full Text: DOI
Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan KMS states and complex multiplication. (English) Zbl 1106.58005 Sel. Math., New Ser. 11, No. 3-4, 325-347 (2005). MSC: 58B34 46L55 11R37 11G18 PDFBibTeX XMLCite \textit{A. Connes} et al., Sel. Math., New Ser. 11, No. 3--4, 325--347 (2005; Zbl 1106.58005) Full Text: DOI arXiv Link