Matilde Marcolli: Research

Recent Work

Preprints:

• pdf Modular forms in the spectral action of Bianchi IX gravitational instantons (with Wentao Fan and Farzad Fathizadeh)
• pdf Prevalence and recoverability of syntactic parameters in sparse distributed memories (with Jeong Joon Park, Ronnel Boettcher, Andrew Zhao, Alex Mun, Kevin Yuh, Vibhor Kumar)
• pdf Spin Glass Models of Syntax and Language Evolution (with Karthik Siva and Jim Tao)
• pdf Persistent Topology of Syntax (with Alexander Port, Iulia Gheorghita, Daniel Guth, John M.Clark, Crystal Liang, Shival Dasu)
• pdf KMS weights on higher rank buildings (with Jake Marcinek)
• pdf Spectral Action Models of Gravity on Packed Swiss Cheese Cosmology (with Adam Ball)
• pdf Spectral Action for Bianchi Type-IX Cosmological Models (with Wentao Fan, Farzad Fathizadeh)
• pdf Symbolic dynamics, modular curves, and Bianchi IX cosmologies (with Yuri Manin)
• pdf Twisted index theory on orbifold symmetric products and the Fractional Quantum Hall Effect (with Kyle Seipp)
• pdf Bost-Connes systems, Categorification, Quantum statistical mechanics, and Weil numbers (with Goncalo Tabuada)
• pdf Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications (with Xiang Ni)
• pdf Principles and Parameters: a coding theory perspective
• pdf Feynman integrals and periods in configuration spaces (with Ozgur Ceyhan)
• pdf Quantum Statistical Mechanics, L-series and Anabelian Geometry (with Gunther Cornelissen)
• pdf Dynamical systems on spectral metric spaces (with Jean Bellissard and Kamran Reihani)

• Feynman motives, World Scientific, 2010.
• pdf Noncommutative Geometry, Quantum Fields and Motives (with Alain Connes), Colloquium Publications, Vol.55, American Mathematical Society, 2008. xxii+785 pp.
• pdf Lectures on Arithmetic Noncommutative Geometry, University Lecture Series, 36. American Mathematical Society, 2005. xii+136 pp. (math.QA/0409520)
• pdf Seiberg-Witten gauge theory, Texts and Readings in Mathematics, Vol. 17, Hindustan Book Agency, 1999.

• pdf Tomography from Entanglement (with Jennifer Lin, Hirosi Ooguri, Bogdan Stoica) published as "Locality of Gravitational Systems from Entanglement of Conformal Field Theories", Physical Review Letters, 114 221601 (2015)
• pdf Some remarks concerning Voevodsky's nilpotence conjecture (with Marcello Bernardara and Goncalo Tabuada) to appear in Crelle
• pdf Entropy algebras and Birkhoff factorization (with Nico Tedeschi) Journal of Geometry and Physics, 97 (2015) 243-265
• pdf Potts models with magnetic field: arithmetic, geometry, and computation (with Shival Dasu) Journal of Geometry and Physics, 97 (2015) 14-24
• pdf Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory (with Alexander Port) Mathematics in Computer Science, Vol.9 (2015) N.4, 391-408
• pdf Unconditional noncommutative motivic Galois groups (with Goncalo Tabuada) Contemporary Mathematics, Vol.647 (2015) 109-115.
• pdf Algebraic renormalization and Feynman integrals in configuration spaces (with Ozgur Ceyhan) Advances in Theoretical and Mathematical Physics, 18 (2014) N.2, 469-511
• pdf Dyson-Schwinger equations in the theory of computation (with Colleen Delaney), in "Feynman Amplitudes, Periods, and Motives", Contemporary Mathematics, Vol.648 (2015) 79-107.
• pdf Big Bang, Blow up, and modular curves: algebraic geometry in cosmology (with Yuri Manin) SIGMA 10 (2014), 073, 20 pages
• pdf Kolmogorov complexity and the asymptotic bound for error-correcting codes (with Yuri Manin) Journal of Differential Geometry, Vol.97 (2014) 91-108.
• pdf Jacobians of Noncommutative Motives (with Goncalo Tabuada) Moscow Mathematical Journal, Vol.14 (2014) N.3, 577-594
• pdf Quantum computation and real multiplication (with John Napp) to appear in Mathematics in Computer Science
• pdf F-zeta geometry, Tate motives, and the Habiro ring (with Catharine Wing Kwan Lo) to appear in International Journal of Number Theory
• pdf Twisted spectral triples and quantum statistical mechanical systems (with Mark Greenfield and Kevin Teh) p-adic Numbers, Ultrametric Analysis, and Applications, Vol.6 (2014) N.2, 81-104.
• pdf Endomotives of Toric Varieties (with Zhaorong Jin) Journal of Geometry and Physics, Vol. 77 (2014) 48-71
• pdf Multifractals, Mumford curves, and Eternal Inflation (with Nicolas Tedeschi) p-Adic Numbers, Ultrametric Analysis and Applications, Vol.6 (2014) N.2, 135-154.
• pdf Moduli Operad over F1 (with Yuri Manin) in "Absolute arithmetic and F1 geometry" (K.Thas, Ed.), pp.331-364, European Mathematical Society, 2013.
• pdf Gauge Networks in Noncommutative Geometry (with Walter van Suijlekom) Journal of Geometry and Physics, Vol.75 (2014) 71-91
• pdf Noncommutative numerical motives, Tannakian categories, and motivic Galois groups (with Goncalo Tabuada) to appear in Journal of the European Mathematical Society
• pdf Noncommutative Artin motives (with Goncalo Tabuada) Selecta Mathematica, Vol.20 (2014) N.1, 315-358.
• pdf From exceptional collections to motivic decompositions via noncommutative motives (with Goncalo Tabuada) J. Reine Angew. Math. 701 (2015) 153-167
• pdf Quantum field theory over F1 (with Dori Bejleri) Journal of Geometry and Physics, 69 (2013) 40-59
• pdf Graph reconstruction and quantum statistical mechanics (with Gunther Cornelissen) Journal of Geometry and Physics, Vol.72 (2013) 110-117.
• pdf A motivic approach to phase transitions in Potts models (with Paolo Aluffi) Journal of Geometry and Physics, Vol.63 (2013) 6-31.
• pdf Asymptotic safety, hypergeometric functions and the Higgs mass in spectral action models (with Christopher Estrada), International Journal of Geometric Methods in Modern Physics, Vol.10 (2013) N.7, 1350036 [30 pages]
• pdf Coupling of gravity to matter, spectral action and cosmic topology (with Branimir Cacic and Kevin Teh) to appear in Journal of Noncommutative Geometry
• pdf Thermodynamic Semirings (with Ryan Thorngren) to appear in Journal of Noncommutative Geometry
• pdf Arithmetic of Potts model hypersurfaces (with Jessica Su) International Journal of Geometric Methods in Modern Physics Vol. 10, No. 4 (2013) 1350005 [22 pages]
• pdf Noncommutative Mixmaster cosmologies (with Christopher Estrada) International Journal of Geometric Methods in Modern Physics, Vol.10 (2013) N.1 [28 pages]
• pdf Noncommutative motives, numerical equivalence, and semi-simplicity (with Goncalo Tabuada) American Journal of Mathematics, Vol.136 (2014) N.1, 59-75
• pdf Kontsevich's noncommutative numerical motives (with Goncalo Tabuada) Compositio Mathematica, Vol.148 (2012) N.6, 1811-1820.
• pdf Codes as fractals and noncommutative spaces (with Christopher Perez) Mathematics in Computer Science, Vol.6 (2012) N.3, 199-215.
• pdf The Ricci flow on noncommutative two-tori (with Tanvir Ahamed Bhuyain) Letters in Mathematical Physics, Vol.101 (2012) N.2, 173-194
• pdf Feynman integrals and motives of configuration spaces (with Ozgur Ceyhan) Communications in Mathematical Physics: Vol.313, N.1 (2012), Page 35-70
• pdf The coupling of topology and inflation in noncommutative cosmology (with Elena Pierpaoli and Kevin Teh) Communications in Mathematical Physics, Vol.309 (2012) N.2, 341-369
• pdf The spectral action and cosmic topology (with Elena Pierpaoli and Kevin Teh) Communications in Mathematical Physics, 304 (2011) 125-174.
• pdf Early Universe models from Noncommutative Geometry (with Elena Pierpaoli) [a smaller file (no graphics) available here ] Advances in Theoretical and Mathematical Physics, Vol.14 (2010) 1373-1432
• pdf Graph hypersurfaces and a dichotomy in the Grothendieck ring (with Paolo Aluffi) Letters in Mathematical Physics, (2011) Vol.95, 223-232.
• pdf Algebro-geometric Feynman rules (with Paolo Aluffi), International Journal of Geometric Methods in Modern Physics, Vol.8 (2011) N.1, 203-237.
• pdf Building cosmological models via noncommutative geometry, International Journal of Geometric Methods in Modern Physics, Vol.8, N.5 (2011) 1131-1168.
• pdf Spin foams and noncommutative geometry (with Domenic Denicola and Ahmad Zainy al-Yasry) Class. Quantum Grav. 27 (2010) 205025 (53pp)
• pdf Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology (with Daniel Kolodrubetz) Physics Letters B 693 (2010) 166-174.
• pdf Open string theory and planar algebras (with Ozgur Ceyhan) J. Phys. A: Math. Theor. 43 (2010) 385401 (12pp)
• pdf Noncommutative geometry and arithmetic (ICM talk) Proceedings of the ICM-2010, Hyderabad, Vol.III, 2057-2077, World Scientific/Hindustan Book Agency, 2010.
• pdf Error-correcting codes and phase transitions (with Yuri Manin) Mathematics in Computer Science, Vol.5 (2011) 133-170.
• pdf Parametric Feynman integrals and determinant hypersurfaces (with Paolo Aluffi) Advances in Theoretical and Mathematical Physics, Vol.14 (2010) 911-963.
• pdf Feynman motives and deletion-contraction relations (with Paolo Aluffi) in "Topology of Algebraic Varieties and Singularities", Contemporary Mathematics, Vol.538 (2011) 21-64.
• pdf Cuntz-Krieger algebras and wavelets on fractals (with Anna Maria Paolucci) Complex Analysis and Operator Theory, Vol.5 (2011) N.1, 41-81.
• pdf Modular index invariants of Mumford curves (with Alan Carey and Adam Rennie) to appear in "Noncommutative Geometry, Arithmetic, and Related Topics", Johns Hopkins University Press, 2011.
• pdf Motivic ideas in noncommutative geometry (an appendix to Introduction to Motives, by R.Sujatha and J.Plazas) to appear in the ESI volume on number theory and physics
• pdf Motivic renormalization and singularities, in "Quanta of Maths", Clay Mathematics Proceedings, Vol.11 (2010) 409-458.
• pdf Feynman integrals and motives, in "European Congress of Mathematics, Amsterdam 14-18 July 2008", pp.293--332, European Mathematical Society, 2010.
• pdf The Weil proof and the geometry of the adeles class space (with Alain Connes and Katia Consani) in "Algebra, Arithmetic, and Geometry: in honor of Yu.I.Manin" (Yu.Tschinkel, Yu.G.Zarhin, Eds.) Progress in Mathematics, Vol.270, Part I, Birkhauser 2009, 339-406.
• pdf Motivic ideas in physics (an appendix to "Motives: an introductory survey for physicists" by Abhijnan Rej) to appear in the "Renormalization, combinatorics and physics" (Ebrahimi-Fard, van Suijlekom, Eds.)
• pdf Cyclotomy and endomotives, P-Adic Numbers, Ultrametric Analysis and Applications, Vol.1 (2009) N.3, 217-263.
• pdf Feynman motives of banana graphs (with Paolo Aluffi) Communications in Number Theory and Physics, Vol.3 (2009) N.1, 1-57.
• ps pdf Modular shadows and the Levy-Mellin infinity-adic transform (with Yuri Manin) in "Modular forms on Schiermonnikoog" (Eds. B.Edixhoven, G. van der Geer, B.Moonen) Cambridge University Press, 2008, pp. 189-238.
• ps pdf Fun with F_1 (with Alain Connes and Katia Consani) Journal of Number Theory, Vol.129 (2009), N.6, 1532-1561.
• pdf ps Supermanifolds from Feynman graphs (with Abhijnan Rej) Journal of Physics A, Vol.41 (2008) 315402 (21pp).
• pdf ps Coverings, correspondences, and noncommutative geometry (with Ahmed Zainy al-Yasry) Journal of Geometry and Physics, Vol.58 (2008) N.12, 1639-1661
• pdf Solvmanifolds and noncommutative tori with real multiplication, Communications in Number Theory and Physics, Volume 2, No. 2 (2008) 423-479
• pdf ps Gravity and the Standard Model with neutrino mixing (with Ali Chamseddine and Alain Connes), Advances in Theoretical and Mathematical Physics, 11 (2007) 991--1090.
• ps pdf Noncommutative geometry and motives: the thermodynamics of endomotives (with Alain Connes and Caterina Consani) math.QA/0512138, Advances in Mathematics, Vol.214 (2007) N.2, 761-831.
• pdf ps Quantum statistical mechanics over function fields (with Caterina Consani) Journal of Number Theory 123 (2007) 487-528.
• ps pdf A walk in the noncommutative garden (with Alain Connes) in "An invitation to Noncommutative Geometry", pp.1-128, World Scientific, 2008.
• pdf ps Zeta functions that hear the shape of a Riemann surface (with Gunther Cornelissen) Journal of Geometry and Physics, Vol.58 (2008) N.5, 619-632
• pdf ps On the K-theory of graph C* algebras (with Gunther Cornelissen and Oliver Lorscheid) Acta Applicandae Mathematicae, Vol.102 (2008) N.1 57-69
• pdf ps Noncommutative geometry on trees and buildings (with Gunther Cornelissen, Kamran Reihani, Alina Vdovina) in "Traces in Geometry, Number Theory, and Quantum Fields", pp. 73-98, Vieweg Verlag, 2007.
• ps pdf KMS states and complex multiplication (with Alain Connes and Niranjan Ramachandran), Selecta Mathematica (N.S.) Vol.11 (2005) N.3
• ps pdf KMS states and complex multiplication, Part II (with Alain Connes and Niranjan Ramachandran) in "Operator Algebras - The Abel Symposium 2004", pp.15--60, Springer Verlag, 2006.
• pdf ps From Physics to Number Theory via Noncommutative Geometry. Part I: Quantum Statistical Mechanics of Q-lattices (with Alain Connes) in "Frontiers in Number Theory, Physics, and Geometry, I" pp.269--350, Springer Verlag, 2006. (math.NT/0404128)
• pdf ps From Physics to Number Theory via Noncommutative Geometry. Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory (with Alain Connes) in "Frontiers in Number Theory, Physics, and Geometry, II" pp.617--713, Springer Verlag, 2006. (hep-th/0411114)
• pdf Modular curves, C* algebras and chaotic cosmology, in "Frontiers in Number Theory, Physics, and Geometry, II" pp.361--372, Springer Verlag, 2006. (math-ph/0312035)
• pdf ps Archimedean cohomology revisited (with Katia Consani) in "Noncommutative Geometry and Number Theory" pp.109--140. Vieweg Verlag, 2006. (math.AG/0407480)
• ps pdf Towards the fractional quantum Hall effect: a noncommutative geometry perspective (with Varghese Mathai) in "Noncommutative Geometry and Number Theory", pp.235--262. Vieweg Verlag, 2006. (cond-mat/0502356)
• ps pdf Quantum fields and motives (with Alain Connes) Journal of Geometry and Physics, Volume 56, (2005) N.1, 55-85 (hep-th/0504085)
• pdf ps Q-lattices: quantum statistical mechanics and Galois theory (with Alain Connes) Journal of Geometry and Physics, Volume 56, (2005) N.1, 2-23
• pdf ps Renormalization and motivic Galois theory (with Alain Connes) International Math. Research Notices (2004) N.76, 4073--4092. (math.NT/0409306)
• pdf ps Variants of equivariant Seiberg-Witten Floer homology (with Bai-Ling Wang) in "Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds", Contemporary Mathematics, Vol. 366 (2005). (math.GT/0211238)
• pdf ps Noncommutative geometry, dynamics, and infinity-adic Arakelov geometry (with Katia Consani), Selecta Mathematica, Vol.10 (2004) N.2, 167-251. (math.AG/0205306)
• pdf ps New perspectives on Arakelov geometry (with Katia Consani), in "Number Theory", CRM Proceedings and Lecture Notes, Vol. 36 (2004) 81-102. (math.AG/0210357)
• pdf ps Spectral triples from Mumford curves (with Katia Consani), International Mathematics Research Notices, 36 (2003) 1945-1972. (math.NT/0210435)
• pdf Limiting modular symbols and the Lyapunov spectrum, Journal of Number Theory, Vol.98 N.2 (2003) 348-376. (math.NT/0111093)
• ps pdf The geometric triangle for 3-dimensional Seiberg-Witten monopoles (with A. Carey and Bai-Ling Wang) Communications in Contemporary Mathematics, Vol.5 N.2 (2003) 197-250.
• pdf ps Triplets spectraux en geometrie d'Arakelov (with Katia Consani), Comptes Rendus Acad. Sci. Paris, Ser. I 335 (2002) 779-784.
• pdf Weak UCP and perturbed monopole equations (with Bernhelm Booss-Bavnbek and Bai-Ling Wang), International Journal of Mathematics, Vol. 13 N.9 (2002) 987-1008.
• pdf ps Continued fractions, modular symbols, and non-commutative geometry (with Yuri I. Manin) Selecta Mathematica, Vol. 8 N.3 (2002) 475-520.
• pdf ps Seiberg-Witten and Casson-Walker invariants for rational homology spheres (with Bai-Ling Wang) Geometriae Dedicata, 91 (2002) N.1, 45-58.
• pdf Holography principle and arithmetic of algebraic curves (with Yuri I. Manin) Advances in Theoretical and Mathematical Physics, Vol.5, N.3 (2001) 617-650.
• pdf ps Equivariant Seiberg-Witten-Floer homology (with Bai-Ling Wang) Communications in Analysis and Geometry, Vol. 9 N.3 (2001) 450-640.
• pdf ps Twisted Higher Index Theory on Good Orbifolds, II: Fractional Quantum Numbers (with Varghese Mathai) Communications in Mathematical Physics, 201 (2001) N.1 55-87
• pdf ps Twisted Higher Index Theory on Good Orbifolds, I: Noncommutative Bloch Theory (with Varghese Mathai) Communications in Contemporary Mathematics, Vol.1 N.4 (1999) 553-587
• Seiberg-Witten Floer homology and Heegaard splittings, International Journal of Mathematics, Vol.7 N.5 (1996) 671-696;
• Gauge groups and characteristic classes, (with M. Spreafico) Expositiones Mathematicae, 15 (1997) 229-249;
• Some remarks on conjugacy classes of bundle gauge groups, Cahiers de Topologie et Geom. Diff. Categ. 37 N.1 (1996) 21-39;
• Lorentz bundles, Proc. XI Internat. Conf. Topology (Trieste 1993), Rend. Ist. Mat. Univ. Trieste, Vol. 25 N. 1-2 (1994) 309-315.

• Combinatorics and Physics (with Kurusch Ebrahimi-Fard and Walter van Suijlekom), American Mathematical Society, 2011.
• Quanta of Maths (with E.Blanchard, D.Ellwood, M.Khalkhali, H.Moscovici, S.Popa), Clay Mathematics Institute and AMS, 2010.
• Quantum groups and noncommutative spaces (with Deepak Parashar), Vieweg Verlag, 2010.
• 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, quantum cohomology, and singularities (with Claus Hertling) Vieweg Verlag, 2003

• ps Number Theory in Physics, contributed to the Encyclopaedia of Mathematical Physics
• pdf Noncommutative geometry and number theory, in Nieuw Archief voor Wiskunde.
• pdf A system of ODE for ASD connections and Dirac monopoles (in Russian)

• pdf Anomalies, Dimensional Regularization, and Noncommutative Geometry (with Alain Connes), unfinished.
• ps Exact triangles in Seiberg-Witten Floer theory. Part II: geometric limits of flow lines (with Bai-Ling Wang)
• ps Exact triangles in Seiberg-Witten Floer theory. Part III: proof of exactness (with Bai-Ling Wang)
• ps Exact triangles in Seiberg-Witten Floer theory. Part IV: Z-graded monopole homology (with Bai-Ling Wang)

All my other writings that are not part of my research work are listed here

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