Matilde Marcolli: Research

Recent Work

Preprints:

• pdf Algebro-geometric Feynman rules (with Paolo Aluffi)
• pdf Modular index invariants of Mumford curves (with Alan Carey and Adam Rennie)
• pdf Feynman motives and deletion-contraction relations (with Paolo Aluffi)
• pdf Motivic ideas in physics (an appendix to "Motives: an introductory survey for physicists" by Abhijnan Rej)
• pdf Open string theory and planar algebras (with Ozgur Ceyhan)
• pdf Early Universe models from Noncommutative Geometry (with Elena Pierpaoli) [a smaller file (no graphics) available here ]
• pdf Error-correcting codes and phase transitions (with Yuri Manin)

• 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 Parametric Feynman integrals and determinant hypersurfaces (with Paolo Aluffi) to appear in Advances in Theoretical and Mathematical Physics.
• pdf Cuntz-Krieger algebras and wavelets on fractals (with Anna Maria Paolucci) to appear in Complex Analysis and Operator Theory.
• pdf Motivic renormalization and singularities, to appear in the Clay Institute volume of Alain Connes 60th anniversary conference.
• pdf Feynman integrals and motives, to appear in the proceedings of the 5th European Congress of Mathematicians
• pdf The Weil proof and the geometry of the adeles class space (with Alain Connes and Katia Consani) to appear in the volume of Yuri Manin's 70th anniversary conference.
• 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 (IMRN) 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 (CCM) 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 (IJM), Vol. 13 N.9 (2002) 987-1008.
• pdf ps Continued fractions, modular symbols, and non-commutative geometry (with Yuri I. Manin) Selecta Mathematica New Ser. (SM), 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 (GD), 91 (2002) N.1, 45-58.
• pdf Holography principle and arithmetic of algebraic curves (with Yuri I. Manin) Advances in Theoretical and Mathematical Physics (ATMP), Vol.5, N.3 (2001) 617-650.
• pdf ps Equivariant Seiberg-Witten-Floer homology (with Bai-Ling Wang) Communications in Analysis and Geometry (CAG), 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 (CCM), Vol.1 N.4 (1999) 553-587
• Seiberg-Witten Floer homology and Heegaard splittings, International Journal of Mathematics (IJM,) 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.

• Arithmetic and Geometry around Quantization (with Ozgur Ceyhan and Yuri Manin) Birkhauser, 2009.
• 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 Mathematics as culture and knowledge, in "Les Dechiffreurs"
• 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)

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