HOME PAGE of Matilde Marcolli

Something about myself

Ph.D. 1997, University of Chicago. Advisor Melvin Rothenberg, UChicago Math Department
Employment History:
- (1997-2000): C.L.E. Moore Instructor, Massachusetts Institute of Technology, Cambridge USA, MIT Math Department
- (2000-2008): Associate Professor (C3), Max Planck Institute for Mathematics, Bonn
- Email: marcolli at mpim-bonn dot mpg dot de
- (2001-) Courtesy Appointment: Florida State University Math Department
- Email: marcolli at math dot fsu dot edu
Current Position: Professor, Department of Mathematics, Caltech

curriculum

MAS6396: NONCOMMUTATIVE GEOMETRY

Spring 2008, FSU Math Department, Tuesday-Thursday 3:35pm, LOV200

Recent Work

Recent preprints (pdf and ps files):

pdf ps Noncommutative Geometry, Quantum Fields and Motives (with Alain Connes) NEW BOOK! (warning: preliminary version)
pdf ps Modular shadows and the Levy-Mellin infinity-adic transform (with Yuri Manin)
pdf The Weil proof and the geometry of the adeles class space (with Alain Connes and Katia Consani)
pdf ps Coverings, correspondences, and noncommutative geometry (with Ahmed Zainy)
pdf ps Supermanifolds from Feynman graphs (with Abhijnan Rej)
pdf Motivic renormalization and singularities
ps pdf Fun with F_1 (with Alain Connes and Katia Consani)

Publications (pdf and ps files):

pdf Solvmanifolds and noncommutative tori with real multiplication, Communications in Number Theory and Physics, Volume 2, No. 2 (2008)
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) to appear in Journal of Geometry and Physics
pdf ps On the K-theory of graph C* algebras (with Gunther Cornelissen and Oliver Lorscheid) to appear in Acta Applicandae Mathematicae
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, 2008.
ps pdf Lectures on Arithmetic Noncommutative Geometry (New Book!) University Lecture Series, 36. American Mathematical Society, 2005. xii+136 pp. (math.QA/0409520)
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
pdf ps Seiberg-Witten gauge theory (book), published in Texts and Readings in Mathematics (TRIM) Vol. 17, Hindustan Book Agency (HBA), 1999
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.