Matilde Marcolli

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Matilde Marcolli
Matilde Marcolli2010.jpg
Marcolli in 2010 at Oberwolfach
Born (1969-11-30) November 30, 1969 (age 47)
Nationality Italy
Fields Mathematics
Institutions University of Bonn, Florida State University, Max Planck Institute for Mathematics, Caltech
Alma mater University of Milan, University of Chicago
Doctoral advisor Melvin Rothenberg

Matilde Marcolli is an Italian mathematical physicist.


Marcolli obtained her Laurea in Physics in 1993 summa cum laude from the University of Milan under the supervision of Renzo Piccinini, with a thesis on Classes of self equivalences of fibre bundles.[1] She moved to the USA in 1994, where she obtained a master's degree (1994) and a PhD (1997) in Mathematics from the University of Chicago, under the supervision of Melvin Rothenberg, with a thesis on Three dimensional aspects of Seiberg-Witten Gauge Theory.[2] Between 1997 and 2000 she worked at the Massachusetts Institute of Technology (MIT) as a C.L.E. Moore instructor in the Department of Mathematics.[3] Between 2000 and 2010 she held a C3 position (German equivalent of associate professor) at the Max Planck Institute for Mathematics in Bonn and held an associate professor position (courtesy) at Florida State University in Tallahassee. She also held an honorary professorship at the University of Bonn. Since 2008 she is full professor of Mathematics in the Division of Physics, Mathematics and Astronomy of the California Institute of Technology in Pasadena. She held visiting positions at the Tata Institute of Fundamental Research in Mumbai, the Kavli Institute for Theoretical Physics in Santa Barbara, the Mittag-Leffler Institute in Stockholm, the Isaac Newton Institute in Cambridge, and the Mathematical Sciences Research Institute in Berkeley, California.[4]


Marcolli's research work has covered different areas of mathematics and theoretical physics: gauge theory and low-dimensional topology,[5][6][7] algebraic-geometric structures in quantum field theory,[8][9][10][11][12] noncommutative geometry with applications to number theory[13][14][15][16][17][18][19][20][21][22][23][24][25] and to physics models, especially related to particle physics,[26] quantum gravity[27] and cosmology,[28][29][30] and to the quantum Hall effect .[31][32] She has collaborated with several other mathematicians and physicists,[33] among them Yuri I. Manin and Alain Connes. Ten graduate students obtained their PhD under her supervision between 2006 and 2010.

Honors and awards[edit]

In 2001 she obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft (DFG)[34] and in 2002 the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation.[35] She was a plenary speaker in the 2008 European Congress of Mathematics in Amsterdam (with a talk on Renormalization, Galois symmetries and motives)[36] and an invited speaker of the 2010 International Congress of Mathematicians in Hyderabad (with a talk on Noncommutative Geometry and Arithmetic).[37]

Publications (books authored)[edit]

  • Seiberg–Witten Gauge Theory. Hindustan Book Agency, New Delhi, 1999.
  • Arithmetic noncommutative geometry. American Mathematical Society, University Lectures Series, 2005.
  • Noncommutative geometry, quantum fields and motives. (with Alain Connes), American Mathematical Society, Colloquium Publications, 2008.
  • Feynman Motives, World Scientific, Singapore, 2009.

Books edited[edit]

  • Frobenius manifolds (with Claus Hertling), Vieweg Verlag, 2003.
  • Noncommutative geometry and Number Theory (with Caterina Consani) Vieweg Verlag, 2005.
  • Traces in Geometry, Number Theory, and Quantum Fields (with Sergio Albeverio, Sylvie Paycha, Jorge Plazas), Vieweg Verlag, 2008.
  • An invitation to Noncommutative Geometry (with Masoud Khalkhali) World Scientific, 2008.
  • Arithmetic and Geometry around Quantization (with Ozgur Ceyhan and Yuri Manin) Birkhauser, 2010.
  • Deformation spaces (with Hossein Abbaspour and Thomas Tradler), Vieweg Verlag, 2010.
  • Quantum groups and noncommutative spaces (with Deepak Parashar), Vieweg Verlag, 2010.


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  5. ^ M.Marcolli and B.L.Wang Equivariant Seiberg-Witten-Floer homology Communications in Analysis and Geometry Vol. 9 N. 3 (2001) 450–640.
  6. ^ M.Marcolli and B.L.Wang Seiberg-Witten and Casson-Walker invariants for rational homology spheres Geometriae Dedicata, 91 (2002) N. 1, 45–58
  7. ^ A.Carey, M.Marcolli, B.L.Wang, The geometric triangle for 3-dimensional Seiberg–Witten monopoles Communications in Contemporary Mathematics (CCM) Vol. 5 N. 2 (2003) 197–250.
  8. ^ A.Connes and M.Marcolli, Renormalization and motivic Galois theory International Math. Research Notices (2004) N.76, 4073–4092.
  9. ^ A.Connes and M.Marcolli, Renormalization, the Riemann–Hilbert correspondence, and motivic Galois theory in "Frontiers in Number Theory, Physics, and Geometry, II" pp. 617–713, Springer Verlag, 2006.
  10. ^ P.Aluffi and M.Marcolli Feynman motives of banana graphs Communications in Number Theory and Physics, Vol. 3 (2009) N. 1, 1–57.
  11. ^ P.Aluffi and M.Marcolli Parametric Feynman integrals and determinant hypersurfaces to appear in Advances in Theoretical and Mathematical Physics.
  12. ^ M.Marcolli, Motivic renormalization and singularities to appear in "Quanta of Maths, in honor of Alain Connes" Clay Mathematical Institute, 2010.
  13. ^ G.Cornelissen and M.Marcolli, Quantum Statistical Mechanics, L-series and Anabelian Geometry, arXiv:1009.0736
  14. ^ Yu. I. Manin and M. Marcolli Error-correcting codes and phase transitions to appear in Mathematics in Computer Science.
  15. ^ M. Marcolli, Solvmanifolds and noncommutative tori with real multiplication, Communications in Number Theory and Physics, Volume 2, No. 2 (2008) 423–479.
  16. ^ Yu. I. Manin and M. Marcolli, Modular shadows and the Levy–Mellin infinity-adic transform in "Modular forms on Schiermonnikoog" (Eds. B.Edixhoven, G. van der Geer, B.Moonen) Cambridge University Press, 2008, pp. 189–238.
  17. ^ C. Consani, M. Marcolli, Quantum statistical mechanics over function fields Journal of Number Theory 123 (2007) 487–528.
  18. ^ A. Connes, C. Consani, M. Marcolli, The Weil proof and the geometry of the adeles class space 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.
  19. ^ A.Connes, C.Consani, M.Marcolli, Noncommutative geometry and motives: the thermodynamics of endomotives Advances in Mathematics, Vol.214 (2007) N. 2, 761–831.
  20. ^ A. Connes, M. Marcolli, N. Ramachandran KMS states and complex multiplication, Selecta Mathematica (N.S.) Vol. 11 (2005) N. 3–4, 325–347.
  21. ^ A.Connes, M. Marcolli, Quantum Statistical Mechanics of Q-lattices in "Frontiers in Number Theory, Physics, and Geometry, I" pp. 269–350, Springer Verlag, 2006.
  22. ^ C.Consani and M.Marcolli, Noncommutative geometry, dynamics, and infinity-adic Arakelov geometry Selecta Mathematica (N.S.) Vol. 10 (2004) N. 2, 167–251.
  23. ^ M.Marcolli, Limiting modular symbols and the Lyapunov spectrum, Journal of Number Theory, Vol. 98 N. 2 (2003) 348–376.
  24. ^ Yu. I. Manin and M. Marcolli, Holography principle and arithmetic of algebraic curves Advances in Theoretical and Mathematical Physics, Vol. 5, N.3 (2001) 617–650.
  25. ^ Yu.I.Manin and M.Marcolli, Continued fractions, modular symbols, and non-commutative geometry Selecta Mathematica (N.S.) Vol. 8 N. 3 (2002) 475–520.
  26. ^ A. Chamseddine, A. Connes, M. Marcolli Gravity and the Standard Model with neutrino mixing Advances in Theoretical and Mathematical Physics, 11 (2007) 991–1090.
  27. ^ D.Denicola, M.Marcolli, A.Zainy al-Yasry, Spin foams and noncommutative geometry Classical and Quantum Gravity, 27 (2010) 205025 (53pp)
  28. ^ M. Marcolli and E. Pierpaoli, Early Universe models from Noncommutative Geometry, arXiv:0908.3683.
  29. ^ M. Marcolli, E. Pierpaoli, K. Teh, The spectral action and cosmic topology, arXiv:1005.2256
  30. ^ D.Kolodrubetz, M.Marcolli, Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology, Physics Letters B 693 (2010) 166–174.
  31. ^ M. Marcolli, V. Mathai, Twisted Higher Index Theory on Good Orbifolds, I: Noncommutative Bloch Theory, Communications in Contemporary Mathematics, Vol. 1 N. 4 (1999) 553–587.
  32. ^ M. Marcolli, V. Mathai, Twisted Higher Index Theory on Good Orbifolds, II: Fractional Quantum Numbers Communications in Mathematical Physics, 201 (2001) N. 1 55–87.
  33. ^ M.Marcolli: Collaborators and students
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