Matilde Marcolli is an Italian mathematical physicist. She has conducted research work in areas of mathematics and theoretical physics; obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft, and the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation. Marcolli has authored and edited numerous books in the field, and since 2008 is a full professor of Mathematics in the Division of Physics, Mathematics and Astronomy of the California Institute of Technology.
Matilde Marcolli | |
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Born | |
Nationality | Italy |
Alma mater | University of Milan, University of Chicago |
Scientific career | |
Fields | Mathematics |
Institutions | University of Bonn, Florida State University, Max Planck Institute for Mathematics, Caltech |
Doctoral advisor | Melvin Rothenberg |
Career
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. 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.[2]
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.[3]
Research
Marcolli's research work has covered different areas of mathematics and theoretical physics: gauge theory and low-dimensional topology,[4][5] algebraic-geometric structures in quantum field theory,[6][7] noncommutative geometry with applications to number theory[8][9] and to physics models, especially related to particle physics,[10] quantum gravity[11] and cosmology,[12][13] and to the quantum Hall effect.[14][15]
She has collaborated with several other mathematicians and physicists,[16] among them Yuri I. Manin and Alain Connes. Ten graduate students obtained their PhD under her supervision between 2006 and 2010.
Honors and awards
In 2001 she obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft (DFG)[17] and in 2002 the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation.[18] She was a plenary speaker in the 2008 European Congress of Mathematics in Amsterdam (with a talk on Renormalization, Galois symmetries and motives)[19] and an invited speaker of the 2010 International Congress of Mathematicians in Hyderabad (with a talk on Noncommutative Geometry and Arithmetic).[20]
Books authored
- Marcolli, Matilde (1999). Seiberg-Witten gauge theory. New Delhi: Hindustan Book Agency. ISBN 9788185931227. OCLC 468606720.
- Marcolli, Matilde; Manin, Jurij Ivanovič (2005). Arithmetic Noncommutative Geometry. American Mathematical Society. ISBN 9780821838334.
- Connes, Alain; Marcolli, Matilde (2008). Noncommutative Geometry, Quantum Fields and Motives. American Mathematical Society. ISBN 9780821874783.
- Marcolli, Matilde (2010). Feynman Motives. Singapore: World Scientific. ISBN 9789814271202.
- Matilde, Marcolli (2017). Noncommutative Cosmology. Singapore: World Scientific. ISBN 9789813202863.
Books edited
- Hertling, Claus; Marcolli, Matilde, eds. (2003). Frobenius Manifolds : Quantum Cohomology and Singularities. Vieweg-Teubner Verlag. ISBN 978-3-322-80238-5.
- Consani, Caterina; Marcolli, Matilde, eds. (2006). Noncommutative geometry and number theory : where arithmetic meets geometry and physics (1st ed.). Vieweg-Teubner Verlag. ISBN 978-3-8348-0170-8.
- Albeverio, Sergio; Marcolli, Matilde; Paycha, Sylvie; Plazas, Jorge (2008). Traces in Number Theory, Geometry and Quantum Fields. Vieweg+Teubner Verlag. ISBN 9783834803719.
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(help) - Khalkhali, Masoud; Marcolli, Matilde (2008). An Invitation to Noncommutative Geometry. World Scientific. ISBN 9789812706164.
- Ceyhan, Özgür; Manin, Yu I.; Marcolli, Matilde (2010). Arithmetic and Geometry Around Quantization. Springer. ISBN 9780817648312.
- Abbaspour, Hossein; Marcolli, Matilde; Tradler, Thomas (2010). Deformation spaces : perspectives on algebro-geometric moduli. Vieweg+Teubner. ISBN 978-3-8348-1271-1.
- Marcolli, Matilde; Parashar, Deepak (2011). Quantum groups and noncommutative spaces perspectives on quantum geometry: a publication of the Max-Planck-Institute for Mathematics, Bonn. Vieweg + Teubner. ISBN 9783834814425. OCLC 793144094.
References
- Citations
- ^ "Renzo A. Piccinini". Archived from the original on 2011-10-06. Retrieved 2011-04-05.
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- ^ "Matilde Marcolli". www.its.caltech.edu.
- ^ Marcolli, Matilde; Wang, Bai-Ling (2001). "Equivariant Seiberg-Witten Floer homology". Communications in Analysis and Geometry. 9 (3): 451–639. doi:10.4310/cag.2001.v9.n3.a1. ISSN 1019-8385.
- ^ Marcolli, Matilde; Wang, Bai-Ling (2002). "Seiberg–Witten and Casson–Walker Invariants for Rational Homology 3-Spheres". Geometriae Dedicata. 91 (1): 45–58. doi:10.1023/a:1016299716922. ISSN 0046-5755.
- ^ Connes, Alain; Marcolli, Matilde (2004). "Renormalization and motivic Galois theory". International Mathematics Research Notices. 2004 (76): 4073. doi:10.1155/s1073792804143122. ISSN 1073-7928.
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: CS1 maint: unflagged free DOI (link) - ^ Connes, Alain; Marcolli, Matilde (2007), "Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory", Frontiers in Number Theory, Physics, and Geometry II, Springer Berlin Heidelberg, pp. 617–713, doi:10.1007/978-3-540-30308-4_13, ISBN 9783540303077
- ^ Cornelissen, Gunther; Marcolli, Matilde (2010). "Quantum Statistical Mechanics, L-series and Anabelian Geometry". arXiv:1009.0736.
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(help) - ^ Manin, Yuri I.; Marcolli, Matilde (2010-03-23). "Error-Correcting Codes and Phase Transitions". Mathematics in Computer Science. 5 (2): 133–170. arXiv:0910.5135. doi:10.1007/s11786-010-0031-8. ISSN 1661-8270.
- ^ Chamseddine, Ali H.; Connes, Alain; Marcolli, Matilde (2007). "Gravity and the standard model with neutrino mixing". Advances in Theoretical and Mathematical Physics. 11 (6): 991–1089. doi:10.4310/atmp.2007.v11.n6.a3. ISSN 1095-0761.
- ^ Denicola, Domenic; Marcolli, Matilde; Zainy al-Yasry, Ahmad (2010-09-22). "Spin foams and noncommutative geometry". Classical and Quantum Gravity. 27 (20): 205025. arXiv:1005.1057. doi:10.1088/0264-9381/27/20/205025. ISSN 0264-9381.
- ^ Cornelissen, Gunther; Marcolli, Matilde (2009). "Early Universe models from Noncommutative Geometry". arXiv:0908.3683.
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(help) - ^ Cornelissen, Gunther; Marcolli, Matilde; Teh, Kevin (2011). "The spectral action and cosmic topology". Commun. Math. Phys. 304: 125–174. arXiv:1005.2256. CiteSeerX 10.1.1.750.9746. doi:10.1007/s00220-011-1211-3.
- ^ Marcolli, Matilde; Mathai, Mathaiavarghese (November 1999). "Twisted Index Theory on Good Orbifolds, I: Noncommutative Bloch Theory". Communications in Contemporary Mathematics. 01 (4): 553–587. arXiv:math/9911102. doi:10.1142/s0219199799000213. ISSN 0219-1997.
- ^ Marcolli, Matilde; Mathai, Varghese (2001-02-01). "Twisted Index Theory on Good Orbifolds, II:¶Fractional Quantum Numbers". Communications in Mathematical Physics. 217 (1): 55–87. arXiv:math/9911103. doi:10.1007/s002200000351. ISSN 0010-3616.
- ^ "Matilde Marcolli: Collaborators and Students". www.its.caltech.edu.
- ^ "DFG - Deutsche Forschungsgemeinschaft - Heinz Maier-Leibnitz-Preis 2001". www.dfg.de.
- ^ "Mathmatecs people" (PDF). www.ams.org.
- ^ "Guide to Amsterdam 5th European Mathematical Congress". www.5ecm.nl.
- ^ "Archived copy". Archived from the original on 2010-02-08. Retrieved 2010-02-17.
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- Sources
- Carey, A. L.; Marcolli, M.; Wang, B. L. (April 2003). "The Geometric Triangle for 3-dimensional Seiberg–witten Monopoles". Communications in Contemporary Mathematics. 05 (2): 197–250. arXiv:math/9907065. doi:10.1142/s0219199703000975. ISSN 0219-1997.
- Aluffi, Paolo; Marcolli, Matilde (2009). "Feynman motives of banana graphs". Communications in Number Theory and Physics. 3 (1): 1–57. doi:10.4310/cntp.2009.v3.n1.a1. ISSN 1931-4523.
- Aluffi, Paolo; Marcolli, Matilde (2010). "Parametric Feynman integrals and determinant hypersurfaces". Advances in Theoretical and Mathematical Physics. 14 (3): 911–964. doi:10.4310/atmp.2010.v14.n3.a5. ISSN 1095-0761.
- M.Marcolli, Motivic renormalization and singularities to appear in "Quanta of Maths, in honor of Alain Connes" Clay Mathematical Institute, 2010.
- Marcolli, Matilde (2008). "Solvmanifolds and noncommutative tori with real multiplication". Communications in Number Theory and Physics. 2 (2): 421–476. doi:10.4310/cntp.2008.v2.n2.a4. ISSN 1931-4523.
- Manin, Yuri I.; Marcolli, Matilde (2008), Modular Forms on Schiermonnikoog, Cambridge University Press, pp. 189–238, CiteSeerX 10.1.1.240.9146, doi:10.1017/cbo9780511543371.012, ISBN 9780511543371
- Consani, Caterina; Marcolli, Matilde (April 2007). "Quantum statistical mechanics over function fields". Journal of Number Theory. 123 (2): 487–528. doi:10.1016/j.jnt.2006.12.002. ISSN 0022-314X.
- Connes, Alain; Consani, Caterina; Marcolli, Matilde (2009), "The Weil Proof and the Geometry of the Adelès Class Space", Algebra, Arithmetic, and Geometry, Birkhäuser Boston, pp. 339–405, arXiv:math/0703392, doi:10.1007/978-0-8176-4745-2_8, ISBN 9780817647445
- Connes, Alain; Consani, Caterina; Marcolli, Matilde (October 2007). "Noncommutative geometry and motives: The thermodynamics of endomotives". Advances in Mathematics. 214 (2): 761–831. doi:10.1016/j.aim.2007.03.006. ISSN 0001-8708.
- Connes, Alain; Marcolli, Matilde; Ramachandran, Niranjan (2005-12-28). "KMS states and complex multiplication". Selecta Mathematica. 11 (3–4): 325–347. arXiv:math/0501424. doi:10.1007/s00029-005-0013-x. ISSN 1022-1824.
- 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.
- Consani, Caterina; Marcolli, Matilde (August 2004). "Noncommutative geometry, dynamics, and ∞-adic Arakelov geometry". Selecta Mathematica. 10 (2): 167–251. CiteSeerX 10.1.1.239.9156. doi:10.1007/s00029-004-0369-3. ISSN 1022-1824.
- Marcolli, Matilde (February 2003). "Limiting modular symbols and the Lyapunov spectrum". Journal of Number Theory. 98 (2): 348–376. doi:10.1016/s0022-314x(02)00044-6. ISSN 0022-314X.
- Manin, Yuri I.; Marcolli, Matilde (2001). "Holography principle and arithmetic of algebraic curves". Advances in Theoretical and Mathematical Physics. 5 (3): 617–650. doi:10.4310/atmp.2001.v5.n3.a6. ISSN 1095-0761.
- Manin, Y. I.; Marcolli, M. (2002-09-01). "Continued fractions, modular symbols, and noncommutative geometry". Selecta Mathematica, New Series. 8 (3): 475–521. CiteSeerX 10.1.1.239.20. doi:10.1007/s00029-002-8113-3. ISSN 1022-1824.
- Kolodrubetz, Daniel; Marcolli, Matilde (September 2010). "Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology". Physics Letters B. 693 (2): 166–174. arXiv:1006.4000. doi:10.1016/j.physletb.2010.08.018. ISSN 0370-2693.
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