nLab Matilde Marcolli

Matilde Marcolli is a mathematician of Italian origin, currently at Caltech, with a background in mathematical physics. She works on very diverse topics such as gauge theories, noncommutative geometry, arithmetic of quantum statistical mechanics, the combinatorics of renormalization, and motives.

She was a recipient of the Sonja Kovalevskaja prize and worked for several years at the Max Planck Institute for Mathematics in Bonn.

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Selected writings

Early discussion of orbifold K-theory via $C^\ast$-algebras:

• Matilde Marcolli, Varghese Mathai: Twisted higher index theory on good orbifolds and fractional quantum numbers [arXiv:math/9803051]

• Matilde Marcolli, Varghese Mathai: Twisted index theory on good orbifolds, I: noncommutative Bloch theory, Communications in Contemporary Mathematics 1 4 (1999) 553-587 [arXiv:math/9911102v1, doi:10.1142/S0219199799000213]

• Matilde Marcolli, Varghese Mathai: Twisted higher index theory on good orbifolds, II: fractional quantum numbers, Commun. Math. Phys. 217 1 (2001) 55-87 [arXiv:math/9911103, doi:10.1007/s002200000351]

On relation of AdS3/CFT2 to hyperbolic geometry and Arakelov geometry of algebraic curves:

• Yuri Manin, Matilde Marcolli, Holography principle and arithmetic of algebraic curves, Adv. Theor. Math. Phys. 5 (2002) 617-650 (arXiv:hep-th/0201036)

On the fractional quantum Hall effect via noncommutative geometry:

• Matilde Marcolli, Varghese Mathai: Towards the fractional quantum Hall effect: a noncommutative geometry perspective, in Noncommutative Geometry and Number Theory, Vieweg (2006) [doi:10.1007/978-3-8348-0352-8_12, arXiv:cond-mat/0502356]

Speculation on quantum field theory over $\mathbb{F}_1$ (via wonderful compactifications of configuration spaces of points):

• Dori Bejleri, Matilde Marcolli, Quantum field theory over $\mathbb{F}_1$, Journal of Geometry and Physics 69 (2013) 40-59 [arXiv:1209.4837, doi:10.1016/j.geomphys.2013.03.002]

On the p-adic AdS/CFT correspondence and tensor networks:

• Matthew Heydeman, Matilde Marcolli, Ingmar Saberi, Bogdan Stoica, Tensor networks, $p$-adic fields, and algebraic curves: arithmetic and the $AdS_3/CFT_2$ correspondence (arXiv:1605.07639)

Discussion of BTZ black holes via tensor networks in the p-adic AdS/CFT correspondence:

• Matthew Heydeman, Matilde Marcolli, Sarthak Parikh, Ingmar Saberi, Nonarchimedean Holographic Entropy from Networks of Perfect Tensors (arXiv:1812.04057)

On Hopf algebras in generative linguistics:

• Matilde Marcolli, Noam Chomsky, Robert Berwick, Mathematical Structure of Syntactic Merge (arXiv:2305.18278)

• Matilde Marcolli, Robert Berwick, Noam Chomsky, Old and New Minimalism: a Hopf algebra comparison (arXiv:2306.10270)

category: people, noncommutative geometry