Matilde Marcolli: Research

Over the years my research work was partially supported by NSF grants DMS-0651925, DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440, DMS-1707882, and DMS-2104330; NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593; ARC grant DP1092682; FQXi grant FQXi-RFP-1 804; the Perimeter Institute for Theoretical Physics.

Books Authored

• Lumen Naturae, MIT Press, 2020.
• Noncommutative Cosmology, World Scientific, 2018.
• Feynman Motives, World Scientific, 2009
• Noncommutative Geometry, Quantum Fields and Motves (with Alain Connes), Colloquium Publications, Vol.55, American Mathematical Society, 2008.
• Arithmetic Noncommutative Geometry, University Lecture Series, Vol.36, American Mathematical Society, 2005,
• Seiberg-Witten Gauge Theory, Hindustan Book Agency, 1999.

Mathematical Linguistics

• pdf Syntax-Semantics Interface: an Algebraic Model (with Robert Berwick and Noam Chomsky)
• pdf Old and New Minimalism: a Hopf Algebra Comparison (with Robert Berwick and Noam Chomsky)
• pdf Mathematical Structure of Syntactic Merge (with Noam Chomsky, Robert Berwick)
• pdf Syntactic structures and the general Markov models (with Sitanshu Gakkhar)
• pdf Topological analysis of syntactic structures (with Alexander Port, Taelin Karidi) Math. Comput. Sci. 16 (2022), no. 1, Paper No. 2, 68 pp.
• pdf Heat Kernel analysis of Syntactic Structures (with Andrew Ortegaray, Robert C. Berwick) Math. Comput. Sci. 15 (2021), no. 4, 643–660.
• pdf Phylogenetics of Indo-European Language families via an Algebro-Geometric Analysis of their Syntactic Structures (with Kevin Shu, Andrew Ortegaray, Robert C. Berwick) Math. Comput. Sci. 15 (2021), no. 4, 803–857.
• pdf Persistent Topology of Syntax (with A. Port, I. Gheorghita, D. Guth, J.M. Clark, C. Liang, S. Dasu) Math. Comput. Sci. 12 (2018) no. 1, 33-50
• pdf Syntactic Phylogenetic Trees (with Kevin Shu, Sharjeel Aziz, Vy-Luan Huynh, David Warrick) in "Foundations of Mathematics and Physics one Century after Hilbert", Springer Verlag, 2018, pp. 417-441
• pdf Spin Glass Models of Syntax and Language Evolution (with Karthik Siva, Jim Tao) Linguistic Analysis, Vol.41 (2017) N.3-4, 559-608
• pdf Prevalence and recoverability of syntactic parameters in sparse distributed memories (with Jeong Joon Park, Ronnel Boettcher, Andrew Zhao, Alex Mun, Kevin Yuh, Vibhor Kumar) in "Geometric Structures of Information 2017", Lecture Notes in Computer Science, Vol. 10589 (2017) 1-8
• pdf Syntactic Structures and Code Parameters (with Kevin Shu) Mathematics in Computer Science, 11 (2017), no. 1, 79-90
• pdf Syntactic Parameters and a Coding Theory Perspective on Entropy and Complexity of Language Families, Entropy, Vol.18 (2016) N.4
• pdf Semantic Spaces (with Yuri Manin) Mathematics in Computer Science, Vol.10 (2016) N.4, 459-477
• pdf Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory (with Alex Port) Math. Comput. Sci. 9 (2015), no. 4, 391-408

Strings and AdS/CFT holography

• pdf Holographic tensor networks from hyperbolic buildings (with Elliott Gesteau and Sarthak Parikh)
• pdf Nonarchimedean Holographic Entropy from Networks of Perfect Tensors (with Matthew Heydeman, Sarthak Parikh, Ingmar Saberi) arXiv:1812.04057 to appear in Advances in Theoretical and Mathematical Physics
• pdf Aspects of p-adic geometry related to entanglement entropy, to appear in "Integrability, Quantization, and Geometry - Dubrovin memorial volume" Proceedings Symposia in Pure Mathematics, American Mathematical Society
• pdf Holographic Codes on Bruhat-Tits buildings and Drinfeld Symmetric Spaces, Pure and Applied Mathematics Quarterly, Vol.16 (2020) N.1, 1-33
• pdf Tensor networks, p-adic fields, and algebraic curves: arithmetic and the AdS3/CFT2 correspondence (with Matthew Heydeman, Ingmar Saberi, Bogdan Stoica) Advances in Theoretical and Mathematical Physics, Vol. 22 (2018) N. 1, 93-176
• pdf Edge length dynamics on graphs with applications to p-adic AdS/CFT (with Steven S. Gubser, Matthew Heydeman, Christian Jepsen, Sarthak Parikh, Ingmar Saberi, Bogdan Stoica, Brian Trundy) J. High Energy Phys. (2017) no. 6, 157
• pdf Locality of gravitational systems from entanglement of conformal field theories (with Jennifer Lin, Hirosi Ooguri, Bogdan Stoica) Physical Review Letters, 114 221601 (2015)
• pdf Multifractals, Mumford curves, and Eternal Inflation (with Nicolas Tedeschi) p-Adic Numbers, Ultrametric Analysis and Applications, Vol.6 (2014) N.2, 135-154
• pdf Open string theory and planar algebras (with Ozgur Ceyhan) J. Phys. A: Math. Theor. 43 (2010) 385401
• pdf Holography principle and arithmetic of algebraic curves (with Yuri Manin) Advances in Theoretical and Mathematical Physics, Vol.5, N.3 (2001) 617-650

Motives and Quantum Field Theory

• pdf Motives of Melonic Graphs (with Paolo Aluffi and Waleed Qaisar) preprint arXiv:2007.08565
• pdf Intersection Theory, Characteristic Classes, and Algebro-Geometric Feynman Rules (with Paolo Aluffi) preprint, for MathemAmplitudes 2019
• pdf Feynman integrals and periods in configuration spaces (with Ozgur Ceyhan) in "Amplitudes, Hodge Theory and Ramification: From Periods and Motives to Feynman Amplitudes", Clay Mathematics Proceedings Vol.~21, Clay Mathematical Institute and American Mathematical Society, 2020, pp.~35-102.
• pdf Feynman quadrics-motive of the massive sunset graph (with Goncalo Tabuada) J. Number Theory 195 (2019), 159-183
• pdf Rota-Baxter algebras, singular hypersurfaces, and renormalization in Kausz compactifications (with Xiang Ni), Journal of Singularities, Vol.15 (2016) 80-117
• pdf Algebraic renormalization and Feynman integrals in configuration spaces (with Ozgur Ceyhan) Advances in Theoretical and Mathematical Physics, Vol.18 (2014) 469-511
• pdf Feynman integrals and motives of configuration spaces (with Ozgur Ceyhan) Communications in Mathematical Physics, Vol.313, N.1 (2012), Page 35-70
• pdf Feynman motives and deletion-contraction relations (with Paolo Aluffi) in "Topology of Algebraic Varieties and Singularities", Contemporary Mathematics, Vol.538 (2011) 21-64, American Mathematical Society
• pdf Graph hypersurfaces and a dichotomy in the Grothendieck ring (with Paolo Aluffi) Letters in Mathematical Physics, (2011) Vol.95, 223-232
• pdf Algebro-geometric Feynman rules (with Paolo Aluffi), International Journal of Geometric Methods in Modern Physics, Vol.8 (2011) N.1, 203-237
• pdf Motivic ideas in physics (an appendix to "Motives: an introductory survey for physicists" by Abhijnan Rej), Contemporary Mathematics, Vol.539 (2011) 407-415
• pdf Parametric Feynman integrals and determinant hypersurfaces (with Paolo Aluffi) Advances in Theoretical and Mathematical Physics, Vol.14 (2010) 911-963
• pdf Motivic renormalization and singularities, in "Quanta of Maths", pp.409-458, Clay Mathematics Institute and American Mathematical Society, 2010
• pdf Feynman Integrals and Motives, in "European Congress of Mathematics, Amsterdam 14-18 July 2008", pp.293-332, European Mathematical Society, 2010
• pdf Feynman motives of banana graphs (with Paolo Aluffi) Communications in Number Theory and Physics, Vol.3 (2009) N.1, 1-57
• pdf Supermanifolds from Feynman graphs, (with Abhijnan Rej) Journal of Physics A, Vol.41 (2008) 315402
• pdf Quantum fields and motives (with Alain Connes) Journal of Geometry and Physics 56 (2006) 55-85
• pdf 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
• pdf Renormalization and motivic Galois theory (with Alain Connes), International Math. Research Notices (2004) N.76, 4073-4092

Number Theory and Quantum Statistical Mechanics, Arithmetic Noncommutative Geometry

• pdf Quantum SUSY Operads (with Noemie Combe and Yuri Manin)
• pdf Quantum Operads (with Noemie Combe and Yuri Manin)
• pdf Homotopy spectra and diophantine equations (with Yuri Manin)
• pdf Birational maps and Nori motives (with Noemie C. Combe and Yuri I. Manin) arXiv:2012.13814
• pdf Quantum Statistical Mechanics and the Boundary of Modular Curves (with Jane Panangaden) preprint arXiv:2006.16897
• pdf Dessins for Modular Operad and Grothendieck-Teichmuller Group (with Noemie C. Combe and Yuri I. Manin) preprint arXiv:2006.13663
• pdf Modular Nori Motives (with Noemie C. Combe and Yuri I.Manin) preprint
• pdf Quantum Statistical Mechanics of the Absolute Galois Group (with Yuri Manin) SIGMA, Symmetry Integrability Geom. Methods Appl. 16 (2020), Paper No. 038, 52 pp.
• pdf Characterization of global fields by Dirichlet L-series (with Gunther Cornelissen, Bart de Smit, Xin Li, Harry Smit) Res. Number Theory 5 (2019), no. 1, 5:7
• pdf Reconstructing global fields from dynamics in the abelianized Galois group (with Gunther Cornelissen, Xin Li, Harry Smit) Selecta Mathematica (N.S.) 25 (2019), no. 2, 25: 24
• pdf Bost-Connes systems, Categorification, Quantum Statistical Mechanics, and Weil Numbers (with Goncalo Tabuada) Journal of Noncommutative Geometry, 11 (2017) no. 1, 1-49
• pdf q-deformations of statistical mechanical systems and motives over finite fields (with Zhi Ren), p-Adic Numbers Ultrametric Anal. Appl. 9 (2017), no. 3, 204-227
• pdf Quantum statistical mechanics in arithmetic topology (with Yujie Xu) Journal of Geometry and Physics, Vol. 114 (2017) 153-183
• pdf KMS weights on higher rank buildings (with Jake Marcinek) p-Adic Numbers Ultrametric Anal. Appl. 8 (2016), no. 1, 45-67
• pdf Endomotives of Toric Varieties (with Zhaorong Jin) Journal of Geometry and Physics, Vol. 77 (2014) 48-71
• pdf Twisted spectral triples and quantum statistical mechanical systems (with Mark Greenfield and Kevin Teh) p-adic Numbers, Ultrametric Analysis, and Applications, Vol.6 (2014) N.2, 81-104
• pdf Graph reconstruction and quantum statistical mechanics (with Gunther Cornelissen) Journal of Geometry and Physics, Vol.72 (2013) 110-117
• pdf Motivic ideas in noncommutative geometry (an appendix to "Motives" by R.Sujatha and J.Plazas) in "Noncommutative Geometry and Physics: Renormalization, Motives, Index Theory", pp.61-87, European Mathematical Society, 2011
• pdf Modular index invariants of Mumford curves (with Alan Carey and Adam Rennie) in "Noncommutative Geometry, Arithmetic, and Related Topics", Johns Hopkins University Press, 2011, pp.31-74
• pdf The Weil Proof and the Geometry of the Adeles Class Space (with Alain Connes and Caterina Consani) in "Algebra, arithmetic, and geometry: in honor of Yu. I. Manin". Vol. I, 339-405, Progr. Math., 269, Birkhaeuser, 2009
• pdf Modular Shadows and the Levy-Mellin infty-adic transform (with Yuri Manin) in "Modular forms on Schiermonnikoog" pp.189-238, Cambridge, 2008
• pdf Solvmanifolds and noncommutative tori with real multiplication. Communications in Number Theory and Physics, Vol.2 (2008) No.2, 423-479
• pdf Zeta functions that hear the shape of a Riemann surface (with Gunther Cornelissen) Journal of Geometry and Physics 58 (2008) 619-632
• pdf On the K-theory of graph C* algebras (with Gunther Cornelissen and Oliver Lorscheid) Acta Applicandae Mathematicae, Voo.102 (2008) N.1, 57-69
• pdf Noncommutative Geometry and Motives: The Thermodynamics of Endomotives (with Alain Connes and Caterina Consani) Advances in Mathematics, Vol.214 (2007) N.2, 761-831
• pdf Quantum statistical mechanics over function fields (with Caterina Consani) Journal of Number Theory, 123 (2007) 487-528
• pdf Q-lattices: quantum statistical mechanics and Galois theory (with Alain Connes) Journal of Geometry and Physics, 56 (2006) 2-23
• pdf 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
• pdf KMS states and complex multiplication (part II) (with Alain Connes and Niranjan Ramachandran) in "Operator Algebras", pp.15-60, Springer Verlag, 2006
• pdf KMS states and complex multiplication (with Alain Connes and Niranjan Ramachandran) Selecta Math. (N.S.) Vol.11 (2005) N.3-4, 325-347
• pdf Noncommutative geometry, dynamics, and infty-adic Arakelov geometry (with Caterina Consani) Selecta Mathematica, New Ser. 10 (2004) N.2, 167-251
• pdf Spectral triples from Mumford curves (with Caterina Consani), International Math. Research Notices, 36 (2003) 1945-1972
• pdf Limiting Modular symbols and the Lyapunov spectrum, Journal of Number Theory, Vol.98 N.2 (2003) 348-376
• pdf Triplets spectraux en geometrie d'Arakelov (with Caterina Consani) Comptes Rendus Acad. Sci. Paris, Ser. I 335 (2002) 779-784
• pdf Continued fractions, modular symbols, and noncommutative geometry, (with Yuri Manin) Selecta Mathematica, New Ser. Vol.8 N.3 (2002) 475-520

Noncommutative Motives

• pdf Some remarks concerning Voevodsky's nilpotence conjecture (with Marcello Bernardara, Goncalo Tabuada) J. Reine Angew. Math. 738 (2018) 299-312
• pdf Noncommutative numerical motives, Tannakian categories, and motivic Galois groups (with Goncalo Tabuada), Journal of the European Mathematical Society (JEMS) 18 (2016), no. 3, 623-655
• pdf From exceptional collections to motivic decompositions via noncommutative motives (with Goncalo Tabuada) J. Reine Angew. Math. 701 (2015) 153-167
• pdf Noncommutative motives, numerical equivalence, and semi-simplicity (with Goncalo Tabuada) American Journal of Mathematics, Vol.136 (2014) N.1, 59-75
• pdf Unconditional noncommutative motivic Galois groups (with Goncalo Tabuada) in "Hodge Theory and Classical Algebraic Geometry" pp.109-115, Contemp. Math. Vol.647, American Mathematical Society, 2015
• pdf Noncommutative Artin motives (with Goncalo Tabuada) Selecta Mathematica, Vol.20 (2014) N.1, 315-358
• pdf Jacobians of Noncommutative Motives (with Goncalo Tabuada) Moscow Mathematical Journal, Vol.14 (2014) N.3, 577-594
• pdf Kontsevich's noncommutative numerical motives (with Goncalo Tabuada) Compositio Mathematica, Vol.148 (2012) N.6, 1811-1820

F1 Geometry

• pdf Bost-Connes systems and F1-structures in Grothendieck rings, spectra, and Nori motives (with Jushua Lieber and Yuri Manin), arXiv:1901.00020, to appear in "Facets of Algebraic Geometry: A Volume in Honour of William Fulton’s 80th Birthday" Cambridge University Press
• pdf Homotopy types and geometries below Spec(Z) (with Yuri Manin) in "Dynamics: topology and numbers", 27-56, Contemp. Math., 744, Amer. Math. Soc. 2020
• pdf Moduli Operad over F1 (with Yuri Manin) in "Absolute arithmetic and F1 geometry", pp. 331-364, European Mathematical Society, 2016
• pdf F-zeta geometry, Tate motives, and the Habiro ring (with Catharine Wing Kwan Lo), International Journal of Number Theory, 11 (2015) N.2, 311-339
• pdf Quantum field theory over F1 (with Dori Bejleri) Journal of Geometry and Physics, 69 (2013) 40-59
• pdf Cyclotomy and endomotives, p-Adic Numbers, Ultrametric Analysis and Applications, Vol.1 (2009) N.3, 217-263
• pdf Fun with F1 (with Alain Connes and Caterina Consani), Journal of Number Theory, Vol.129 (2009), N.6, 1532-1561

Geometric Models of Particle Physics, Gravity and Cosmology

• pdf Gluing Noncommutative Twistor Spaces (with Roger Penrose), arXiv:2012.02823, to appear in the Oxford Quarterly Math Journal
• pdf Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson-Walker Cosmologies (with Farzad Fathizadeh and Yeorgia Kafkoulis) Ann. Henri Poincare, 21 (2020), no. 4, 1329-1382
• pdf Modular forms in the spectral action of Bianchi IX gravitational instantons (with Wentao Fan, Farzad Fathizadeh) Journal of High Energy Physics (2019) 234
• pdf Adinkras, Dessins, Origami, and Supersymmetry Spectral Triples (with Nick Zolman), p-Adic Numbers Ultrametric Anal. Appl. 11 (2019), no. 3, 223-247
• pdf Motives and periods in Bianchi IX gravity models (with Wentao Fan, Farzad Fathizadeh) Lett. Math. Phys. 108 (2018), no. 12, 2729-2747
• pdf Periods and motives in the spectral action of Robertson-Walker spacetimes (with F. Fathizadeh) Comm. Math. Phys. 356 (2017), no. 2, 641-671
• pdf Spectral action gravity and cosmological models, Comptes Rendus Physique, Vol. 18 (2017) N. 3-4, 226-234
• pdf Spectral Action Models of Gravity on Packed Swiss Cheese Cosmology (with Adam Ball) Classical Quantum Gravity 33 (2016), no. 11, 115018
• pdf Symbolic dynamics, modular curves, and Bianchi IX cosmologies (with Yuri Manin) Annales de la Faculte des Sciences de Toulouse, Vol. XXV (2016) N.2-3, 313-338
• pdf Spectral Action for Bianchi Type-IX Cosmological Models (with Wentao Fan, Farzad Fathizadeh) J. High Energy Phys. 2015, no. 10, 085
• pdf Big Bang, Blow up, and modular curves: algebraic geometry in cosmology (with Yuri Manin) SIGMA 10 (2014), 073
• pdf Coupling of gravity to matter, spectral action and cosmic topology (with Branimir Cacic and Kevin Teh) Journal of Noncommutative Geometry, Vol.8 (2014) N.2, 473-504
• pdf Gauge Networks in Noncommutative Geometry (with Walter van Suijlekom) Journal of Geometry and Physics, Vol.75 (2014) 71-91
• pdf Asymptotic safety, hypergeometric functions and the Higgs mass in spectral action models (with Christopher Estrada), International Journal of Geometric Methods in Modern Physics, Vol.10 (2013) N.7, 1350036
• pdf Noncommutative Mixmaster cosmologies (with Christopher Estrada) International Journal of Geometric Methods in Modern Physics, Vol.10 (2013) N.1
• pdf The coupling of topology and inflation in noncommutative cosmology (with Elena Pierpaoli and Kevin Teh) Communications in Mathemat- ical Physics, Vol.309 (2012) N.2, 341-369.
• pdf The Ricci flow on noncommutative two-tori (with Tanvir Ahamed Bhuyain) Letters in Mathematical Physics, Vol.101 (2012) N.2, 173-194
• pdf The spectral action and cosmic topology (with Elena Pierpaoli and Kevin Teh) Communications in Mathematical Physics, 304 (2011) 125-174
• pdf Building cosmological models via noncommutative geometry, International Journal of Geometric Methods in Modern Physics, Vol.8, N.5 (2011) 1131-1168
• pdf Early Universe models from Noncommutative Geometry (with Elena Pierpaoli) Advances in Theoretical and Mathematical Physics, Vol.14 (2010) 1373-1432
• pdf Spin foams and noncommutative geometry (with Domenic Denicola and Ahmad Zainy al-Yasry) Class. Quantum Grav. 27 (2010) 205025
• pdf Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology (with Daniel Kolodrubetz) Physics Letters B 693 (2010) 166-174
• pdf A Walk in the Noncommutative Garden (with Alain Connes) in "An invitation to Noncommutative Geometry", pp.1-128, World Scientific, 2008
• pdf Coverings, correspondences, and noncommutative geometry (with Ahmed Zainy al-Yasry) Journal of Geometry and Physics, Vol.58 (2008) N.12, 1639-1661
• pdf Gravity and the Standard Model with Neutrino Mixing (with Ali Chamsedding and Alain Connes) Advances in Theoretical and Mathematical Physics, 11 (2007) 991-1089
• pdf Modular curves, C*-algebras, and chaotic cosmology, in "Frontiers in Number Theory Physics and Geometry, II", pp.361-372, Springer Verlag, 2006

Classical and Quantum Information, Coding Theory, Computation

• pdf Computability questions in the sphere packing problem (with Yuri Manin)
• pdf Cohn-Elkies functions from Gabor frames (with Yuri Manin)
• pdf Pareto optimization in categories, preprint, 2022
• pdf Categorical Hopfield Networks
• pdf Topological Models of Neural Information Networks
• pdf Geometry of Information: Classical and Quantum aspects (with N.C.Combe and Yu.I.Manin)
• pdf Homotopy theoretic and categorical models of neural information networks (with Yuri Manin) preprint arXiv:2006.15136
• pdf Nori diagrams and persistent homology (with Yuri Manin) Math. Comput. Sci. 14 (2020), no. 1, 77-102
• pdf Asymptotic bounds for spherical codes (with Yuri Manin) Izvestiya Mat. 83 (2019) N.3, 117-141
• pdf Motivic Information, Boll. Unione Mat. Ital., Vol.12 (2019) N.1-2, 19-41
• pdf Gamma Spaces and Information, Journal of Geometry and Physics, 140 (2019) 26-55
• pdf Entropy algebras and Birkhoff factorization (with Nicolas Tedeschi) J. Geom. Phys. 97 (2015), 243-265
• pdf Quantum computation and real multiplication (with John Napp) Mathematics in Computer Science, 9 (2015), no. 1, 63-84
• pdf Dyson-Schwinger equations in the theory of computation (with Colleen Delaney) in "Feynman amplitudes, periods and motives", pp.79-107, Contemp. Math., Vol.648, Amer. Math. Soc., 2015
• pdf Information algebras and their applications, in "Geometric Science of Information" pp. 271-276, Lecture Notes in Comput. Sci., 9389, Springer, 2015
• pdf Kolmogorov complexity and the asymptotic bound for error-correcting codes (with Yuri Manin) Journal of Differential Geometry, Vol.97 (2014) 91-108
• pdf Thermodynamic Semirings (with Ryan Thorngren) Journal of Noncommutative Geometry, Vol.8 (2014) N.2, 337-392
• pdf Codes as fractals and noncommutative spaces (with Christopher Perez) Mathematics in Computer Science, Vol.6 (2012) N.3, 199-215
• pdf Error-correcting codes and phase transitions (with Yuri Manin) Mathematics in Computer Science, Vol.5 (2011) 133-170
• pdf Cuntz-Krieger algebras and wavelets on fractals (with Anna Maria Paolucci) Complex Analysis and Operator Theory, Vol.5 (2011) N.1, 41-81

Quantum Hall Systems, Anyons, Statistical Physics

• pdf Anyon Networks from Geometric Models of Matter (with Michael Atiyah) to appear in The Quarterly Journal of Mathematics, Oxford
• pdf Anyons in Geometric Models of Matter (with Michael Atiyah) J. High Energy Phys. (2017) no. 7, 076
• pdf Twisted index theory on orbifold symmetric products and the fractional quantum Hall effect (with Kyle Seipp) Adv. Theor. Math. Phys. 21 (2017) no. 2, 451-501
• pdf Potts models with magnetic field: arithmetic, geometry, and computation (with Shival Dasu) J. Geom. Phys. 97 (2015), 14-24
• pdf Arithmetic of Potts model hypersurfaces (with Jessica Su) International Journal of Geometric Methods in Modern Physics Vol. 10, No. 4 (2013) 1350005
• pdf A motivic approach to phase transitions in Potts models (with Paolo Aluffi) Journal of Geometry and Physics, Vol.63 (2013) 6-31
• 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
• pdf Twisted index theory on good orbifolds II: Fractional quantum numbers (with Varghese Mathai), Communications in Mathematical Physics, Vol.217 (2001) N.1 55-87
• pdf Twisted index theory on good orbifolds I: Noncommutative Bloch theory (with Varghese Mathai), Communications in Contemporary Mathematics, Vol.1 (1999) N.4, 553-587

Gauge Theory and Low Dimensional Topology

• pdf 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) 225-238
• pdf The geometric triangle for 3-dimensional Seiberg-Witten monopoles (with Alan Carey and Bai-Ling Wang) Communications in Contemporary Mathematics, Vol.5 N.2 (2003) 197-250
• pdf Weak UCP and perturbed monopole equations (with Bernhelm Booss-Bavnbek and Bai-Ling Wang), International Journal of Mathematics, Vol. 13 N.9 (2002) 987-1008
• pdf Seiberg-Witten and Casson-Walker invariant for rational homology spheres (with Bai-Ling Wang) Geometriae Dedicata, Vol.91 (2002) 45-58
• pdf Equivariant Seiberg-Witten Floer homology (with Bai-Ling Wang) Communications in Analysis and Geometry, Vol.9 N.3 (2001) 451-639
• pdf Seiberg-Witten Floer Homology and Heegaard Splittings, International Journal of Mathematics, Vol.7 (1996) N.5, 671-696
• pdf Gauge groups and characteristic classes, (with Mauro Spreafico), Expositiones Mathematicae, Vol.15 (1997) N.3, 229-249
• pdf Some remarks on conjugacy classes of bundle gauge groups, Cahiers Topologie Geom. Differentielle Categ. 37 (1996) N.1, 21-39

Books Edited

• Combinatorics and Physics (with Kurusch Ebrahimi-Fard and Walter van Suijlekom), American Mathematical Society, 2011.
• Quanta of Maths (with E.Blanchard, D.Ellwood, M.Khalkhali, H.Moscovici, S.Popa), Clay Mathematics Institute and AMS, 2010.
• Quantum groups and noncommutative spaces (with Deepak Parashar), Vieweg Verlag, 2010.
• Deformation spaces (with Hossein Abbaspour and Thomas Tradler) Vieweg Verlag, 2010.
• Arithmetic and Geometry around Quantization (with Ozgur Ceyhan and Yuri Manin) Birkhauser, 2010.
• 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

Miscellaneous mathematical writings

• ps Number Theory in Physics, contributed to the Encyclopaedia of Mathematical Physics
• pdf Noncommutative geometry and number theory, in Nieuw Archief voor Wiskunde.
• pdf A system of ODE for ASD connections and Dirac monopoles (in Russian)

Old unfinished projects

• 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)

Back to my home page