Matilde Marcolli: SURFers

SURF (Summer Undergraduate Research Fellowships) is a research opportunity program for undergraduates at Caltech. For more information, or if you are interested in a SURF project in this research area, please consult the SURF page of Caltech.

SURFers 2009

Daniel Kolodrubetz: RGE flow in Noncommutative Cosmology
- pdf Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology (Daniel Kolodrubetz and Matilde Marcolli) Physics Letters B 693 (2010) 166-174
Domenic Denicola: Loop quantum gravity and Noncommutative Geometry
- pdf Spin foams and noncommutative geometry (Domenic Denicola, Matilde Marcolli and Ahmad Zainy al-Yasry) Classical and Quantum Gravity 27 (2010) 205025 (53pp)

SURFers 2010

Tanvir Ahamed Bhuyain: Ricci flow in noncommutative geometry
- pdf The Ricci flow on noncommutative two-tori (Tanvir Ahamed Bhuyain and Matilde Marcolli) Letters in Mathematical Physics, Vol.101 (2012) N.2, 173-194
Christopher Estrada: Spectral action, noncommutative tori, and chaotic cosmology
- pdf Noncommutative mixmaster cosmologies (Christopher Estrada and Matilde Marcolli) International Journal of Geometric Methods in Modern Physics, 10 (2013), no. 1, 1250086 [28 pages]
Christopher Perez: Fractals and algebro-geometric codes
- pdf Codes as fractals and noncommutative spaces (Matilde Marcolli and Christopher Perez) Mathematics in Computer Science, 6 (2012), no. 3, 199-215.

SURFers 2011

Dori Bejleri: Quantum field theory and the field with one element
- pdf Quantum field theory over F1 (Dori Bejleri and Matilde Marcolli) Journal of Geometry and Physics, Vol. 69 (2013) 40-59.
Christopher Estrada: Noncommutative geometry and the Standard Model
- pdf Asymptotic safety, hypergeometric functions and the Higgs mass in spectral action models (Christopher Estrada and Matilde Marcolli) International Journal of Geometric Methods in Modern Physics, Vol.10 (2013) N.7, 1350036 [30 pages]
Jessica Su: Multivariate Tutte polynomials, Potts models and arithmetic
- pdf Arithmetic of Potts Model Hypersurfaces (Matilde Marcolli and Jessica Su) International Journal of Geometric Methods in Modern Physics, Vol. 10, No. 4 (2013) 1350005 [22 pages]
Ryan Thorngren: Entropy and the field with one element
- pdf Thermodynamic Semirings (Matilde Marcolli and Ryan Thorngren) Journal of Noncommutative Geometry, Vol.8 (2014) N.2, 337-392

Jonathan Paprocki (GeorgiaTech): Graph algebras and BPS state counting

SURFers 2012

Colleen Delaney: Renormalization and computation
- pdf Dyson-Schwinger equations in the theory of computation (Colleen Delaney and Matilde Marcolli) in "Feynman Amplitudes, Periods, and Motives", Contemporary Mathematics, Vol.648 (2015) 79-107
Mark Greenfield: Quantum statistical mechanical systems and spectral triples
- pdf Type III sigma-spectral triples and quantum statistical mechanical systems (Mark Greenfield, Matilde Marcolli, and Kevin Teh), p-adic Numbers, Ultrametric Analysis, and Applications, Vol.6 (2014) N.2, 81-104
Wade Hann-Caruthers: Potts models with external magnetic field
Justin Khim: Noncommutative 3-tori and Random Surfaces
Nicolas Tedeschi: The multifractal formalism in noncommutative geometry
- pdf Multifractals, Mumford curves, and Eternal Inflation (Matilde Marcolli and Nicolas Tedeschi) P-Adic Numbers, Ultrametric Analysis and Applications, Vol.6 (2014) N.2, 135-154

SURFers 2013

Zhaorong Jin: endomotives and toric varieties
- pdf Endomotives of Toric Varieties (Zhaorong Jin and Matilde Marcolli) Journal of Geometry and Physics, Vol. 77 (2014) 48-71
Catharine Lo: Roots of unity and the field with one element
- pdf F-zeta geometry, Tate motives, and the Habiro ring (Catharine Lo and Matilde Marcolli) International Journal of Number Theory, 11 (2015), no. 2, 311-339
John Napp: Noncommutative geometry of anyon systems
- pdf Quantum computation and real multiplication (Matilde Marcolli and John Napp) Mathematics in Computer Science 9 (2015), no. 1, 63-84
Nicolas Tedeschi: Entropy and algebraic renormalization
- pdf Entropy algebras and Birkhoff factorization (Matilde Marcolli and Nicolas Tedeschi) Journal of Geometry and Physics, 97 (2015), 243-265

Iulia Gheorghita: Path algebras and spectral triples
Gjergji Zaimi: Frobenius manifolds in information geometry

SURFers 2014

Adam Ball: Spectral action gravity of swiss cheese cosmology
- pdf Spectral Action models of gravity on Packed Swiss Cheese Cosmology (Adam Ball and Matilde Marcolli)
Shival Dasu: Arithmetic of Potts models with magnetic field
- pdf Potts models with magnetic field: arithmetic, geometry, and computation (Shival Dasu and Matilde Marcolli) Journal of Geometry and Physics, 97 (2015), 14-24
Jace Marcinek: Noncommutative geometry of Tits buildings
- pdf KMS weight on higher rank buildings (Jake Marcinek and Matilde Marcolli) to appear in P-adic Numbers, Ultrametric Analysis, and Applications
Matthew Morgan: Spin glass models in computational linguistics
Alex Port: Graph Grammars and quantum field theory
- pdf Graph Grammars, insertion Lie algebras, and quantum field theory (Matilde Marcolli and Alex Port) Mathematics in Computer Science: Volume 9, Issue 4 (2015) 391-408

Kyle Seipp: orbifold symmetric products and the fractional quantum Hall effect
- pdf Twisted index theory on orbifold symmetric products and the fractional quantum Hall effect (Matilde Marcolli and Kyle Seipp)

SURFers 2015

Yujie Xu: Quantum Statistical Mechanics of 3-manifolds
- pdf Quantum statistical mechanics in arithmetic topology (Matilde Marcolli and Yujie Xu) Journal of Geometry and Physics, Vol. 114 (2017) 153-183
Nick Zolman: Supersymmetry and Combinatorics
- pdf Adinkras, Dessins, Origami, and Supersymmetry Spectral Triples (Matilde Marcolli and Nick Zolman), p-Adic Numbers Ultrametric Anal. Appl. 11 (2019), no. 3, 223-247
Marcus Bintz: Tropical Graph Hypersurfaces
Preston Rasmussen: Geometric flows in Quantum Information

Ethan Torres: the Higgs portal and stability in the Noncommutative Standard Model

SURFers 2016

Kevin Shu: Syntactic Linguistic Phylogenetics
- pdf Syntactic Structures and Code Parameters (Kevin Shu and Matilde Marcolli) Mathematics in Computer Science, 11 (2017), no. 1, 79-90
- pdf Phylogenetics of Indo-European Language families via an Algebro-Geometric Analysis of their Syntactic Structures (Kevin Shu, Andrew Ortegaray, Robert C. Berwick, Matilde Marcolli) to appear in Mathematics in Computer Science
- pdf Syntactic Phylogenetic Trees (Kevin Shu, Sharjeel Aziz, Vy-Luan Huynh, David Warrick, Matilde Marcolli) in "Foundations of Mathematics and Physics one Century after Hilbert", Springer Verlag, 2018, pp. 417-441
Yeorgia Kafkoulis: Multifractal Robertson-Walker Cosmologies
- pdf Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson-Walker Cosmologies (Farzad Fathizadeh, Yeorgia Kafkoulis, Matilde Marcolli) Ann. Henri Poincare, 21 (2020), no. 4, 1329-1382
Zhi Ren: q-Deformations of the Bost-Connes system
- pdf q-deformations of statistical mechanical systems and motives over finite fields (Matilde Marcolli, Zhi Ren), p-Adic Numbers Ultrametric Anal. Appl. 9 (2017), no. 3, 204-227

SURFers 2017

Andrew Ortegaray: Geometric Models of Syntax
- pdf Phylogenetics of Indo-European Language families via an Algebro-Geometric Analysis of their Syntactic Structures (Kevin Shu, Andrew Ortegaray, Robert C. Berwick, Matilde Marcolli) to appear in Mathematics in Computer Science
- pdf Heat Kernel analysis of Syntactic Structures (Andrew Ortegaray, Robert C. Berwick, Matilde Marcolli) to appear in Mathematics in Computer Science
Eitan Borgnia: Tutte Graph Embeddings and P-adic Holography
Erik Herrera: Entropy of Spectral Triples
Yeorgia Kafkoulis: Spectral Action of Apollonian Packings
- pdf Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson-Walker Cosmologies (Farzad Fathizadeh, Yeorgia Kafkoulis, Matilde Marcolli) Ann. Henri Poincare, 21 (2020), no. 4, 1329-1382
Crystal Lliang: Formal Languages and Quasicrystals

SURFers/WAVErs 2021

Pedro Guicardi (Cornell University): Fractality in Cosmic Topology with Spectral Modelds of Gravity
- pdf Fractality in Cosmic Topology Models with Spectral Action Gravity

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