Matilde Marcolli: Slides

A selection of slides of talks

Older talks
• Renormalization
• Fractional Quantum Hall Effect
• Quantum Statistical Mechanics on Function Fields
• Quantum Statistical Mechanics of Q-lattices
• Noncommutative Geometry and Arithmetic (2003)
• Noncommutative Geometry and Arithmetic (2007)
• Modular Shadows
• Holography Principle
• Solvmanifolds and noncommutative tori
• Coverings and correspondences
• Zeta functions and Riemann surfaces
• Standard Model with Neutrino Mixing
• Renormalization, Galois Symmetries, and motives (ECM Amsterdam)
• Bost-Connes, F_1, 3-manifolds
• Feynman Integrals and Algebraic Geometry
• Noncommutative geometry and the field with one element
• Early Universe Models from Noncommutative Geometry
• Cosmology and the Poisson summation formula

The Cuernavaca Lectures (April 2010):
• Noncommutative Geometry Models for Particle Physics and Cosmology
• Quantum Field Theory and Motives
• How Noncommutative Geometry Looks at Arithmetic

ICM talk
• Noncommutative Geometry and Arithmetic

Adem Memorial Lectures, Cinvestav, Mexico City, January 2011
• Cosmology and the Poisson summation formula
• Solvmanifolds and noncommutative tori with real multiplication
• Quantum statistical mechanics, L-series and anabelian geometry

Harvard Colloquium
• Quantum statistical mechanics and anabelian geometry (March 24, 2011)

String-Math Conference, Philadelphia
• Motives in Quantum Field Theory (June 9, 2011)

"Noncommutative geometry models in particle physics and cosmology", lectures at the Villa de Leyva summer school "Geometric, Algebraic and Topological methods for Quantum Field Theory" (July 3-8, 2011)
• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4

MPI, December 2011
• Noncommutative Numerical Motives and the Tannakian formalism

Lorentz Center, March 2012
• Quantum Statistical Mechanics, Kolmogorov Complexity, and the asymptotic bound of error-correcting codes

Two informal talks at the Banff meeting "Novel approaches to the finite simple groups", April 2012
• From CFT to CFT?
• Multiplicative genera for noncommutative manifolds?

talk at workshop "Fractal Geometry and Dynamical Systems", UC Riverside, June 2012
• Cuntz-Krieger algebras and wavelets on fractals

AlbertoFest, Cuernavaca, Mexico, January 2013
• Feynman integrals in configuration space and mixed Tate motives

Evans Lecture, UC Berkeley - MSRI, April 2013
• A motivic approach to Potts models

Hodge Theory and Classical Algebraic Geometry - OSU, May 2013
• Noncommutative motives and their Jacobians

Plenary Lecture at PRIMA Congress, Shanghai, June 2013
• F1 Geometry of Moduli Spaces

Lectures in Beijing, August 2013
• Noncommutative Motives and their Applications Kavli Institute for Theoretical Physics China (KITPC)
• Quantum Field Theory and Motives Beijing International Center for Mathematical Research (BICMR) Beijing University
• A motivic approach to Potts models Kavli Institute for Theoretical Physics China (KITPC) and Morningside Center
• Feynman integral and motives in configuration spaces Kavli Institute for Theoretical Physics China (KITPC) and Morningside Center
• Quantum Statistical Mechanics and Anabelian Geometry Tsinghua University Institute for Advanced Study
• Noncommutative geometry and cosmology Kavli Institute for Theoretical Physics China (KITPC) and Morningside Center

Plenary talk AMS Meeting Riverside, November 2013
• Feynman integrals and motives

Plenary talk at String-Math 2014, Edmonton
• Feynman integrals and motives in momentum and configuration spaces

MIT Topology Seminar
• Feynman integrals, sigular hypersurfaces, and motives

Cosmology Seminar Perimeter Institute
• Spectral Action Models of Gravity and Packed Swiss Cheese Cosmology

Algebraic Geometry Seminar, University of Edinburgh
• Motives in Quantum Field Theory

Geometry for Signal Processing and Machine Learning Workshop, Estes Park
• Geometric Models for Linguistics

Algebra, Geometry and Physics Seminar, Max Planck Institute Bonn
• Arithmetic Structures in Spectral Models of Gravity

Arbeitstagung Physical Mathematics, in honor of Yuri Manin, Max Planck Institute Bonn, June 2017
• Non-Archimedean Holography

Topological and Geometrical Structures of Information, CIRM Luminy, August 2017
• The Geometry of Syntax

Geometric Science of Information, Paris, November 2017
• Prevalence and Recoverability of Syntactic Parameters in Sparse Distributed Memories

Utrecht Lectures, April 2018
• Mathematics Colloquium: The Geometry of Syntax
• Centre for Complex Systems Studies Seminar: Codes and Complexity
• Theoretical Linguistics Colloquium: The Geometry of Syntax (Part 2)

Combinatorial structures in perturbative QFT 2, Waterloo University, May 2018
• Feynman quadrics, Prym varieties, and the motive of the Sunset Graph

invited plenary talk at MOL2019: Mathematics of Language, University of Toronto, Canada
• Toward a Geometry of Syntax

New Geometries of Quantum Dynamics, Fields Institute, Canada
• Spectral gravity models on multifractal Robertson-Walker cosmologies

Conference "Michael Atiyah - Forays into Physics", Newton Institute, Cambridge UK, October 2019
• Anyons, networks, and codes in geometric models of matter

AMS Meeting Denver: Session on Singularities and Characteristic Classes
• Motives of intersections of quadrics and the Feynman integral of the massive sunset graph

Focus Program on New Geometric Methods in Neuroscience, Fields Institute, Toronto, Canada
• Homotopy Theory and Neural Information Networks

Hot Topic Workshop: Topological Insights in Neuroscience, MSRI, May 2021
• Homotopy Theoretic and Categorical Models of Neural Information Networks

Canadian Mathematical Society, 75th Anniversary Summer Meeting, June 2020(2021)
• Entropy, Holography, and p-adic Geometry

Geometric Science of Information, Sorbonne, Paris, July 2021
• Topological Models of Neural Information Networks

Algebra, Geometry and Physics: a Mathematical Mosaic, Yuri Manin's 85th birthday conference, MPI Bonn, March 2022
• Categorical dynamics: from Hopfield to Pareto

Algebra, Geometry and Physics Seminar: A Homage, MPI Bonn, February 2023
• The Last Lecture: Computability Questions in the Sphere Packing Problem

Utrecht Theoretical Linguistics, June 2023
• A mathematical model of syntactic Merge

Lecture Series at MIT Linguistics Department, December 2023
• Mathematical Structure of Syntactic Merge: An Algebraic Model for Generative Linguistics

Merkin Center meeting Algebraic Models of Generative Linguistics, March 2024
• Mathematical Structure of Syntactic Merge

Stony Brook, Run Run Shaw Lecture, Mathematics Colloquium, Linguistics Colloquium, March 2024
• Algebraic Models for Linguistics Inspired by Theoretical Physics
• Mathematical structures in generative linguistics
• Mathematical Structure of Syntactic Merge

General audience talks

• The Notion of Space in Mathematics through the lens of Modern Art (general audience lecture, Century Books, Pasadena, July 19, 2016)
• The Train and the Cosmos: Visionary Modernity (general audience lecture at Century Books, Pasadena, December 2015)
• Entropy and Art: the view beyond Arnheim (general audience lecture, Century Books, Pasadena, March 10, 2015)
• Structures of Randomness (general audience lecture, Century Books, Pasadena, December 2014)
• Plentiful Nothingness: the Void in Modern Art and Modern Science (general audience lecture, Century Books, Pasadena, February 2014)
• Still Life as a Model of Spacetime (general audience lecture, Century Books, Pasadena, December 2012)
• The geometry and physics of numbers (general audience talk, Revolution Books, Berkeley, May 2013)
• Can you hear the shape of the cosmos? (general audience talk, Revolution Books, Berkeley, April 2011)
• The dark heart of our brightness: bipolar disorder and scientific creativity (general audience lecture given at Caltech, April 2010)
• Mathematicians look at particle physics (general audience talk for the "Year of Mathematics" Bonn 2008 and Revolution Books Berkeley, March 2009)
• The notion of space in mathematics (general audience talk at Revolution Books, Berkeley, April 2009)

Lectures on video

• Noncommutative motives and their applications I MSRI 2013
• Noncommutative motives and their applications II MSRI 2013
• Cosmology and the Poisson summation formula Perimeter Institute 2011
• Spin foams and noncommutative geometry Perimeter Institute 2011
• The dark heart of our brightness: bipolar disorder and scientific creativity Caltech 2010 (second lecture on the video)
• Feynman integrals and algebraic geometry JAMI workshop 2009
• KMS states and complex multiplication Banff 2006
• Quantum Field Theory and Motives 1, Vanderbilt 2005
• Quantum Field Theory and Motives 2, Vanderbilt 2005
• Quantum Field Theory and Motives 3, Vanderbilt 2005
• Quantum Field Theory and Motives 4, Vanderbilt 2005

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