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Caltech
Division of Physics, Mathematics and Astronomy

Matilde Marcolli

Robert F. Christy Professor of Mathematics and Computing and Mathematical Sciences
Laurea, University Degli Studi, 1993; M.Sc., University of Chicago, 1994; Ph.D., 1997. Caltech, Professor, 2008-19, Christy Professor, 2019-.

Research Interests: Mathematical and Computational Linguistics, Mathematical Structures in Quantum Physics, Noncommutative Geometry

Overview

Matilde's work spans several areas of research at the interface between mathematics and theoretical physics, with a recent growing interest in the interaction between these two subjects and information theory. On the mathematical side, her work began in low dimensional topology, and later branched out to include non-commutative geometry, and algebraic and arithmetic geometry. On the physics side, her work focused mostly on quantum field theory, quantum statistical mechanics, geometric models for cosmology and particle physics, and quantum Hall systems. Her more recent work in connections with information theory and computer science involves the application of methods from geometry and statistical physics to coding theory and to mathematical and computational linguistics, as well as geometric aspects of quantum information.

Selected Awards

  • Geometric Science of Information Achievement Award, 2021
  • PROSE Award, Mathematics Category, for the book Lumen Naturae, MIT Press

Caltech Affiliations

PhD Thesis: Three-Dimensional Aspects of Seiberg-Witten Gauge Theory

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Selected Publications

For a complete publications list, see feeds.library.caltech.edu

Related Courses

Ma 191 abc. Selected Topics in Mathematics. 9 units (3-0-6); first, second, third terms, 2025-26. Each term we expect to give between 0 and 6 (most often 2-3) topics courses in advanced mathematics covering an area of current research interest. These courses will be given as sections of 191. Students may register for this course multiple times even for multiple sections in a single term. The topics and instructors for each term and course descriptions will be listed on the math option website each term prior to the start of registration for that term.
Instructors: T. Yu, Pham, Zhang, Yang, Heinaevaara, Looi, Svoboda, Marcolli, El-Maazouz, Flach, Dong
Ma 4/104. Introduction to Mathematical Chaos. 9 units (3-0-6); third term, 2025-26. An introduction to the mathematics of "chaos." Period doubling universality, and related topics; interval maps, symbolic itineraries, stable/unstable manifold theorem, strange attractors, iteration of complex analytic maps, applications to multidimensional dynamics systems and real-world problems. Possibly some additional topics, such as Sarkovski's theorem, absolutely continuous invariant measures, sensitivity to initial conditions, and the horseshoe map.
Instructor: Marcolli
Ma/CS 6/106 abc. Introduction to Discrete Mathematics. 9 units (3-0-6); first, second, third terms, 2025-26. Prerequisites: for Ma/CS 6 c, Ma/CS 6 a or Ma 5 a or instructor's permission. First term: a survey emphasizing graph theory, algorithms, and applications of algebraic structures. Graphs: paths, trees, circuits, breadth-first and depth-first searches, colorings, matchings. Enumeration techniques; formal power series; combinatorial interpretations. Topics from coding and cryptography, including Hamming codes and RSA. Second term: directed graphs; networks; combinatorial optimization; linear programming. Permutation groups; counting nonisomorphic structures. Topics from extremal graph and set theory, and partially ordered sets. Third term: syntax and semantics of propositional and first-order logic. Introduction to the Godel completeness and incompleteness theorems. Elements of computability theory and computational complexity. Discussion of the P=NP problem.
Instructors: T. Yu, Babecki, Marcolli