The Geometry of Machine Learning Dates: September 15–18, 2025 Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA 02138 Despite the extraordinary progress in large language models, mathematicians suspect that other dimensions of intelligence must be defined and simulated to complete the picture. Geometric and symbolic reasoning are among these. In fact, there seems […]
Quantum Field Theory and Physical Mathematics Seminar Speaker: Chuck Doran (Alberta/CMSA) Title: Orientifolds for F-theory on K3 Surfaces Abstract: Compactification of F-theory on an elliptically fibered K3 surface provides a framework to encode type IIB string theory on elliptic curves, with the Kaehler modulus of the elliptic curve encoded in the complex structure of the elliptic fibers. In […]
Colloquium Speaker: Michael Freedman (Harvard CMSA and Logical Intelligence) Title: Topological Manifolds – The First 100 Years Abstract: I’ll review manifold topology in the topological category from its start with work of Rado (1925) and Kneser (1926) to the present. Work of Moise, Mazur, Kirby, Siebenmann, Sullivan, Kruskal, and the speaker will be discussed. In my view […]
Geometry of Machine Learning Special Lecture: Yann LeCun Title: Self-Supervised Learning, JEPA, World Models, and the future of AI Date: Tuesday, Sep. 16, 2025 Time: 5:00 pm ET Location: Harvard Science Center, Hall C & via Zoom Webinar
https://youtu.be/60X5M1FhmUc Millennium Prize Problems Lecture Date: September 17, 2025 Location: Harvard Science Center Hall D & via Zoom Webinar Time: 5:00–6:00 pm Speaker: Michael Freedman, Harvard CMSA and Logical Intelligence Title: The Poincaré Conjecture and Mathematical Discovery Abstract: The AI age requires us to re-examine what mathematics is about. The Seven Millenium Problems provide an […]
Differential Geometry and Physics Seminar Speaker: Robert Moscrop, CMSA Title: Moduli spaces of 4d N=2 quantum field theories Abstract: Supersymmetry endows quantum field theories with several rich algebraic and geometric structures associated to their moduli space of vacua, providing powerful tools to study such theories non-perturbatively. For example, in four-dimensional theories with eight supercharges, the […]
Member Seminar Speaker: Max Hubner Title: Top-Down Perspectives on Symmetry Theories Abstract: I will review the construction and utility of symmetry theories for string constructed quantum field theories. Symmetry theories are extra-dimensional auxiliary theories separating aspects of a quantum field theory's symmetries from many of its more messy features. For QFTs with extra-dimensional string constructions the […]
Quantum Field Theory and Physical Mathematics Seminar Speaker: Max Hübner (Uppsala & CMSA) Title: Non-Supersymmetric Orbifolds, Quivers and Chen-Ruan Orbifold Cohomology Abstract: We consider D3-brane probes of non-supersymmetric orbifolds and IIA on the same class of non-supersymmetric orbifolds. Both setups are characterized, in part, by quivers (which in the latter case relate for example to D0-brane probes) from which […]
Colloquium Speaker: David Nelson, Harvard Title: Turbulent Mixing and Antagonistic Microorganisms Abstract: Unlike coffee and cream that homogenize when stirred, growing micro-organisms (e.g., bacteria and baker’s yeast) can actively kill each other and avoid mixing. How do such antagonistic interactions impact the growth and survival of competing strains, while being spatially advected by turbulent flows? […]
Differential Geometry and Physics Seminar Speaker: Teng Fei, Rutgers Title: Degeneration of Calabi-Yau 3-folds and 3-forms Abstract: We study the geometries associated to various 3-forms on a symplectic 6-manifold of different orbital types. As an application, we demonstrate how this can be used to find Lagrangian foliations and other geometric structures of interest arising from […]
Member Seminar Speaker: Iacopo Brivio Title: Sections of fibrations onto curves in characteristic p>0 Abstract: This talk is based on joint work in progress with Ben Church. Using symplectic geometry, Pieloch showed that every smooth fibration $f\colon X\to \mathbb{P}^1$ of complex projective varieties always admits a section. I will explain how this theorem can be recovered using […]
Quantum Field Theory and Physical Mathematics Seminar Speaker: Minghao Wang, Boston University Title: Graph integrals on Kahler manifolds Abstract: I will talk about my recent work with Junrong Yan. We proved the convergence of Graph integrals on analytic Kahler manifolds in the sense of Cauchy principal values, which are originally from holomorphic quantum field theories. […]