Today

  • Learning diffusion models in high-dimensions

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Member Seminar Speaker: Hugo Cui Title: Learning diffusion models in high-dimensions Abstract: We consider the problem of learning a generative model parametrized by a two-layer auto-encoder, and trained with online stochastic gradient descent, to sample from a high-dimensional data distribution with an underlying low-dimensional structure. We provide a tight asymptotic characterization of low-dimensional projections of […]

  • Mathematical Physics and Algebraic Geometry Seminar

    (Strictly) Non-minimal Elliptic Threefolds and the Distance Conjecture

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Mathematical Physics and Algebraic Geometry Seminar Speaker: Rafael Álvarez García (Harvard University) Title: (Strictly) Non-minimal Elliptic Threefolds and the Distance Conjecture Abstract: We analyze infinite-distance limits in the complex structure moduli space of six-dimensional F-theory, providing an algebro-geometric classification and a physical interpretation. From the point of view of the Swampland Program, the motivation is to understand the […]

  • Learning Dynamical Transport without Data

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    https://youtu.be/mwpbMSNZOh0 New Technologies in Mathematics Seminar Speaker: Michael Albergo (Harvard) Title: Learning Dynamical Transport without Data Abstract: Algorithms based on dynamical transport of measure, such as score-based diffusion models, have resulted in great progress in the field of generative modeling. However, these algorithms rely on access to an abundance of data from the target distribution. […]

  • Homotopical Methods for Free and Interacting Fermionic SPTs

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Quantum Field Theory and Physical Mathematics Seminar Speaker: Cameron Krulewski, MIT Title: Homotopical Methods for Free and Interacting Fermionic SPTs Abstract: We develop and compute homotopical "free-to-interacting maps" to compare classifications of fermionic symmetry-protected topological phases (SPTs), determining when such phases are stable under interactions or, alternatively, interaction-enabled. Generalizing work of Freed-Hopkins, we construct maps […]

  • The Toda Lattice as a Soliton Gas

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Colloquium Speaker: Amol Aggarwal, Columbia University Title: The Toda Lattice as a Soliton Gas Abstract: A basic tenet of integrable systems is that, under sufficiently irregular initial data, they can be thought of as dense collections of many solitons, or “soliton gases.” In this talk we focus on the Toda lattice, which is an archetypal example of […]

  • The Andersen-Kashaev volume conjecture for FAMED geometric triangulations  

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Quantum Field Theory and Physical Mathematics Seminar Speaker: Ka Ho Wong (Yale) Title: The Andersen-Kashaev volume conjecture for FAMED geometric triangulations Abstract: In the early 2010s, Andersen and Kashaev defined a TQFT based on quantum Teichmuller theory. In particular, they define a partition function for every ordered ideal triangulation of hyperbolic knot complement in $\mathbb{S}^3$ […]

  • Mathematical Physics and Algebraic Geometry Seminar

    Verlinde’s formula in logarithmic conformal field theory

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Mathematical Physics and Algebraic Geometry Seminar Speaker: Thomas Creutzig (University of Alberta) Title: Verlinde's formula in logarithmic conformal field theory Abstract: Two-dimensional conformal field theories lead to rich mathematical structure. For example its chiral algebra is a vertex algebra and the axioms of rational conformal field theory define modular tensor categories. A highlight of this development […]

  • Positive scalar curvature with point singularities

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    https://youtu.be/m9B003wQ0PY General Relativity Seminar Speaker: Rudolf Zeidler, Mathematical Institute, University of Münster Title: Positive scalar curvature with point singularities Abstract: I will explain a certain topological construction of positive scalar curvature metrics with uniformly Euclidean ($L^\infty$) point singularities. This provides counterexamples to a conjecture of Schoen. It also shows that there are metrics with uniformly Euclidean […]

  • Comments on Non-Invertible Symmetries in K3 CFTs and the Conway Moonshine Module

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Quantum Field Theory and Physical Mathematics Seminar Speaker: Sarah Harrison, Northeastern Title: Comments on Non-Invertible Symmetries in K3 CFTs and the Conway Moonshine Module Abstract: There is an established connection between discrete symmetry groups of K3 non-linear sigma models and a distinguished N=1 chiral SCFT called the Conway moonshine module. More specifically, all symmetry groups […]

  • A Tetrahedral Approach to Calabi-Yau Geometry

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Member Seminar Speaker: Charles Doran, CMSA Title: A Tetrahedral Approach to Calabi-Yau Geometry Abstract:  We will open with a quick introduction to the what and why of Calabi-Yau geometry.  Following this, we will consider the problem of deforming tetrahedra while preserving the areas of their faces, following our noses to discover a beautiful path to […]

  • Mathematical Physics and Algebraic Geometry Seminar

    Physical Yukawa Couplings in Heterotic String Compactifications

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Mathematical Physics and Algebraic Geometry Seminar Speaker: Giorgi Butbaia, University of New Hampshire Title: Physical Yukawa Couplings in Heterotic String Compactifications Abstract: Calabi-Yau compactifications of the $E_8\times E_8$ heterotic string provide a promising route to recovering the four-dimensional particle physics described by the Standard Model. While the topology of the Calabi-Yau space determines the overall […]

  • Featured

    Large value estimates in number theory and computer science

    CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

    Colloquium Speaker: Larry Guth, MIT Title: Large value estimates in number theory and computer science Abstract: A large value estimate for a matrix M is a simple type of estimate in quantitative linear algebra. Estimates of this type appear in many parts of math, both pure and applied. One example is the large value problem for […]