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  1. Summer Graduate School Topological and Geometric Structures in Low Dimensions (SLMath)

    Organizers: LEAD Kenneth Bromberg (University of Utah), Kathryn Mann (Cornell University)
    Image
    <p>Laminations arise naturally in hyperbolic geometry and (pseudo-) Anosov flows [Image by Jeffrey Brock]</p>

    This school will serve as an introduction to the SLMath semester “Topological and Geometric Structures in Low-Dimensions”.  The school consists of two mini-courses: one on Teichmüller Theory and Hyperbolic 3-Manifolds and the other on Anosov Flows on Geometric 3-Manifolds.  Both topics lie at the interface of low-dimensional geometric topology (specifically, surfaces, foliations, and 3-manifolds) and low-dimensional dynamics.  The first course will be targeted towards students who have completed the standard first year graduate courses in geometry, topology, and analysis while the second course will geared towards more advanced students who are closer to beginning research. However, we expect that all students will benefit from both courses.

    Updated on Apr 21, 2025 03:17 PM PDT
  2. Summer Graduate School Mathematics of Generative Models

    Organizers: Jianfeng Lu (Duke University), Eric Vanden-Eijnden (New York University, Courant Institute)
    1136 image
    <p>Artificial image generation by flow-based generative models starting from noise</p>

    The overarching goal of this summer school is to expose students to the latest developments in the mathematics of generative models. Our ultimate goal is to teach them how to conduct research in this exciting area in machine learning and use their knowledge to make contributions to applied mathematics using these new tools.

    Updated on Jul 09, 2025 01:11 PM PDT
  3. Summer Graduate School Joint SLMath-Oxford-OIST School: Analysis of Partial Differential Equations (Okinawa Institute of Science and Technology)

    Organizers: Ugur Abdulla (Okinawa Institute of Science and Technology), Gui-Qiang Chen (University of Oxford)

    This two week summer school, jointly organized by SLMath with OIST, will offer the following two mini-courses:

    1. Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form
      This course will present some recent developments in the theory of divergence-measure fields via measure-theoretic analysis and its applications to the analysis of nonlinear PDEs of conservative form – nonlinear conservation laws.
    2. Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs
      This course will present some recent developments precisely characterizing the regularity of the point at ∞ for second order elliptic and parabolic PDEs and broadly extending the role of the Wiener test in classical analysis.

    Updated on Jul 09, 2025 01:35 PM PDT
  4. Summer Graduate School Singularities in commutative algebra through cohomological methods

    Organizers: Benjamin Briggs (University of Copenhagen; University of Utah), EloĆ­sa Grifo (University of Nebraska), Josh Pollitz (Syracuse University)
    1150 image
    <p>Homotopy measures how spheres can be tangled in spaces; the logo shows a sphere tangled in a grove of California redwoods<br />The background painting is &ldquo;Giant Redwood Trees of California&rdquo; by Albert Bierstadt in 1874</p>

    The goal of this school will be to introduce students to several powerful cohomological tools that were brought to commutative algebra by Avramov in the 80s and 90s: Lie algebra methods from homotopy theory, and support theoretic methods from the representation theory of finite groups. These tools have have seen a huge array of applications that continue to grow, with several major developments in recent years, opening new connections to algebraic topology, noncommutative algebraic geometry, and representation theory.

    Updated on Jul 08, 2025 02:04 PM PDT
  5. Summer Graduate School Moduli of Varieties

    Organizers: Kenneth Ascher (University of California, Irvine), Dori Bejleri (Massachusetts Institute of Technology), Kristin DeVleming (University of California, San Diego)
    1135 image
    <p>A wall-crossing in a moduli problem</p>

    One of the central problems in algebraic geometry is to classify so-called algebraic varieties: geometric shapes cut out by polynomial equations. Algebraic varieties are parametrized by certain moduli spaces (roughly: parameter spaces whose points correspond to these different varieties). The geometry of these moduli spaces encodes the ways of continuously deforming these shapes. Furthermore, classification questions for algebraic varieties often boil down to understanding the geometry of these moduli spaces. In the past few years, powerful new tools have been developed in moduli theory, especially for higher dimensional varieties – those which are of complex dimension at least two. The goal of this summer school is to provide an introduction to many of these recently emerging breakthroughs to enable graduate students to begin working in this area. The program will be motivated and often guided by examples and is intended to be accessible to a wide variety of students

    Updated on Jul 08, 2025 01:48 PM PDT