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Institute for Pure and Applied Mathematics (IPAM), UCLA

Geometric structures associated with bipartite graphs on surfaces have recently emerged and turn out to be crucial for studying a variety of problems. On the one hand, probabilists working in statistical mechanics are interested in finding appropriate embeddings of planar graphs that lead to discrete complex analysis theories, which are well suited for observing conformally invariant objects in the scaling limit. In the course of doing so, they established deep connections between specific immersions of the underlying graphs, integrability of the models, and Harnack curves. On the other hand, several spaces of geometric objects have recently been found to be parametrized by weighted bipartite graphs on surfaces, relating them to cluster algebras and integrable systems. These include objects from discrete differential geometry (e.g. Q-nets, Darboux maps), positive Grassmannians, and higher Teichmüller spaces. Moreover, connections between knot theory and the dimer model have started to emerge and beg for a better understanding.

Part of the Long Program Geometry, Statistical Mechanics, and Integrability

Mathematische Physik,    Thermodynamik, Hydrodynamik und Statistische Mechanik

Northwestern University

Microlocal Analysis and Quantum Dynamics 2024 is supported by the RTG “Dynamics: Classical, Modern, and Quantum”. The events are part of Northwestern’s 2023-2024 Emphasis Year, “Asymptotics in Geometry and Analysis: the Mathematics of Steve Zelditch”.

school and conference

Kurse und Veranstaltungen für Studenten der Mathematik,    Quantenmechanik und Quantentechnologie

Simons Laufer Mathematical Sciences Institute (SLMath)

This workshop aims to prepare the participants for the main program: Special Geometric Structures and Analysis. There will be introductory lectures to recent results in geometry and analysis; more precisely in Kähler geometry, special holonomy, microlocal analysis and geometric measure theory

Kähler manifolds, Kahler metrics, Einstein metrics, canonical metrics, special holonomy, Calabi-Yau, geometric elliptic and parabolic PDEs, Pluripotential Theory, variational approach, Monge-Ampère equation, area minimizing currents, semicalibrated currents, minimal surfaces

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

Simons Laufer Mathematical Sciences Institute (SLMath)

Many exciting breakthroughs in combinatorics involve innovative applications of techniques from a wide range of areas such as harmonic analysis, polynomial and linear algebraic methods, spectral graph theory, and representation theory. This workshop will present recent developments in this area and facilitate discussions of research problems.

extremal combinatorics, extremal graph theory, probabilistic combinatorics, discrete geometry, additive combinatorics, combinatorial geometry, incidence geometry, arithmetic progressions, Discrete analysis

Graphentheorie und Kombinatorik,    Algebra

Simons Laufer Mathematical Sciences Institute (SLMath)

In recent years techniques from harmonic analysis viz. projection theorems have found striking applications in finitary analysis on homogenous spaces. Such quantitative results have many potential applications to analytic number theory. This workshop will bring together researchers in these areas to further explore these connections.