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Simons Laufer Mathematical Sciences Institute (SLMath)

The Introductory Workshop will feature lecture series devoted to some recent breakthrough results in commutative algebra, and to new developments in core areas of the field. It will also highlight links to other areas such as arithmetic geometry, representation theory, noncommutative geometry, and singularity theory.

Commutative rings, computational commutative algebra, D-modules, free resolutions, Gröbner deformations, Homological conjectures, Lech's conjecture, maximal Cohen-Macaulay modules, McKay correspondence, mixed characteristic, multiplicities, perfectoid spaces, prismatic cohomology, symbolic powers, syzygies, Tight closure theory

Mathematical Sciences Research Institute (MSRI)

This introductory workshop will consist of a combination of minicourses addressing core topics in noncommutative algebraic geometry and research lectures describing recent developments in the field. The workshop will focus on subjects connected to algebraic geometry, category theory, and mirror symmetry such as categorical and noncommutative resolutions, deformation theory, derived categories in algebraic geometry, derived algebraic geometry, infinity categories, and enumerative geometry.

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

Analysis,    Quantenmechanik und Quantentechnologie

Simons Laufer Mathematical Sciences Institute (SLMath)

This workshop will include introductory lectures on each of the four main topics of the program: geometric flows, geometric problems in mathematical relativity, global Riemannian geometry, and minimal submanifolds. The workshop will also have semi-expository lectures on recent advances and breakthroughs involving interactions between the four main topics. This will set the stage and provide important context for the semester-long program itself.

mean curvature flow, Ricci flow, fully nonlinear flows, general relativity, mass, Ricci curvature, scalar curvature, sectional curvature, symmetry, Riemannian geometry, group actions, minimal surfaces, stability and index

Geometrie und Topologie,    Algebra

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,    Analysis

Simons Laufer Mathematical Sciences Institute (SLMath)

Networks, graph driven algorithms, and dynamics on graphs such as epidemics, random walks and centrality measures all play a major role, both in our daily lives as well as many scientific and engineering disciplines. This introductory workshop will bring together experts and junior researchers in combinatorics, probability, and statistics to share a broad vision of major challenges and objectives, with a primary focus on models of random graphs and their limits, network inference, dynamic processes on networks and algorithms and optimization on random structures.

Network models and random graphs, statistcal learning and network inference, counting and sampling discrete structures, dynamics on networks, probabilistic analysis of network algorithms

Simons Laufer Mathematical Sciences Institute (SLMath)

This workshop will feature leading experts in several major areas of graph theory, including extremal, probabilistic and structural aspects of the field. Introductory lectures will form an important part of the program, providing background and motivation, and aimed at a general mathematical audience. Complementing these, research talks will share exciting recent developments in graph theory.

extremal graph theory, random graphs, probabilistic methods, structural graph theory, Ramsey theory