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AIM Workshop: Symmetry-breaking of optimal shapes
17. Jun 2024 - 21. Jun 2024 • American Institute of Mathematics, Pasadena, California, Vereinigte Staaten
Veranstalter:
American Institute of Mathematics (AIM)
Zusammenfassung:
This workshop, sponsored by AIM and the NSF, investigates Shape Optimization problems for which symmetry-breaking is believed to occur: the energy functional is radially symmetric and yet its minimizer fails to enjoy full symmetry. Unlike in many other problems, the optimal shape is not the ball. The ball does solve many natural shape optimization problems for geometric and physical models, including the classical isoperimetric inequality and inequalities for capacity and the first eigenvalue of the Laplacian under Dirichlet, Robin or Neumann boundary conditions. Thus it becomes particularly fascinating to investigate problems where the ball is NOT the best, and to determine the optimal shape in those situations.
Themen:
The main topics for the workshop are: Topic 1: Examples where the ball is non-optimal. Topic 2: Techniques for identifying optimal shapes: shaking, tensorization, geometric flows, first or second order arguments to prove the optimal shape must be a polygon or polytope, free boundaries analysis. Topic 3: Notable conjectures including Polya's capacity problem, Neumann spectral problems, problems from convex geometry, isodiametric capacity maximizers, Alexandrov's conjecture for intrinsic diameter.
Eintrags-ID:
1598214
Verwandte Fachgebiete:
2
PCMI 2024 Research Topic: Motivic Homotopy
07. Jul 2024 - 27. Jul 2024 • Princeton, New Jersey, Vereinigte Staaten
Veranstalter:
Institute for Advanced Study, Princeton, New Jersey
Eintrags-ID:
1607252
3
The Mordell conjecture 100 years later
08. Jul 2024 - 12. Jul 2024 • MIT, Cambridge, MA, Vereinigte Staaten
Veranstalter:
Massachusetts Institute of Technology (MIT)
Eintrags-ID:
1540063
4
AIM Workshop: Scissors congruences, algebraic K-theory and Steinberg modules
08. Jul 2024 - 12. Jul 2024 • American Institute of Mathematics, Pasadena, California, Vereinigte Staaten
Veranstalter:
American Institute of Mathematics (AIM)
Zusammenfassung:
This workshop, sponsored by AIM and the NSF, will be devoted to connections between scissors congruence K-theory and Steinberg modules. Scissors congruence is the study of when objects such as polyhedra, manifolds, varieties, etc. are equivalent under decomposition into pieces. In the last decade, the introduction of K-theoretic constructions in the study of scissors congruence problems by Campbell and Zakharevich has seen exciting applications and opened new avenues of attack on this problem. Generalizing results for classical scissors congruence groups, Malkiewich showed that scissors congruence groups can be described as group homology with coefficients in Steinberg modules. Steinberg modules are certain representations that are relevant to the study of representations of linear groups, algebraic K-theory, and the cohomology of arithmetic groups. The goal of the workshop is to bring together researchers studying scissors congruence K-theory and as well as Steinberg modules, in order to explore interactions between the two fields.
Themen:
The main topics for the workshop are: Scissors congruence K-theory Resolutions of Steinberg modules (Co)algebraic structures of Steinberg modules and scissors congruence spectra Connections with more classical forms of K-theory
Eintrags-ID:
1598166
Verwandte Fachgebiete:
5
Introduction to the Theory of Algebraic Curves
08. Jul 2024 - 19. Jul 2024 • Berkeley, Kalifornien, Vereinigte Staaten
Veranstalter:
Simons Laufer Mathematical Sciences Institute (SLMath)
Zusammenfassung:
In the last few years, there have been extraordinary developments in many aspects of curve theory. Beginning with many examples in low genus, this summer school will introduce the participants to the background behind these developments in the following areas: moduli spaces of stable curves Brill–Noether theory the extrinsic geometry of the curves in projective space We will also include an introduction to some open problems at the forefront of these active areas.
Eintrags-ID:
1587553
6
Workshop on Definability, Decidability, and Computability
28. Jul 2024 - 02. Aug 2024 • Harvard University, Cambridge, MA, Vereinigte Staaten
7
Introductory Workshop: New Frontiers in Curvature
26. Aug 2024 - 30. Aug 2024 • Berkeley, Kalifornien, Vereinigte Staaten
Veranstalter:
Simons Laufer Mathematical Sciences Institute (SLMath)
Zusammenfassung:
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.
Themen:
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
Eintrags-ID:
1571252
8
RTD — Representation Theory Days (in honor of George Lusztig).
09. Nov 2024 - 11. Nov 2024 • Cambridge, Massachusetts, Vereinigte Staaten
Veranstalter:
Massachusetts Institute of Technology
Kontakt:
Email: kristims@mit.edu
Themen:
Representation, group, Lie algebra
Eintrags-ID:
1623051
9
Algebraic and Analytic Methods in Combinatorics
17. Mär 2025 - 21. Mär 2025 • Berkeley, Kalifornien, Vereinigte Staaten
Veranstalter:
Simons Laufer Mathematical Sciences Institute (SLMath)
Zusammenfassung:
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.
Themen:
extremal combinatorics, extremal graph theory, probabilistic combinatorics, discrete geometry, additive combinatorics, combinatorial geometry, incidence geometry, arithmetic progressions, Discrete analysis
Eintrags-ID:
1571399
Verwandte Fachgebiete:


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Stand vom 9. Juni 2024