Closed Geodesics and Intersection Numbers in Dynamics and Geometry
Explorez les techniques analytiques en dynamique et géométrie, en mettant l'accent sur les géodésiques fermées et les nombres d'intersection.
Scalar Curvature Rigidity in Manifolds
Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.
Regularising Manifolds Using Ricci Flow
Explore Ricci flow's applications in deforming and regularizing manifolds, including its use in identifying topology and proving geometric theorems.
A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Part 1
Explore Gromov's angle shrinking problem and its role in proving the dihedral extremality/rigidity conjecture through a new index theorem for manifolds with polyhedral boundary.
A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Lecture 2
Explore a stable algebraic version of Gromov's angle shrinking problem and its application to dihedral rigidity conjecture, focusing on Fredholm index computation.
Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension
Explore nonnegative Ricci curvature, nilpotency, and Hausdorff dimension in relation to universal covers, minimal representing loops, and asymptotic cones of manifolds.
Stability of Llarull's Theorem in All Dimensions
Explore stability of Llarull's theorem in all dimensions using spin geometry, with results in intrinsic flat and C^0-convergence outside small sets.
Spaces with Ricci Curvature Lower Bounds
Explore recent findings on spaces with nonnegative Ricci curvature, including singular set dimensions, fractal-like Weyl's laws, and nonproper Busemann functions in manifolds.
Ricci Curvature, Fundamental Group and the Milnor Conjecture - Part 2
Explore advanced concepts in topology and geometry, focusing on counterexamples to the Milnor conjecture and their construction using mapping class groups and asymptotic cones.
Index Theory and Applications to Scalar Curvature
Explore index theorems for compact manifolds with boundary and their applications to scalar curvature geometry, focusing on Dirac operators and boundary value problems.
Positive Mass Theorem and Positive Scalar Curvature with Singularities
Explore recent developments in positive mass theorem and scalar curvature, focusing on singular metrics and isolated conical singularities in mathematical physics.
Positive Scalar Curvature with Point Singularities
Explore topological construction of positive scalar curvature metrics with Euclidean point singularities, challenging Schoen's conjecture and geometric flow limitations.
A Tour of Monopole Floer Spectra - Part 1
Explore monopole Floer spectra theory with insights from Matthew Stoffregen of Michigan State University in this comprehensive mathematical lecture.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond
Explore countable subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions. Examine model theory applications.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 1
Explore countable subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions. Gain insights into model theory applications.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 2
Explore finitely generated subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 3
Explore finitely generated subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions.
Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 4
Explore finitely generated subgroups of homeomorphism groups, focusing on regularity in dimension one and potential generalizations to higher dimensions.
Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology
Explore algebraic presentations of 4- and 3-manifolds, focusing on categories of n-cobordisms and their relation to low-dimensional topology and combinatorial group theory.
Interactions Between Computers and Spectral Geometry
Explorez les avancées récentes en géométrie spectrale, mettant en lumière le rôle crucial de l'assistance informatique dans les découvertes et les défis futurs.
Scalar Curvature Rigidity of Polytopes
Explore Riemannian metrics and scalar curvature positivity in differential geometry. Delve into Gromov's comparison principle for polytopes and recent advancements in verifying his conjecture.