Cohomological Hall Algebra of Cyclic Quivers and Integral Form of Affine Yangians
Explore the intricate world of Hall algebra-type constructions and their applications in a lecture by Shivang Jindal from the University of Edinburgh. Delve into the complexities of studying algebras related to the moduli space of representations of the…
Birkhoff Sums as Distributions in Dynamical Systems
Explore Birkhoff sums as distributions in dynamical systems, examining regularity results for hyperbolic systems and applications to deformation theory in one-dimensional dynamical systems.
Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 4
Delve into spectrum rigidity and joint integrability for Anosov systems on tori. Explore topological conjugacy of non-invertible Anosov maps on 2-torus and its implications for smooth conjugacy along stable foliations.
Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 3
Delve into spectrum rigidity and joint integrability for Anosov systems on tori. Explore the equivalence between geometric rigidity and dynamical spectral rigidity in Anosov diffeomorphisms, focusing on irreducible cases with split stable bundles.
Classification of Combinatorial Surfaces - Algebraic Topology - NJ Wildberger
Introduction to the classification of connected compact combinatorial surfaces in algebraic topology, covering key concepts like polygons, vertices, traversing, Euler number, and orientability.
Two-Dimensional Objects - The Torus and Genus - Algebraic Topology
Explore surfaces like cylinders and tori, understanding their properties and connections to complex function theory. Learn about genus and how planes cover different surfaces.
Symmetric and Symmetrized Topological Complexity of the Torus
Explore symmetric and symmetrized topological complexity of the torus, completing the description for closed surfaces using obstruction theory and explicit resolution of integers over full braid group.
Equidistribution of Linear Random Walks on the Torus
Explores quantitative equidistribution for linear random walks on the torus, presenting recent progress relaxing the proximality assumption in Bourgain et al.'s work. Joint research with Nicolas de Saxcé.
Fundamental Group of Surfaces - Multiplication and Properties
Explores fundamental group of surfaces, proving loop multiplication forms a group. Covers torus and projective plane, with examples and a problem on describing fundamental groups.
Delta Complexes, Betti Numbers, and Torsion in Algebraic Topology
Explore homology groups of torus and projective plane using delta-complexes. Learn about Betti numbers and torsion in algebraic topology, with practical computations and insights into fundamental concepts.
Covering Spaces and Fundamental Groups - Algebraic Topology Lecture 28
Exploring covering spaces and fundamental groups, focusing on torus examples and key lemmas to understand relationships between covering spaces and base spaces.
Higher Rank Voronoi Decompositions and Metric Degenerations of Tori
Explore higher rank Voronoi decompositions and their applications in studying asymptotic geometry of Riemann surfaces and moduli spaces.
Strict Ergodicity and Transformation of the Torus
Explore strict ergodicity and torus transformations in advanced mathematics, focusing on dynamic geometry concepts and their applications.
KAM Tori for the Nonlinear Klein-Gordon Equation in the Non-Relativistic Limit
Explore effective theories in classical and quantum particle systems, focusing on KAM tori for the Nonlinear Klein Gordon equation in the non-relativistic limit.
Dirac Eigenvalue Optimization and Harmonic Maps
Explore Dirac eigenvalue optimization, comparing it to Laplace eigenvalues and examining critical metrics' correspondence with harmonic maps to complex projective spaces.
Macdonald Dualities in Genus One and Two
Explore Macdonald/Koornwinder polynomial dualities, from spherical Double Affine Hecke Algebra on a torus to genus two Macdonald theory, with Philippe Di Francesco.
Isomonodromy-CFT Correspondence on a Torus and Modular Transformation of c=1 Toric Conformal Blocks
Explore isomonodromy-CFT correspondence on tori and modular transformations of c=1 toric conformal blocks, delving into advanced concepts in mathematical physics.
The Bizarre Shape of the Universe - Exploring Topology and Geometry in Cosmology
Explore the universe's shape through topology, geometry, and recent research. Delve into flat geometries, 2D and 3D torus models, and the search for closed loops in space.
Magnetic Bundle in the Multilayer Model of the Fractional Quantum Hall Effect on a Torus
Explore the magnetic bundle in multilayer models of fractional quantum Hall effect on a torus, delving into advanced concepts in quantum physics and topology.