Manfred Denker: Toral Automorphisms Driven by Continued Fractions
Explore toral automorphisms driven by continued fractions, discussing Poisson limits, homoclinic groups, and Steiner's theorem in dynamical systems and number theory.
The Restriction Problem and the Polynomial Method - Lecture I
Explore Stein's restriction conjecture, the Kakeya conjecture, and the polynomial method in harmonic analysis. Learn about wave packet decomposition and its applications in studying hypersurface-supported functions.
Random Matrix Theory and its Applications - Lecture 2
Explore advanced concepts in random matrix theory, including linear algebra basics, operators, transformations, eigenvectors, and various matrix ensembles, with applications in statistical physics.
Spacetime, Quantum Mechanics and Positive Geometry by Nima Arkani Hamed
Explore the intersection of spacetime, quantum mechanics, and positive geometry, delving into scattering amplitudes, the mystery of time, and emergent phenomena in theoretical physics.
Quantum Field Theory as the Language of Physics by Nathan Seiberg
Explore quantum field theory's role as the universal language of physics, its applications, limitations, and potential reformulation in this insightful talk by Nathan Seiberg.
Convergence of Scattering Data and Non-Linear Fourier Transform - Part 1
Explore canonical systems, spectral problems, and Hilbert spaces of entire functions in this advanced mathematical analysis lecture on scattering data and non-linear Fourier transform.
Introduction to Contact Geometry by Dheeraj Kulkarni
Explore contact geometry fundamentals, including Frobenius theorem, contactomorphisms, and Gray stability theorem. Learn about symplectic structures and their relation to contact manifolds.
Quantum Toric Geometry II - Non-Commutative Geometric Invariant Theory
Explore quantum geometric invariant theory, extending classical GIT to non-commutative cases. Gain insights into cutting-edge research in quantum toric geometry.
Quantization of Moduli Spaces of Local Systems at Roots of Unity
Explore quantization of G-local system moduli spaces on decorated surfaces, discussing applications to quantum topology and quantum group representations.
Toward Homological Mirror Symmetry for Intrinsic Mirror Pairs
Exploration of homological mirror symmetry for intrinsic mirror pairs, comparing algebraic-geometric and symplectic approaches using quantum cohomology and VFC machinery.
Mirrors of Curves and Their Fukaya Categories II
Exploración avanzada de la simetría especular homológica para curvas, enfocándose en la geometría simpléctica de sus espejos y las categorías de Fukaya. Incluye discusiones sobre modelos de Landau-Ginzburg y geometría tropical.
Mirrors of Curves and Their Fukaya Categories I
Explores homological mirror symmetry for curves, focusing on symplectic geometry of mirrors and comparing coherent sheaves to Fukaya categories. Discusses Landau-Ginzburg models and fiberwise wrapped Fukaya categories.
Homological Mirror Symmetry - Coulomb Branches & Rozansky-Witten Theory Pt. II
Explore Rozansky-Witten theory and its connection to homological mirror symmetry, from basics to modern developments involving non-compact and infinite-dimensional target spaces.
Homological Mirror Symmetry - Coulomb Branches and Rozansky-Witten Theory
Explore Rozansky-Witten theory and its connection to homological mirror symmetry, from basics to modern developments involving non-compact spaces and ongoing research.
Homological Mirror Symmetry- Non-Holomorphic Deformations of Landau-Ginzburg Models
Explore non-holomorphic deformations of Landau-Ginzburg models, examining derived moduli spaces, Frobenius manifold structures, and Gromov-Witten invariants in symplectic geometry.
Homological Mirror Symmetry for Theta Divisors
Explore complex moduli of theta divisors in abelian varieties and their mirror Landau-Ginzburg models, focusing on global homological mirror symmetry across the entire moduli space.
Homological Mirror Symmetry - Yan Soibelman
Explore holomorphic Floer theory, wall-crossing structures, and their connections to Chern-Simons theory. Discover the interplay between complex symplectic geometry and quantum field theory in this advanced mathematics lecture.
Quivers, Curve Counting, and Fermionic Sums in Topology
Explore connections between quantum groups, vertex algebras, and quiver representations in topology. Discover how fermionic forms link these areas, shedding new light on enumerative geometry and curve counting.
On the P=W Conjecture I
Exploration of the P=W conjecture for character varieties, its mirror version in Fano mirror symmetry, and applications to Hodge theory of Landau-Ginzburg models. Discusses recent developments and ongoing research in the field.
Blow Up Formulae and Invariants I - Blow-Up Formula for Quantum Cohomology
Exploration of Gromov-Witten invariants in blown up complex algebraic varieties, proposing a formula and proof approach via equivariant localization. Insights into quantum cohomology and algebraic geometry.
Blow Up Formulae and Invariants II - Dimension Theory
Explore numerical invariants in meromorphic connections, their relation to singularity theory, and applications to non-rationality criteria for Fano varieties.