Maria Esteban - Spectral Results and Open Problems for Dirac-Coulomb Operators With Charge Distributions
Explore spectral results and open problems for Dirac-Coulomb operators with general charge distributions, focusing on self-adjoint extensions, eigenvalue characterizations, and electron stability conditions.
Multiscale Inverse Problem, from Schroedinger to Newton to Boltzmann - IPAM at UCLA
Explore multiscale inverse problems across quantum, classical, and statistical physics, connecting Schroedinger, Newton, and Boltzmann equations to reveal universal mathematical principles in diverse scientific domains.
On the 5-Vertex Model
Exploration of the 5-vertex model, a generalization of lozenge tiling, discussing free energy, surface tension, and probabilities. Insights into asymptotic algebraic combinatorics and lattice path models.
Building Manifolds from Error Correcting Codes - IPAM at UCLA
Explore the intersection of error correcting codes and manifold construction, delving into quantum error correction, topology, and complex mathematical concepts.
Landscape Function and Its Relations With Eigenvectors of a Schrödinger Operator
Explore landscape functions and their connections to Schrodinger operator eigenvectors, covering effective potentials, energy computations, and exponential decay in various contexts.
CoFTs for GLSMs
Explore enumerative invariants for GLSMs, generalizing Gromov-Witten and FJRW theories. Learn about virtual fundamental classes, Atiyah classes, and matrix factorizations in this context.
Homological Mirror Symmetry for Log Calabi-Yau Surfaces
Explore homological mirror symmetry for log Calabi-Yau surfaces, including construction of mirror Landau-Ginzburg models and connections to SYZ fibrations and previous research.
Is There Geometric Recursion for the Moduli Space of Toric Varieties?
Explore moduli space of quantum toric varieties, drawing parallels with geometric recursion. Delve into quantum lattices, tori, and CP1, examining group actions, calibration, and quantum geometric invariant theory.
A Proposal for Open DT Invariants
Explore open DT invariants, refined invariance, and boundary conditions in moduli spaces with Sergei Gukov. Delve into generating series, topological vertex, and infinite projects in this advanced mathematics lecture.
Homological Mirror Symmetry - Atsushi Takahashi, Osaka University
Exploring generalized root systems of type D, constructing Frobenius manifolds, and examining their potential applications in algebraic geometry and mathematical physics.
Homological Mirror Symmetry - Categorical Donaldson-Thomas Theory of C^3 and Beyond
Explore advanced concepts in Donaldson-Thomas theory, including categorifications, refinements, and applications to C^3 and beyond, with a focus on categorical invariants and correspondences.
Functional Inequalities and Improvements: Stability - Part 2
Explore functional inequalities, their optimal constants, and stability properties. Learn strategies for addressing these issues and recent developments in improved inequalities for non-optimizers.
Higgs Bundles on Elliptic Surfaces and Logarithmic Transformations
Explore Higgs bundles on elliptic surfaces and their transformations, examining vector bundles' importance in mathematics and the impact of logarithmic transformations on these structures.
From Turaev to Rokhlin via VOA Characters and Curve Counting
Explore q-series invariants of 3-manifolds, their properties, and connections to topology, vertex algebras, and enumerative problems. Gain insights into recent developments in this mathematical field.
Mirror Symmetry for Character Varieties and Field Theory by Sergey Galkin
Explore mirror symmetry for character varieties, using threespace mirrors to construct SU(2) character variety mirrors on Riemann surfaces, with applications in topological field theory and random walks.
Phases to Phases - An Invitation to Topological Phases of Many Particles by Vijay Shenoy
Explore topological phases in many-particle systems, covering quantum condensed matter physics, electronic phases, and the tenfold way. Gain insights into topological insulators and their potential technological applications.
Geometry and Topology in Quantum Mechanics - Mathematical Properties
Explore geometric phases in quantum mechanics, from foundational concepts to advanced topics like Berry phases and null phase curves, with applications in optics and condensed matter physics.
Introductory Lectures on First-Order Convex Optimization - Lecture 1
Explore first-order convex optimization, covering gradient descent, complexity, smoothness, and Nesterov's accelerated algorithm. Gain insights into theoretical foundations and practical applications in machine learning.
Modular Forms by Mahesh Kakde
Comprehensive exploration of modular forms, covering definitions, properties, and applications. Delves into Eisenstein series, theta functions, and related mathematical concepts for advanced learners in number theory.
Topology, Correlations and Superconductivity in Magic Angle Graphene - Lecture 2
Explore topology, correlations, and superconductivity in magic angle graphene. Dive into band structures, symmetries, and experimental findings. Gain insights on flat bands, Landau levels, and correlated electron paradigms.
Asymmetry in Dynamics
Explore symmetries in dynamical systems and progress on Smale's conjecture about generic smooth systems having only trivial symmetries. Delve into complex analytic, Hamiltonian, and smooth dynamics.