Curve Counting, Geometric Representation Theory, and Quantum Integrable Systems - Lecture 2
Delve into advanced mathematical concepts exploring curve counting, geometric representation theory, and quantum integrable systems with Professor Andrei Okounkov's expert analysis and insights.
Stringing Madhava's Pi - A Quantum Field Theory Perspective
Delve into quantum field theory's connection to Madhava's historical calculation of pi, exploring mathematical principles and their modern theoretical physics applications.
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.
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.
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.
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.
The Positive Grassmannian, the Amplituhedron, and Cluster Algebras
Explore the positive Grassmannian and amplituhedron, delving into their combinatorial structures and connections to physics, integrable systems, and scattering amplitudes using oriented matroids, tropical geometry, and cluster algebras.
Weingarten Calculus and Its Applications
Explore Weingarten calculus and its applications in compact groups, quantum probability, and random matrix theory, with insights on theoretical properties and recent developments.
Allen Knutson- Schubert Calculus and Quiver Varieties
Explore Schubert calculus, quiver varieties, and their connections through puzzle rules, Yang-Baxter equations, and representation theory in this advanced mathematics lecture.
Phase-Field Models for Motion by Mean Curvature - Lecture 2
Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.
Regularity of Free Boundaries in Obstacle Problems - Lecture III
Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.
Virtual Invariants of Moduli Spaces of Sheaves on Surfaces and Vafa-Witten Invariants I
Explore virtual invariants of moduli spaces, Vafa-Witten invariants, and related mathematical concepts in this advanced seminar on algebraic geometry and theoretical physics.
Holomorphic Floer Theory, Quantum Wave Functions and Resurgence
Explore holomorphic Floer theory, exponential integrals, and resurgence in algebraic geometry. Discover connections to quantum wave functions and infinite-dimensional applications.
Topological Recursion, Virasoro-W-Algebra Constraints, and Kontsevich-Soibelman
Explore Virasoro and W-algebra constraints in topological recursion, Kontsevich-Soibelman operators, and their connection to Conformal Field Theory in this advanced mathematics lecture.
Functoriality in Gromov Witten Theory
Explore advanced concepts in Gromov-Witten theory, including quantum Lefschetz, quantum Leray-Hirsch, and functoriality in birational transformations, presented by Yuan-Pin Lee from the University of Utah.
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.
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 - 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.