The Hamilton-Jacobi Equation: Past and Present
Explore the historical and contemporary significance of the Hamilton-Jacobi equation in mathematics with insights from Ryan Hynd of the University of Pennsylvania.
From Newton to Boltzmann - Fluctuations and Large Deviations in Hard Sphere Gas Dynamics
Explore macroscopic fluctuations in hard sphere gases, including deviations from the Boltzmann equation, central limit theorem, and large deviation bounds in the Boltzmann-Grad limit.
Tropical Geometry and Shallow Water Waves
Explore the fascinating intersection of tropical geometry and shallow water waves in this engaging lecture by Harvard mathematician Lauren Kiyomi Williams.
A Local Torelli Theorem for Log Symplectic Manifolds
Explore log symplectic manifolds, their moduli space, and local Torelli theorem. Discover new components in Pn's moduli space of log symplectic structures.
The Circle and Projective Homogeneous Coordinates in Universal Hyperbolic Geometry - Lecture 7b
Explores projective geometry as the foundation of universal hyperbolic geometry, focusing on the circle in projective homogeneous coordinates and its significance in mathematics and physics.
Relativistic Dot Products and Complex Numbers in Linear Algebra - Part 2
Exploring triality of dot products and associated complex numbers in chromogeometry, organized within 2x2 matrices. Delves into interactions between three geometries.
Duality, Polarity and Projective Linear Algebra - Differential Geometry Lecture 11
Explores projective geometry, quadratic forms, and pole-polar duality in relation to the unit circle. Connects these concepts to Lorentz/Einstein/Minkowski geometry and Apollonius' work.
The Rotation Problem and Hamilton's Discovery of Quaternions - Part 4
Practical implementation of quaternions for 3D rotations, focusing on half-turns and vector trigonometry. Explores quaternion multiplication and its geometric interpretation for rotations.
Central Polynumber Algebra and Baby Weyl Character Formula - Math Foundations 236
Explores central polynumber algebra and Weyl character formula, focusing on SU(2) and SU(3) representations. Connects to particle physics and quaternions, emphasizing polynumbers over complex exponentials.
Atoms, Electrons and Birational Invariants in Hodge Structures
Explore new A,B Hodge structures and their non-rationality applications in algebraic geometry, bridging concepts from physics to advanced mathematical theory.
Introduction to Cluster Algebras - Part 1
Explore cluster algebras, quivers, and mutation through examples, with a focus on the Grassmannian. Gain insights into this fundamental algebraic structure and its applications.
Introduction to Discrete Integrable Systems - Part 2
Explore fundamental concepts of discrete integrable systems in differential geometry, focusing on applications in statistical mechanics and geometric structures.
Dimer Models and Random Tilings - Part 1
Explore dimer models and random tilings with Cédric Boutillier. Learn about Kasteleyn's theory, combinatorial correspondences, and asymptotic methods for studying perfect matchings on lattices.
Fourier Analysis of Equivariant Quantum Cohomology II - 1-27-2024
Explore advanced concepts in Fourier analysis and equivariant quantum cohomology, building on previous research in homological mirror symmetry and mathematical physics.
Homological Mirror Symmetry - Recent Developments and Future Directions
Survey of recent developments in Homological Mirror Symmetry, exploring new results and future directions. Part of a conference honoring Jeffrey Fuqua's contributions to mathematics.
On Kissing Number of Hyperbolic Manifolds
Explore hyperbolic manifolds' kissing numbers with Plinio G. P. Murillo. Delve into Zariski dense subgroups, number theory, and geometric applications in this theoretical sciences lecture.
Introduction to Bruhat-Tits Theory - Lecture 2
Explore Bruhat-Tits theory in this advanced mathematics lecture, focusing on Zariski dense subgroups and their applications in algebraic geometry and number theory.
Things We Can Learn by Looking at Random Manifolds
Explore insights gained from studying random manifolds, covering applications in geometry, topology, and mathematical physics. Uncover connections between diverse mathematical fields.
Random Walks on Group Extensions
Explore random walks on group extensions in this advanced mathematics lecture, covering Zariski dense subgroups and their applications in algebraic geometry and number theory.
The Existence Problem of Compact Quotients of Pseudo-Riemannian Homogeneous Spaces
Explore the existence of compact quotients in pseudo-Riemannian homogeneous spaces, delving into advanced geometric concepts and their applications in mathematical physics and topology.
Dimers and M-curves: Limit Shapes from Riemann Surfaces
Explore dimer models, M-curves, and limit shapes through algebraic geometry, integrating Riemann surfaces and Schottky uniformization. Gain insights into statistical mechanics and discrete geometry.