Lectures related to Volume form

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Dynamics of Steady Euler Flows: New Results

Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.

Essential Coexistence Phenomenon in Hamiltonian Dynamics

By Yakov Pesin delves into the essential coexistence phenomenon in Hamiltonian dynamics, exploring types I and II and providing examples and proofs.

Differential Forms: Basics and Applications

Introduces the concept of differential forms and their applications in n-dimensional manifolds, including the Levi-Civita tensor and volume form.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Linear Request Problem: Rigorous Results

Delves into the linear request problem, infinitesimal perturbations, transport plans, and the main theorem from 2018.

Cramer's Rule and Volume

Covers Cramer's Rule, matrix inverse, determinants, and volume in linear algebra.

Change of Variables Formula

Explores the change of variables formula for integration using different coordinate systems to simplify calculations.

Symplectic Geometry

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

Volumes of Solids: Calculating Volumes of Solid Bodies

Covers the calculation of volumes of solid bodies using slices and integrating the cross-sectional area.

Kinetic Theory: Distribution Function Evolution

Explores the evolution of the distribution function describing particles in phase space.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Calculating Center of Gravity in Analytical Geometry

Covers the calculation of the center of gravity in analytical geometry.

Electromagnetic Waves: Energy Density and Poynting Vector

Explains the energy density and Poynting vector in electromagnetic waves.

Compact Manifolds Classification

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Weil Representation and Heis Operators

Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.

Deformable Bodies: Stress Tensors and Divergence Theorem

Explores stress tensors and the divergence theorem in deformable bodies through examples and demonstrations.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Turbulence: Numerical Flow Simulation

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.