# Meetings

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Today

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Future

There's no meetings for that time

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Past

March 3, 2017

noon - 2 p.m.

March 9, 2017

noon - 2 p.m.

March 16, 2017

noon - 2 p.m.

March 30, 2017

noon - 2 p.m.

April 20, 2017

noon - 2 p.m.

April 27, 2017

noon - 2 p.m.

May 11, 2017

noon - 2 p.m.

May 18, 2017

noon - 2 p.m.

May 25, 2017

noon - 2 p.m.

June 1, 2017

noon - 2 p.m.

March 7, 2018

10 a.m. - noon

March 14, 2018

10 a.m. - noon

March 23, 2018

10 a.m. - noon

Part 3. Transmission lines

April 13, 2018

noon - 2 p.m.

Affine spaces as a manifold

April 17, 2018

noon - 2 p.m.

Pre-Einstein models of spacetime

April 18, 2018

10 a.m. - noon

April 20, 2018

10 a.m. - noon

April 20, 2018

noon - 2 p.m.

Tensors, pseudotensors and densities

April 24, 2018

noon - 2 p.m.

Tensor fields on manifolds

April 27, 2018

10 a.m. - noon

April 27, 2018

noon - 2 p.m.

Connections, curvature and torsion

April 27, 2018

noon - 2 p.m.

May 11, 2018

10 a.m. - noon

May 11, 2018

noon - 2 p.m.

Newton's spacetime part II

May 15, 2018

noon - 2 p.m.

May 18, 2018

10 a.m. - noon

May 22, 2018

noon - 2 p.m.

Linearization of Einstein's equations

May 25, 2018

10 a.m. - noon

Part 9. Optics without lenses

May 25, 2018

noon - 2 p.m.

Gravitational waves in linearized Einstein's gravity

May 29, 2018

noon - 2 p.m.

Symmetries and the de Siter spacetime

June 1, 2018

noon - 2 p.m.

Schwarzschild solution and his spherically symmetric friends

June 5, 2018

noon - 2 p.m.

Basic physics in Schwarzschild spacetime; Kruskal coordinates

June 8, 2018

noon - 2 p.m.

Geodesics in Schwarzschild spacetime; deflection of light

June 26, 2018

noon - 2 p.m.

June 29, 2018

noon - 2 p.m.

Oct. 2, 2018

1 p.m. - 3 p.m.

Oct. 9, 2018

1 p.m. - 3 p.m.

Oct. 16, 2018

1 p.m. - 3 p.m.

Oct. 23, 2018

1 p.m. - 3 p.m.

Oct. 30, 2018

1 p.m. - 3 p.m.

Nov. 6, 2018

1 p.m. - 3 p.m.

Nov. 13, 2018

1 p.m. - 3 p.m.

Nov. 20, 2018

1 p.m. - 3 p.m.

Nov. 27, 2018

1 p.m. - 3 p.m.

Dec. 4, 2018

1 p.m. - 3 p.m.

Dec. 11, 2018

1 p.m. - 3 p.m.

Feb. 4, 2019

1 p.m. - 3 p.m.

Part 1, from classical to quantum mechanics

Feb. 11, 2019

1 p.m. - 3 p.m.

Part 2, discussion of the Schroedinger equation

Feb. 18, 2019

1 p.m. - 3 p.m.

Part 3, states, operators and measurements

Feb. 25, 2019

1 p.m. - 3 p.m.

Part 4, projective measurement in any base

March 4, 2019

1 p.m. - 3 p.m.

Part 5: Bloch sphere and Qbit states

March 11, 2019

1 p.m. - 3 p.m.

March 18, 2019

1 p.m. - 3 p.m.

Part 7: relationship between SU(2) and SO(3) groups

March 25, 2019

1 p.m. - 3 p.m.

April 1, 2019

1 p.m. - 3 p.m.

April 8, 2019

1 p.m. - 3 p.m.

Part 10, complex quantum gates

April 15, 2019

1 p.m. - 3 p.m.

Part 11, Grover's Algorithm 1

April 22, 2019

1 p.m. - 3 p.m.

Part 12, Grover's Algorithm 2

Oct. 2, 2019

10 a.m. - noon

Time and space, Euclidean geometry

Oct. 8, 2019

10 a.m. - noon

Lecture 1. - An introduction

Oct. 9, 2019

10 a.m. - noon

The structure of space-time according to Newton; The string equation, i.e. the wave equation in two-dimensional space-time; Mathematical properties of the wave equation in two dimensions

Oct. 15, 2019

10 a.m. - noon

Lecture 2. - Basic parameters of accretion flow

Oct. 16, 2019

10 a.m. - noon

Initial-boundary problem for the wave equation (string equation); Hyperbolicity and ellipticity of partial differential equations.

Oct. 22, 2019

10 a.m. - noon

Lecture 3. - Examples of accretion flow in astrophysical objects

Oct. 23, 2019

10 a.m. - noon

Fourier transform and its applications; Euclidean rotation group; Lorentz transformations as symmetries of the wave equation; Equation of sound propagation

Oct. 29, 2019

10 a.m. - noon

Lecture 4. - Spherical accretion

Oct. 30, 2019

10 a.m. - noon

Sound propagation equation II. Continuity equation; Initial problem for the wave equation in three spatial dimensions

Nov. 5, 2019

10 a.m. - noon

Lecture 5. - Motion of a test particle in the gravitational field of a black hole

Nov. 6, 2019

10 a.m. - noon

Exponential function and trigonometric functions: key facts

Nov. 12, 2019

10 a.m. - noon

Lecture 6. - Classical accretion disks

Nov. 13, 2019

10 a.m. - noon

The Michelson-Morley experiment and the metric structure of space-time; Lorentz group and its effect on the electromagnetic field

Nov. 19, 2019

10 a.m. - noon

Lecture 7. - Radiation transfer

Nov. 20, 2019

10 a.m. - noon

Maxwell's equations and their symmetries: Lorentz transformations; Clock synchronization. Time measurement and distance measurement

Nov. 26, 2019

10 a.m. - noon

Lecture 8. - Compton process and two-phase medium of accretion flow

Nov. 27, 2019

10 a.m. - noon

Electromagnetic field. How to describe a vector in a curvilinear system; A short excursion into differential geometry: vectors and covectors; Tensors and differential forms. Geometric description of t

Dec. 3, 2019

10 a.m. - noon

Lecture 9. - Time evolution of accretion disks, stationarity, stability

Dec. 4, 2019

10 a.m. - noon

Geometric digression: external differential. Maxwell's first pair of equations; Lorentz transformation of the electromagnetic field; Equations of motion of a charged particle in an electromagnetic fie

Dec. 10, 2019

10 a.m. - noon

Lecture 10. - Mathematical description of variability

Dec. 11, 2019

10 a.m. - noon

Four-shoot. Relativistic law of conservation of energy: E=mc^2

Dec. 17, 2019

10 a.m. - noon

Lecture 11. - Magneto-hydrodynamic simulations of accretion flows

Jan. 7, 2020

10 a.m. - noon

Lecture 12. - Gamma-ray bursts, jet formation, and unsolved problems

Jan. 14, 2020

10 a.m. - noon

Lecture 13. - Applications: main sequence stars, white dwarfs

Jan. 21, 2020

10 a.m. - noon

Lecture 14. - Applications: neutron stars and galactic black holes

Jan. 28, 2020

10 a.m. - noon

Lecture 15. - Applications: active galactic nuclei

Feb. 24, 2020

noon - 2 p.m.

Lecture 1. - Preliminaries: well-posedness, linearity and superposition principle

March 2, 2020

8 a.m. - 10 a.m.

What is gravity?; First law of dynamics: global and local inertial frames

March 2, 2020

noon - 2 p.m.

Lecture 2. - Quasilinear PDEs and the method of characteristics

March 3, 2020

8 a.m. - 10 a.m.

March 9, 2020

8 a.m. - 10 a.m.

What is a local frame of reference; Description of the reference system using connection coefficients

March 9, 2020

noon - 2 p.m.

Lecture 3. - How to solve PDE a(x,y)u_x+b(x,y)u_y=0, and characteristic curves

March 10, 2020

8 a.m. - 10 a.m.

March 16, 2020

8 a.m. - 10 a.m.

Equation of a line in a spherical coordinate system; Curvature tensor

March 16, 2020

noon - 2 p.m.

Lecture 4. - Method of characteristics: the main theorem, and what can go wrong

March 23, 2020

8 a.m. - 10 a.m.

Riemann tensor. Principles of "least action"; Variational principles in field theory and control theory

March 23, 2020

noon - 2 p.m.

Lecture 5. - Second order linear PDEs in two variables

March 30, 2020

8 a.m. - 10 a.m.

About the fact that in dynamic field theories it is not allowed to determine a priori the value of the field at the boundary; Variational formulation of electrodynamics. Covariant derivative I.

March 30, 2020

noon - 2 p.m.

Lecture 6. - The wave equation in one spatial dimension

March 31, 2020

8 a.m. - 10 a.m.

April 6, 2020

8 a.m. - 10 a.m.

Covariant derivative II. Examples and applications.; Levi-Civity connection or "metric connection"

April 6, 2020

noon - 2 p.m.

Lecture 7. - D'Alambert formula for the wave equation

April 7, 2020

8 a.m. - 10 a.m.

April 13, 2020

8 a.m. - 10 a.m.

The geodesic is the great circle of a metric connection; Decomposition of the curvature tensor into irreducible components

April 13, 2020

noon - 2 p.m.

Lecture 8. - The domain of dependence and the region of influence for 2D wave equation

April 20, 2020

8 a.m. - 10 a.m.

Derivation of the dynamics of the gravitational field from the variational principle; Metrics enter the arena

April 20, 2020

noon - 2 p.m.

Lecture 9. - Separation of variables. The heat equation in one spatial dimension part 1.

April 21, 2020

8 a.m. - 10 a.m.

April 27, 2020

8 a.m. - 10 a.m.

Einstein's vacuum equations. Cosmological constant; Einstein's equations in the presence of matter

April 27, 2020

noon - 2 p.m.

Lecture 10. - Separation of variables. The heat equation in one spatial dimension part 2.

April 28, 2020

8 a.m. - 10 a.m.

May 4, 2020

8 a.m. - 10 a.m.

Properties of the metric Riemann tensor; Derivation of gravitational field equations using the Hilbert method

May 4, 2020

noon - 2 p.m.

Lecture 11. - Separation of variables for the wave equation

May 11, 2020

8 a.m. - 10 a.m.

Three different ways of deriving Einstein's equations from the variational principle; Three variation rules - completion. Introduction to the linear theory of gravity

May 11, 2020

noon - 2 p.m.

Lecture 12. - Separation of variables: the nonhomogeneous case

May 12, 2020

8 a.m. - 10 a.m.

May 18, 2020

8 a.m. - 10 a.m.

A linear approximation of Einstein's theory of gravity; Spherically symmetric configurations of the gravitational field

May 18, 2020

noon - 2 p.m.

Lecture 13. - Uniqueness of solutions to the wave equation and the heat equation

May 19, 2020

8 a.m. - 10 a.m.

May 25, 2020

8 a.m. - 10 a.m.

External curvature. Theorem Gauss-Codazzi

May 25, 2020

noon - 2 p.m.

Lecture 14. - Sturm-Liouville systems. Part 1.

May 26, 2020

8 a.m. - 10 a.m.

June 1, 2020

8 a.m. - 10 a.m.

Schwarzschild metric; Surprising properties of Schwarzschild's solution. Black holes

June 1, 2020

noon - 2 p.m.

Lecture 15A. - Sturm-Liouville systems. Part 2.

June 8, 2020

8 a.m. - 10 a.m.

Outskirts: gravitational waves, cosmological models, quantization; Outskirts: graviton, unification, black matter

June 8, 2020

noon - 2 p.m.

Lecture 15B. - Sturm-Liouville systems. Part 3.

June 15, 2020

noon - 2 p.m.

Lecture 16. - Sturm-Liouville systems. Part 4.

June 22, 2020

noon - 2 p.m.

Lecture 17. - Laplace equation. Part 1. Harmonic polynomials in 2 dimensions.

June 29, 2020

noon - 2 p.m.

Lecture 18. - Laplace and Poisson equations. Preliminaries.

July 6, 2020

noon - 2 p.m.

Lecture 19. - Laplace equation. Part 3. Separation of variables in circular domains.

Feb. 23, 2021

noon - 2 p.m.

Affine space; How to describe a vector in curvilinear coordinates

March 2, 2021

noon - 2 p.m.

Vectors, covectors and transport operators; Tangential beam. Vector field commutator

March 9, 2021

noon - 2 p.m.

Transport operators in coordinates. A vector tangent to the curve; Dynamic systems. One-parameter, local transformation group

March 16, 2021

noon - 2 p.m.

Lie derivative. Vector field commutator

March 23, 2021

noon - 2 p.m.

Commutativity of single-parameter groups and the commutator of vector fields; Distributions, foliations, formations Frobenius on integrability

March 30, 2021

noon - 2 p.m.

Integrable distributions. Curve orientation. Vector field integration; Force field potential. Differential forms and their external product.

April 6, 2021

noon - 2 p.m.

Operations on differential forms; Integration of differential forms. External differential.

April 13, 2021

noon - 2 p.m.

Lie derivative of the differential form. Sundries with border; Stokes' theorem

April 20, 2021

noon - 2 p.m.

Once again, theorem Stokes. Closed forms and complete forms; Poincare's lemma. Cohomologies. Dual representation of the differential form.

April 27, 2021

noon - 2 p.m.

Once again, dual representation. Riemann geometry; Metric tensor. Isomorphism between vectors and covectors. Scalar product of differential forms.

May 4, 2021

noon - 2 p.m.

Form of volume. Surface area: oriented, non-oriented, zero; Curve length. Dualism ("Star") by Hodge

May 11, 2021

noon - 2 p.m.

Once again about Hodge's duality ("star"). Laplace-Beltrami operator; A simple formula for the Laplacian in arbitrary curvilinear coordinates

May 18, 2021

noon - 2 p.m.

Vector analysis; Continuity equation. Tensors. Spherical functions.

May 25, 2021

noon - 2 p.m.

Local reference frames. Gravitational field; Curvature theory. Covariant derivative of tensor fields. Metric connection

Oct. 7, 2021

11 a.m. - 1 p.m.

Oct. 14, 2021

11 a.m. - 1 p.m.

Oct. 21, 2021

11 a.m. - 1 p.m.

Oct. 28, 2021

11 a.m. - 1 p.m.

Nov. 4, 2021

11 a.m. - 1 p.m.

Nov. 18, 2021

11 a.m. - 1 p.m.

Nov. 25, 2021

11 a.m. - 1 p.m.

Dec. 2, 2021

11 a.m. - 1 p.m.

Dec. 9, 2021

11 a.m. - 1 p.m.

Dec. 16, 2021

11 a.m. - 1 p.m.

Jan. 13, 2022

11 a.m. - 1 p.m.

Jan. 26, 2022

11 a.m. - 1 p.m.

Jan. 27, 2022

11 a.m. - 1 p.m.

Feb. 3, 2022

11 a.m. - 1 p.m.

Feb. 7, 2023

4 p.m. - 6 p.m.

1. Affine and Euclidean Geometry: The modern approach

Feb. 14, 2023

4 p.m. - 6 p.m.

2. Aristotle versus Galilei-Newton. Different visions of space an time

Feb. 21, 2023

4 p.m. - 6 p.m.

3. Cartesian (flat), spherical and Lobachewskian geometries. Wave equation

Feb. 28, 2023

4 p.m. - 6 p.m.

4. Propagation of sound: 3D wave equation.Lorentz's transformations: symmetries of the wave equation

March 7, 2023

4 p.m. - 6 p.m.

5. Lorentz transformation continued. Initial value problem. Huyghens principle

March 14, 2023

4 p.m. - 6 p.m.

6. Wave equation in 4D spacetime

March 21, 2023

4 p.m. - 6 p.m.

7. Initial value problem. Strong Huygens principle. Maxwell equations