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June 14, 2024
11:30 a.m. - 1 p.m.
End of CLUES 2024
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CLUES 2024
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June 12, 2024
noon - 2 p.m.
Test CLUES
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CLUES 2024
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June 11, 2024
4 p.m. - 6 p.m.
Session 2.4
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CLUES 2024
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June 11, 2024
2 p.m. - 3:30 p.m.
Session 2.3
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CLUES 2024
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June 11, 2024
11:30 a.m. - 1 p.m.
Session 2.2
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CLUES 2024
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June 11, 2024
9:30 a.m. - 11 a.m.
Session 2.1
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June 10, 2024
4 p.m. - 6 p.m.
Session 1.3
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June 10, 2024
2 p.m. - 3:30 p.m.
Session 1.2
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June 10, 2024
10:30 a.m. - 1 p.m.
Session 1.1
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Past

March 3, 2017
noon - 2 p.m.
Lecture 1.
March 9, 2017
noon - 2 p.m.
Lecture 2.
March 16, 2017
noon - 2 p.m.
Lecture 3.
March 30, 2017
noon - 2 p.m.
Lecture 4.
April 20, 2017
noon - 2 p.m.
Lecture 5.
April 27, 2017
noon - 2 p.m.
Lecture 6.
May 11, 2017
noon - 2 p.m.
Lecture 7.
May 18, 2017
noon - 2 p.m.
Lecture 8.
May 25, 2017
noon - 2 p.m.
Lecture 9.
June 1, 2017
noon - 2 p.m.
Lecture 10.
March 7, 2018
10 a.m. - noon
Part 1.
March 14, 2018
10 a.m. - noon
Part 2.
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
Part 4. Waveguides
April 20, 2018
10 a.m. - noon
Part 5. Green functions
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
Part 6. Antennas
April 27, 2018
noon - 2 p.m.
Connections, curvature and torsion
April 27, 2018
noon - 2 p.m.
Newton's spacetime
May 11, 2018
10 a.m. - noon
Part 7. Optics and Light
May 11, 2018
noon - 2 p.m.
Newton's spacetime part II
May 15, 2018
noon - 2 p.m.
Einstein's spacetimes
May 18, 2018
10 a.m. - noon
Part 8. Optics
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.
Spherical stars
June 29, 2018
noon - 2 p.m.
Cosmological models
Oct. 2, 2018
1 p.m. - 3 p.m.
Lecture 1.
Oct. 9, 2018
1 p.m. - 3 p.m.
Lecture 2.
Oct. 16, 2018
1 p.m. - 3 p.m.
Lecture 3.
Oct. 23, 2018
1 p.m. - 3 p.m.
Lecture 4.
Oct. 30, 2018
1 p.m. - 3 p.m.
Lecture 5.
Nov. 6, 2018
1 p.m. - 3 p.m.
Lecture 6.
Nov. 13, 2018
1 p.m. - 3 p.m.
Lecture 7.
Nov. 20, 2018
1 p.m. - 3 p.m.
Lecture 8.
Nov. 27, 2018
1 p.m. - 3 p.m.
Lecture 9.
Dec. 4, 2018
1 p.m. - 3 p.m.
Lecture 10.
Dec. 11, 2018
1 p.m. - 3 p.m.
Lecture 11.
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.
Part 6, Pauli matrices
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.
Part 8, entangled states
April 1, 2019
1 p.m. - 3 p.m.
Part 9, quantum gates
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
Piotr Waluk
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.
Lecture 1.
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.
Lecture 2.
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.
Lecture 3.
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.
Lecture 4.
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.
Lecture 5.
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.
Lecture 6.
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.
Lecture 7.
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.
Lecture 8.
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.
Lecture 9.
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.
Lecture 1.
Oct. 14, 2021
11 a.m. - 1 p.m.
Lecture 2.
Oct. 21, 2021
11 a.m. - 1 p.m.
Lecture 3.
Oct. 28, 2021
11 a.m. - 1 p.m.
Lecture 4.
Nov. 4, 2021
11 a.m. - 1 p.m.
Lecture 5.
Nov. 18, 2021
11 a.m. - 1 p.m.
Lecture 6.
Nov. 25, 2021
11 a.m. - 1 p.m.
Lecture 7.
Dec. 2, 2021
11 a.m. - 1 p.m.
Lecture 8.
Dec. 9, 2021
11 a.m. - 1 p.m.
Lecture 9.
Dec. 16, 2021
11 a.m. - 1 p.m.
Lecture 10.
Jan. 13, 2022
11 a.m. - 1 p.m.
Lecture 11.
Jan. 26, 2022
11 a.m. - 1 p.m.
Lecture 12.
Jan. 27, 2022
11 a.m. - 1 p.m.
Lecture 13.
Feb. 3, 2022
11 a.m. - 1 p.m.
Lecture 14.
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
March 28, 2023
4 p.m. - 6 p.m.
8. Dynamics of the Maxwell field.Pedestrian theory of spherical functions.Michelson-Morley experiment
April 4, 2023
4 p.m. - 6 p.m.
9. Hyperbolic versus elliptic equations. Electromagnetic field as a 4D-differential two-form
April 11, 2023
4 p.m. - 6 p.m.
10. Electromagnetic field as a differential 2-form and its Lorentz transformation
April 18, 2023
4 p.m. - 6 p.m.
11. Lorentz transformation of the electromagnetic field—continued
April 25, 2023
4 p.m. - 6 p.m.
12. Tensors versus tensor densities. Stokes theorem
May 2, 2023
4 p.m. - 6 p.m.
13. Maxwell equations in any curvilinear coordinate system
May 9, 2023
4 p.m. - 6 p.m.
14. Motion of a charged particle. Lorentz force. E=mc^2
May 16, 2023
4 p.m. - 6 p.m.
15. Lorentz force continued. Apparent "paradoxes" of the Relativity Theory
July 3, 2023
9:30 a.m. - 11 a.m.
Analysis of observational datasets
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PRECISE
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July 3, 2023
11 a.m. - 11:30 a.m.
Coffee Break
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PRECISE
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July 3, 2023
11:30 a.m. - 1 p.m.
Analysis of observational datasets
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PRECISE
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July 3, 2023
1 p.m. - 2:30 p.m.
Lunch
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PRECISE
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July 3, 2023
2:30 p.m. - 4 p.m.
Hands-on cosmological N-body simulations
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PRECISE
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July 3, 2023
4 p.m. - 4:30 p.m.
Coffee Break
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PRECISE
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July 3, 2023
4:30 p.m. - 6 p.m.
Hands-on cosmological N-body simulations
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PRECISE
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July 4, 2023
9:30 a.m. - 11 a.m.
Analysis of observational datasets
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PRECISE
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July 4, 2023
11 a.m. - 11:30 a.m.
Coffee Break
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PRECISE
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July 4, 2023
11:30 a.m. - 1 p.m.
Analysis of observational datasets
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PRECISE
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July 4, 2023
1 p.m. - 2:30 p.m.
Lunch
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PRECISE
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July 4, 2023
2:30 p.m. - 4 p.m.
Statistical Analysis in Cosmology
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July 4, 2023
4 p.m. - 4:30 p.m.
Coffee Break
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PRECISE
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July 4, 2023
4:30 p.m. - 6 p.m.
Statistical Analysis in Cosmology
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PRECISE
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July 5, 2023
9:30 a.m. - 11 a.m.
Hands-on cosmological N-body simulations
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July 5, 2023
11 a.m. - 11:30 a.m.
Coffee Break
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PRECISE
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July 5, 2023
11:30 a.m. - 1 p.m.
Hands-on cosmological N-body simulations
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July 5, 2023
1 p.m. - 2:30 p.m.
Lunch
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PRECISE
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July 5, 2023
2:30 p.m. - 4 p.m.
Statistical Analysis in Cosmology
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July 5, 2023
4 p.m. - 4:30 p.m.
Coffee Break
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PRECISE
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July 5, 2023
4:30 p.m. - 6 p.m.
Statistical Analysis in Cosmology
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July 6, 2023
9:30 a.m. - 11 a.m.
Analysis of observational datasets
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PRECISE
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July 6, 2023
11 a.m. - 11:30 a.m.
Coffee Break
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PRECISE
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July 6, 2023
11:30 a.m. - 1 p.m.
Analysis of observational datasets
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PRECISE
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July 6, 2023
1 p.m. - 2:30 p.m.
Lunch
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PRECISE
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July 6, 2023
2:30 p.m. - 4 p.m.
Hands-on cosmological N-body simulations
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PRECISE
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July 6, 2023
4 p.m. - 4:30 p.m.
Coffee Break
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PRECISE
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July 6, 2023
4:30 p.m. - 6 p.m.
Hands-on cosmological N-body simulations
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PRECISE
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July 7, 2023
9:30 a.m. - 11 a.m.
Statistical Analysis in Cosmology
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PRECISE
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July 7, 2023
11 a.m. - 11:30 a.m.
Coffee Break
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PRECISE
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July 7, 2023
11:30 a.m. - 1 p.m.
Statistical Analysis in Cosmology
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July 7, 2023
1 p.m. - 2:30 p.m.
Lunch
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203
Sept. 5, 2023
1 p.m. - 4 p.m.
Defense of the doctoral dissertation
Declaration of Accessibility
Software development:
Andrzej Sawicki
Polish National Agency for Academic Exchange
The Project is financed by the Polish National Agency for Academic Exchange under the Foreign Promotion Programme