Канал: Masoud Khalkhali

Weyl's Law at 101

Weyl's Law at 101

Things you need to know before starting quantum field theory 11, Feynman Theorem 2

Things you need to know before starting quantum field theory 11, Feynman Theorem 2

Things you need to know before starting quantum field theory 10, Feynman Theorem 1

Things you need to know before starting quantum field theory 10, Feynman Theorem 1

Who is afraid of infinity?

Who is afraid of infinity?

Things you need to know before starting quantum field theory 9

Things you need to know before starting quantum field theory 9

Things you need to know before starting quantum field theory 8

Things you need to know before starting quantum field theory 8

Things you need to know before starting quantum field theory 7

Things you need to know before starting quantum field theory 7

Things you need to know before starting quantum field theory 6

Things you need to know before starting quantum field theory 6

Things you need to know before starting quantum field theory 5

Things you need to know before starting quantum field theory 5

Things you need to know before starting quantum field theory 4

Things you need to know before starting quantum field theory 4

Things you need to know before starting quantum field theory 3

Things you need to know before starting quantum field theory 3

Things you need to know before starting quantum field theory 2

Things you need to know before starting quantum field theory 2

Things you need to know before starting quantum field theory 1

Things you need to know before starting quantum field theory 1

Introduction to analytic number theory 19: Functional equation for Dirichlet L-functions

Introduction to analytic number theory 19: Functional equation for Dirichlet L-functions

Introduction to analytic number theory 17: Class number formula examples

Introduction to analytic number theory 17: Class number formula examples

Introduction to analytic number theory 18: Zeta function of Gaussian integers

Introduction to analytic number theory 18: Zeta function of Gaussian integers

Introduction to analytic number theory 16: The zeta function of Gaussian integers

Introduction to analytic number theory 16: The zeta function of Gaussian integers

Introduction to analytic number theory 15. More on analytic continuation, Dedekind zeta

Introduction to analytic number theory 15. More on analytic continuation, Dedekind zeta

Introduction to analytic number theory 14: A quick summary of Riemann's 1859 paper

Introduction to analytic number theory 14: A quick summary of Riemann's 1859 paper

Introduction to analytic number theory 13: Riemann-von Mangoldt explicit formula

Introduction to analytic number theory 13: Riemann-von Mangoldt explicit formula

Introduction to analytic number theory 12: special values of zeta function

Introduction to analytic number theory 12: special values of zeta function

Introduction to analytic number theory 11: zeros of the zeta function 1

Introduction to analytic number theory 11: zeros of the zeta function 1

Introduction to analytic number theory 10: The functional equation for zeta function

Introduction to analytic number theory 10: The functional equation for zeta function

Introduction to analytic number theory 9: Gamma function

Introduction to analytic number theory 9: Gamma function

Introduction to analytic number theory 8

Introduction to analytic number theory 8

Introduction to analytic number theory 7

Introduction to analytic number theory 7

Introduction to analytic number theory 6: An example by Euler

Introduction to analytic number theory 6: An example by Euler

Introduction to analytic number theory 5: Dirichlet series continued

Introduction to analytic number theory 5: Dirichlet series continued

Introduction to analytic number theory 4: Dirichlet series

Introduction to analytic number theory 4: Dirichlet series

Introduction to analytic number theory 3: convergence domain of Dirichlet series.

Introduction to analytic number theory 3: convergence domain of Dirichlet series.

Introduction to analytic number theory 2: Dirichlet characters and Dirichlet L-functions.

Introduction to analytic number theory 2: Dirichlet characters and Dirichlet L-functions.

Introduction to analytic number theory 1: Euler, zeta function, and distribution of primes.

Introduction to analytic number theory 1: Euler, zeta function, and distribution of primes.

Wick's theorem

Wick's theorem

Witt Algebra, Conformal Group, Virasoro Algebra (2)

Witt Algebra, Conformal Group, Virasoro Algebra (2)

Witt Algebra, Conformal Group, Virasoro Algebra (1)

Witt Algebra, Conformal Group, Virasoro Algebra (1)

Finite dimensional representations of the Lorentz group. Lecture 4

Finite dimensional representations of the Lorentz group. Lecture 4

Finite dimensional representations of the Lorentz group. Lecture 3

Finite dimensional representations of the Lorentz group. Lecture 3

Finite dimensional representations of the Lorentz group. Lecture 2

Finite dimensional representations of the Lorentz group. Lecture 2

Finite dimensional representations of the Lorentz group. Lecture 1

Finite dimensional representations of the Lorentz group. Lecture 1

A Trace Formula for GL_3 (F_q)

A Trace Formula for GL_3 (F_q)

Trace Formulae, Laplacian and Heat Kernel for Graphs

Trace Formulae, Laplacian and Heat Kernel for Graphs

Index Theory Lecture 34 (Last Lecture): Some Applications of the Atiyah-Singer Index Theorem.

Index Theory Lecture 34 (Last Lecture): Some Applications of the Atiyah-Singer Index Theorem.

Index Theory Lecture 33: Proof of the Atiyah-Singer index theorem for the Dirac operator.

Index Theory Lecture 33: Proof of the Atiyah-Singer index theorem for the Dirac operator.

Index Theory Lecture 32: Quantum harmonic oscillator, Mehler's formula, Getzler rescaling.

Index Theory Lecture 32: Quantum harmonic oscillator, Mehler's formula, Getzler rescaling.

Index Theory Lecture 31: Berezin super trace formula, quantum harmonic oscillators.

Index Theory Lecture 31: Berezin super trace formula, quantum harmonic oscillators.

Index Theory Lecture 30: MacKean-Singer formula, Heat Kernel Expansion

Index Theory Lecture 30: MacKean-Singer formula, Heat Kernel Expansion

Index Theory Lecture 29: The Index Problem

Index Theory Lecture 29: The Index Problem

Index Theory Lecture 28: Generalized Dirac operators, Spin^c manifolds

Index Theory Lecture 28: Generalized Dirac operators, Spin^c manifolds

Index Theory Lecture 27: Pfaffians and the Euler Class. Generalized Dirac Operators.

Index Theory Lecture 27: Pfaffians and the Euler Class. Generalized Dirac Operators.

Index Theory Lecture 26: More characteristic classes.

Index Theory Lecture 26: More characteristic classes.

Index Theory Lecture 25: Chern-Weil theory continued

Index Theory Lecture 25: Chern-Weil theory continued

Index Theory Lecture 24: Chern-Weil theory continued

Index Theory Lecture 24: Chern-Weil theory continued

Index Theory Lecture 23 : Characteristic Classes and Chern-Weil theory I

Index Theory Lecture 23 : Characteristic Classes and Chern-Weil theory I

Index Theory Lecture 22: Review of Differential Geometry continued

Index Theory Lecture 22: Review of Differential Geometry continued

Index Theory Lecture 21: Vector Bundles, Connection and Curvature.

Index Theory Lecture 21: Vector Bundles, Connection and Curvature.

Index Theory Lecture 20: Spin groups, Classification of Complex Clifford Algebras

Index Theory Lecture 20: Spin groups, Classification of Complex Clifford Algebras

Index Theory Lecture 19: Clifford Algebras and Spin Groups.

Index Theory Lecture 19: Clifford Algebras and Spin Groups.

Index Theory Lecture 18: What is the Atiyah-Singer Index Theorem?

Index Theory Lecture 18: What is the Atiyah-Singer Index Theorem?

Student Presentations

Student Presentations

Student Presentations

Student Presentations

Student presentations

Student presentations

Student Presentations

Student Presentations

Introduction to Spectral Geometry 24: Final Lecture; Selberg Trace Formula 2

Introduction to Spectral Geometry 24: Final Lecture; Selberg Trace Formula 2

Index Theory Lecture 16: Proof of Atiyah-Bott fixed point theorem

Index Theory Lecture 16: Proof of Atiyah-Bott fixed point theorem

Introduction to Spectral Geometry 16: The Modular Surface

Introduction to Spectral Geometry 16: The Modular Surface

Introduction to Spectral Geometry 23: Selberg trace formula I

Introduction to Spectral Geometry 23: Selberg trace formula I

Introduction to Spectral Geometry 22: Heisenberg groups and Stone-von Neumann theorem

Introduction to Spectral Geometry 22: Heisenberg groups and Stone-von Neumann theorem

Introduction to Spectral Geometry 21: Kramers-Wannier duality in Ising model

Introduction to Spectral Geometry 21: Kramers-Wannier duality in Ising model

Introduction to Spectral Geometry 20: Pre-trace formula 2

Introduction to Spectral Geometry 20: Pre-trace formula 2

Introduction to Spectral Geometry 19: Pre-trace formula I

Introduction to Spectral Geometry 19: Pre-trace formula I

Introduction to Spectral Geometry 18: Ihara Determinant Formula

Introduction to Spectral Geometry 18: Ihara Determinant Formula

Introduction to Spectral Geometry 17: Ihara zeta functions

Introduction to Spectral Geometry 17: Ihara zeta functions

Introduction to Spectral Geometry 15: Reidmeister Torsion and Analytic Torsion

Introduction to Spectral Geometry 15: Reidmeister Torsion and Analytic Torsion

Introduction to Spectral Geometry 14: Zeta Regularized Products and Analytic Torsion

Introduction to Spectral Geometry 14: Zeta Regularized Products and Analytic Torsion

Introduction to Spectral Geometry 13: Zeta Regularized Determinants

Introduction to Spectral Geometry 13: Zeta Regularized Determinants

Introduction To Spectral Geometry, Lecture 12: Spectral Zeta Functions

Introduction To Spectral Geometry, Lecture 12: Spectral Zeta Functions

Introduction to Spectral Geometry, Lecture 11: Heat Trace Asymptotics II

Introduction to Spectral Geometry, Lecture 11: Heat Trace Asymptotics II

Introduction to Spectral Geometry, Lecture 10: Heat Trace Asymptotics and Weyl's Law

Introduction to Spectral Geometry, Lecture 10: Heat Trace Asymptotics and Weyl's Law

Introduction to Spectral Geometry, Lecture 9: Heat Equation and Heat Kernel

Introduction to Spectral Geometry, Lecture 9: Heat Equation and Heat Kernel

Introduction to Spectral Geometry, Lecture 8: Spectrum of Spheres and Spherical Harmonics

Introduction to Spectral Geometry, Lecture 8: Spectrum of Spheres and Spherical Harmonics

Introduction to Spectral Geometry, Lecture 7: Lattice Theta Functions and Modular Forms

Introduction to Spectral Geometry, Lecture 7: Lattice Theta Functions and Modular Forms

Introduction to Spectral Geometry, Lecture 6: Poisson Summation and Jacobi Inversion Formula

Introduction to Spectral Geometry, Lecture 6: Poisson Summation and Jacobi Inversion Formula

Introduction to Spectral Geometry, Lecture 5: Milnor's Counterexample

Introduction to Spectral Geometry, Lecture 5: Milnor's Counterexample

Introduction to Spectral Geometry, Lecture 4: Isospectrality for Flat Tori

Introduction to Spectral Geometry, Lecture 4: Isospectrality for Flat Tori

Introduction to Spectral Geometry, Lecture 3: Spectral Decomposition Theorem

Introduction to Spectral Geometry, Lecture 3: Spectral Decomposition Theorem

Introduction to Spectral Geometry, Lecture 2: Flat Tori and Circular Drums Spectrum

Introduction to Spectral Geometry, Lecture 2: Flat Tori and Circular Drums Spectrum

Introduction to Spectral Geometry, Lecture 1: Weyl's Asysmptotic Law

Introduction to Spectral Geometry, Lecture 1: Weyl's Asysmptotic Law

Advanced Calculus Lecture 33: Review 3

Advanced Calculus Lecture 33: Review 3

Advanced Calculus Lecture 32: Review 2

Advanced Calculus Lecture 32: Review 2

Index Theory Lecture 17 : Dirac Equation 1

Index Theory Lecture 17 : Dirac Equation 1

Advanced Calculus Lecture 31, Review Session 1

Advanced Calculus Lecture 31, Review Session 1

Advanced Calculus Lecture 30: Divergence and Curl (continuation)

Advanced Calculus Lecture 30: Divergence and Curl (continuation)

Advanced Calculus Lecture 29, Flux and Circulation

Advanced Calculus Lecture 29, Flux and Circulation

Advanced Calculus Lecture 28: Vector Fields

Advanced Calculus Lecture 28: Vector Fields

Advanced Calculus Lecture 27: Examples of Lagrange Multipliers

Advanced Calculus Lecture 27: Examples of Lagrange Multipliers

Advanced Calculus Lecture 26: Lagrange Multipliers

Advanced Calculus Lecture 26: Lagrange Multipliers

Advanced Calculus Lecture 25: Absolute Maxima and Minima, Boundary Points.

Advanced Calculus Lecture 25: Absolute Maxima and Minima, Boundary Points.

Advanced Calculus Lecture 24: Critical Points, the Second Derivative Test

Advanced Calculus Lecture 24: Critical Points, the Second Derivative Test

Index Theory Lecture 15: Atiyah-Bott Lefschetz fixed point theorem

Index Theory Lecture 15: Atiyah-Bott Lefschetz fixed point theorem

Advanced Calculus Lecture 23: Gradient and Directional Derivatives (2)

Advanced Calculus Lecture 23: Gradient and Directional Derivatives (2)

Advanced Calculus Lecture 22: Directional Derivative, Gradient.

Advanced Calculus Lecture 22: Directional Derivative, Gradient.

Index Theory Lecture 14: Tutorial on Poisson Summation Formula

Index Theory Lecture 14: Tutorial on Poisson Summation Formula

Index Theory Lecture 13: McKean-Singer formula; heat kernel asymptotics.

Index Theory Lecture 13: McKean-Singer formula; heat kernel asymptotics.

Advanced Calculus Lecture 21: Review and Tutorial

Advanced Calculus Lecture 21: Review and Tutorial

Advanced Calculus Lecture 20: Implicit partial differentiation

Advanced Calculus Lecture 20: Implicit partial differentiation

Advanced Calculus Lecture 19: Chain Rule

Advanced Calculus Lecture 19: Chain Rule

Index Theory Lecture 12: Spectral decomposition and Heat Kernel

Index Theory Lecture 12: Spectral decomposition and Heat Kernel

Advanced Calculus Lecture 18: Mixed Partial Derivatives

Advanced Calculus Lecture 18: Mixed Partial Derivatives

Advanced Calculus Lecture 17: Tangent planes to surfaces

Advanced Calculus Lecture 17: Tangent planes to surfaces

Advanced Calculus Lecture 16: Level Curves, Level Surfaces

Advanced Calculus Lecture 16: Level Curves, Level Surfaces

Index Theory Lecture 11: The Signature complex, more examples of Hodge decomposition.

Index Theory Lecture 11: The Signature complex, more examples of Hodge decomposition.

Advanced Calculus Lecture 15: Limit and Continuity, Partial Derivatives

Advanced Calculus Lecture 15: Limit and Continuity, Partial Derivatives

Advanced Calculus Lecture 14: Kepler's second Law; Multivariable Functions

Advanced Calculus Lecture 14: Kepler's second Law; Multivariable Functions

Index Theory Lecture 10: Tutorial on Hodge Decomposition

Index Theory Lecture 10: Tutorial on Hodge Decomposition

Advanced Calculus Lecture 13: Curvature Formulas

Advanced Calculus Lecture 13: Curvature Formulas

Advanced Calculus Lecture 12: Arc-length parametrization, curvature

Advanced Calculus Lecture 12: Arc-length parametrization, curvature

Multivariable Calculus Lecture 11: Unit Tangent Vector, Arc Length

Multivariable Calculus Lecture 11: Unit Tangent Vector, Arc Length

Index Theory Lecture 9: Elliptic Finiteness and Regularity, Hodge Decomposition

Index Theory Lecture 9: Elliptic Finiteness and Regularity, Hodge Decomposition

Advanced Calculus Lecture 10: Vector valued functions

Advanced Calculus Lecture 10: Vector valued functions

Advanced Calculus Lecture 9: Cylindrical and Spherical Coordinates

Advanced Calculus Lecture 9: Cylindrical and Spherical Coordinates

Advanced Calculus Lecture 8: Quadric surfaces

Advanced Calculus Lecture 8: Quadric surfaces

Index Theory Lecture 8: Algebra of pseudodifferential operators

Index Theory Lecture 8: Algebra of pseudodifferential operators

Advanced Calculus Lecture 7: Equation of a plane

Advanced Calculus Lecture 7: Equation of a plane

Advanced Calculus Lecture 6: Lines and planes in space

Advanced Calculus Lecture 6: Lines and planes in space

Advanced Calculus Lecture 5: Cross products (continued)

Advanced Calculus Lecture 5: Cross products (continued)

Index Theory Lecture 7: Sobolev space theory

Index Theory Lecture 7: Sobolev space theory

Advanced Calculus Lecture 4: Cross Products

Advanced Calculus Lecture 4: Cross Products

Advanced Calculus Lecture 3: Some applications of the dot product

Advanced Calculus Lecture 3: Some applications of the dot product

Index Theory Lecture 6: A tutorial on elliptic complexes.

Index Theory Lecture 6: A tutorial on elliptic complexes.

Index Theory Lecture 5: Elliptic complexes.

Index Theory Lecture 5: Elliptic complexes.

Index Theory Lecture 4 (Part 2): Atiyah-Jaenich theorem, elliptic PDE's.

Index Theory Lecture 4 (Part 2): Atiyah-Jaenich theorem, elliptic PDE's.

Index Theory Lecture 4 (part 1): Atiyah-Jaenich theorem, elliptic PDE's.

Index Theory Lecture 4 (part 1): Atiyah-Jaenich theorem, elliptic PDE's.

Index Theory Lecture 3: Homotopy invariance, index theory of Toeplitz operators.

Index Theory Lecture 3: Homotopy invariance, index theory of Toeplitz operators.

Index Theory Lecture 2: Fredholm and compact operators

Index Theory Lecture 2: Fredholm and compact operators

Index Theory Lecture 1: Algebraic theory of index

Index Theory Lecture 1: Algebraic theory of index

Advanced Calculus Lecture 2: The dot product.

Advanced Calculus Lecture 2: The dot product.

Advanced Calculus Lecture 1: What is a vector?

Advanced Calculus Lecture 1: What is a vector?