Fields Institute Courses

Von Neumann Conditional Expectations and Noncommutative Representing Measures

Explore conditional expectations, representing measures, and their applications in analytic function spaces. Delve into generalized Hardy spaces, Takasaki's theorem, and noncommutative theories.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Mini-Course on Non-Commutative Function Theory - Part 3

Explore non-commutative function theory, focusing on rational functions, linear pencils, and Hardy space concepts. Delve into factorization theorems and zero sets in this advanced mathematical exploration.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Monotonicity, Convexity, and Realization of Noncommutative Functions

Explore noncommutative functions, focusing on monotonicity, convexity, and realization. Delve into classical representations and modern approaches in matrix analysis and functional calculus.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Mini-Course on Non-Commutative Function Theory - Part 2

Explore non-commutative function theory, covering square summable series, homogeneous sums, and the Rhoda string theorem in this advanced mathematical lecture.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Topics in Pure Model Theory - Lecture 10

Explore advanced concepts in pure model theory, including simple theory, invariant types, and symmetry, with expert insights from Itay Kaplan of The Hebrew University of Jerusalem.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Shift Operators on Harmonic Hilbert Function Spaces - Von Neumann Inequality - Harmonic Polynomials

Exploring shift operators, von Neumann inequality, and harmonic polynomials in function spaces, with focus on spherical harmonics and their applications in analysis.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

Wold Decompositions for Representations of C-Algebras Associated with Noncommutative Varieties

Explore noncommutative varieties and C*-algebras through Wold decompositions, covering topics from Berezin kernels to polydomains in this advanced mathematical lecture.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Two Weight Norm Inequalities for Singular and Fractional Integral Operators in Rn

Explore singular and fractional integral operators in Rn, focusing on two weight norm inequalities. Learn about A2 and AP weights, pivotal conditions, and cancellation properties.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Topics in Applied Model Theory - Lecture 9

Explore finite fields, antibiotic geometry, and perfect fields in this advanced lecture on applied model theory by Zoé Chatzidakis.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Sums of Squares and Applications to Hypoellipticity

Explore sums of squares in differential equations, focusing on hypoellipticity. Learn about key theorems, counterexamples, and applications in this advanced mathematics lecture.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

SGD in the Large - Average-Case Analysis, Asymptotics, and Stepsize Criticality

Explore average-case analysis, asymptotics, and stepsize criticality in stochastic gradient descent, with insights on optimization problems and stochastic momentum techniques.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Generators of C0-Semigroups of Weighted Composition Operators

Explore generators of C0-semigroups and weighted composition operators in analytic function spaces, examining key assumptions, proofs, and recent developments in the field.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Totally Positive Kernels, Polya Frequency Functions, and Their Transforms

Explore total positivity in mathematics, including real-rooted polynomials, composition operators, and Hankel kernels. Gain insights into preservers of TN kernels and TP kernel approximations.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Topics in Pure Model Theory - Lecture 8

Explore stable theory, nonforking, and Kim's lemma in pure model theory with Prof. Itay Kaplan, delving into advanced concepts and proofs in this comprehensive lecture.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video

Modelling Immunity to Malaria

Explore mathematical models of malaria immunity, examining within-host dynamics, antigenic variation, and population-level impacts to enhance understanding and control strategies.

• YouTube
• 29 minutes
• Self-Paced
• Free Video