Monotonicity Courses and Certifications

Fields Institute

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
• On-Demand
• Free Video

ACM SIGPLAN

Monotonicity and the Precision of Program Analysis

Explore the connection between program monotonicity and analysis precision. Learn how monotone behavior enables complete abstract interpretation for numeric invariant inference.

• YouTube
• 21 minutes
• On-Demand
• Free Video

ICTP Mathematics

Monotonicity Formulae and Non-Collapsing Estimates for Mean Curvature Flow with Applications - Lecture 2

Explore monotonicity formulae and non-collapsing estimates in mean curvature flow, with insights on their applications and implications for geometric analysis.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

International Mathematical Union

Enlargements - A Bridge Between Maximal Monotonicity and Convexity

Explore connections between maximally monotone operators and convex functions through enlargements, offering insights into variational problems and new distance measures for point-to-set maps.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Society for Industrial and Applied Mathematics

Monotonicity Method for Extreme, Singular and Degenerate Inclusions in Electrical Impedance Tomography

Explores advanced mathematical techniques for electrical impedance tomography, focusing on the monotonicity method's application to extreme, singular, and degenerate inclusions in conductivity reconstruction.

• YouTube
• 53 minutes
• On-Demand
• Conference Talk

Association for Computing Machinery (ACM)

Dynamic Algorithms for LIS and Distance to Monotonicity

Explore dynamic algorithms for Longest Increasing Subsequence and Distance to Monotonicity, covering Patience Sorting, runtime improvements, and grid packing techniques.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Simons Institute

The Long Path to Square Root of d Monotonicity Testers

Explore directed isoperimetry and its application to monotonicity testing, analyzing directed random walks on product domains for optimal testers in Boolean functions on hypergrids.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Simons Institute

Monotonicity Testing, Routing, and the Lehman-Ron Theorem on Hypercube Properties

Explore connections between monotonicity testing, routing on hypercubes, and Lehman-Ron theorem. Gain insights into efficient property testers and low-congestion flows on directed hypercubes.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Monotonicity of Entropy in Families of Interval Maps - Lecture 2

Explore the transfer operator, holomorphic motions, and entropy monotonicity in interval maps. Gain insights into applications in rational dynamics and quadratic families.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Monotonicity of Entropy in Families of Interval Maps - Lecture 1

Explore the transfer operator, holomorphic motions, and entropy monotonicity in interval maps. Gain insights into applications in rational dynamics and quadratic families.

• YouTube
• 1 hour 28 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Long Path to √d Monotonicity Testers - Lecture 1

Explore the mathematical journey toward developing square root of d monotonicity testers in this theoretical computer science lecture by C. Seshadhri.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Long Path to √d Monotonicity Testers - Lecture 2

Explore advanced monotonicity testing algorithms and their square root complexity bounds through theoretical analysis and geometric insights.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Institute for Advanced Study

On Minkowski's Monotonicity Problem in Convex Geometry

Delve into the geometric analysis of Minkowski's mixed volume monotonicity problem, exploring recent advances and connections to classical surface theory and convex geometry fundamentals.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Conference GSI

Monotonicity of the Scalar Curvature of the Quantum Exponential Family for Transverse-Field Ising

Explore scalar curvature monotonicity in quantum exponential family for transverse-field Ising chains, examining finite-size effects and implications for Petz conjecture.

• YouTube
• 21 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Complete Monotonicity and Dual Volumes of Positive Geometries - Lecture 2

Delve into the mathematical aspects of positive geometries in scattering amplitudes, focusing on complete monotonicity and dual volumes in this advanced theoretical physics lecture.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video