Course: LTCC - London Taught Course Centre (Queen Mary Courses)

Topic outline

Select topic General

General

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- Select activity Announcements
  
  Announcements Forum
Select topic Shengwen Wang: Introduction to Mean Curvature Flow

Shengwen Wang: Introduction to Mean Curvature Flow

Not available
Select topic Ginestra Bianconi: Maximum Entropy Models for Complex Networks

Ginestra Bianconi: Maximum Entropy Models for Complex Networks
MAXIMUM ENTROPY MODELS OF COMPLEX NETWORKS: SLIDES AND HANDWRITTEN NOTES
Lesson 1: Introduction to complex networks and maximum entropy principle
Lesson 2: Maximum Entropy principle Microcanonical and canonical network ensembles, Handwritten notes
Lesson 3: Random graphs and canonical ensembles with expected degree sequence,correlated and uncorrelated networks, Handwritten notes
Lesson 4: Canonical ensembles in the uncorrelated limit, the configuration model and the non-equivalence of ensembles
Lesson 5: Two star and Strauss model. Spatial networks ensembles and latent variables, Block models and inference, Handwritten notes
MAXIMUM ENTROPY MODELS OF COMPLEX NETWORKS: LIVE LECTURES (RECORDING AVAILABLE BY FOLLOWING THE LECTURE LINK)

Mondays 14 February -14 March 3:50pm-5:50pm

The course will take place online in the Blackboard Collaborate see link (Guest Link sent by private email)
Select topic Alexander Sodin: Introduction to Harmonic Analysis

Alexander Sodin: Introduction to Harmonic Analysis
- Select activity Lecture 1
  
  Lecture 1 File
  
  297.1 MB
- Select activity Notes from Lecture 1
  
  Notes from Lecture 1 File
  
  12.2 MB
- Select activity Exercise sheet 1
  
  Exercise sheet 1 File
  
  263.8 KB
- Select activity Exercise sheet 2
  
  Exercise sheet 2 File
  
  1.2 MB
- Select activity Lecture 3 (poor quality recording)
  
  Lecture 3 (poor quality recording) File
  
  243.6 MB
- Select activity Exercise sheet 3
  
  Exercise sheet 3 File
  
  230.0 KB
- Select activity Lecture 4 (poor quality recording)
  
  Lecture 4 (poor quality recording) File
  
  243.1 MB
- Select activity Exercise sheet 4
  
  Exercise sheet 4 File
  
  2.0 MB
- Select activity Lecture 5 (poor quality recording)
  
  Lecture 5 (poor quality recording) File
  
  224.3 MB
- Select activity Exercise sheet 5
  
  Exercise sheet 5 File
  
  334.8 KB
- Select activity Lecture notes (thanks to Artem Artemev)
  
  Lecture notes (thanks to Artem Artemev) File
  
  331.6 KB
Select topic Juan Valiente Kroon: Mathematical Topics in General Relativity

Juan Valiente Kroon: Mathematical Topics in General Relativity
- Select activity The lectures are structured as follows:LECTURE 1: ...
  
  The lectures are structured as follows:
  LECTURE 1: introduction and refresher of differential geometry
  LECTURE 2: the Einstein equations as a wave equation and selected topics of Lorentzian and Riemannian Differential Geometry including embeddings and submanifolds, intrinsic metrics, extrinsic curvature, Gauss-Codazzi and Codazzi-Mainardi equations
  LECTURE 3: the ADM evolution equations
  LECTURE 4: the constraint equations of General Relativity and time independent solutions
  LECTURE 5: energy and momentum in GR; Killing initial data. Wrap up.
- Select activity Lecture notes
  
  Lecture notes File
  
  These are the official lecture notes on which the course is based.
  
  428.3 KB
- Select activity General Course information
  
  General Course information File
  
  74.6 KB
- Select activity Slides for Lecture 1
  
  Slides for Lecture 1 File
  
  549.9 KB
- Select activity Problem sheet 1
  
  Problem sheet 1 File
  
  This (optional) problem sheet provides some practice on some of the topics discussed in the lectures.
  
  140.6 KB
- Select activity Recording of Lecture 1
  
  Recording of Lecture 1 QMplus Media Video
- Select activity Slides for Lecture 2
  
  Slides for Lecture 2 File
  
  283.4 KB
- Select activity Problem sheet 2
  
  Problem sheet 2 File
  
  144.5 KB
- Select activity Recording of Lecture 2
  
  Recording of Lecture 2 QMplus Media Video
- Select activity Slide for Lecture 3
  
  Slide for Lecture 3 File
  
  456.7 KB
- Select activity Problem sheet 3
  
  Problem sheet 3 File
  
  136.3 KB
- Select activity Recordings of Lecture 3
  
  Recordings of Lecture 3 QMplus Media Video
- Select activity Slides for Lectures 4 and 5
  
  Slides for Lectures 4 and 5 File
  
  414.3 KB
- Select activity Problem sheet 4
  
  Problem sheet 4 File
  
  126.3 KB
- Select activity Assessment problems
  
  Assessment problems File
  
  The assessment problems are due for the 8th March 2021.
  
  138.9 KB
- Select activity Lecture 4 recordings - part one
  
  Lecture 4 recordings - part one QMplus Media Video
- Select activity Lecture 4 - part b
  
  Lecture 4 - part b QMplus Media Video
Select topic Alexander Gnedin: Measure Theoretic Probability

Alexander Gnedin: Measure Theoretic Probability
- Select activity MTP24, Lecture 1 slides
  
  MTP24, Lecture 1 slides File
  
  MTP24, 15/01/24, Lecture 1 slides
  
  191.0 KB
- Select activity Lecture 1: Basics of Measure Theory
  
  Lecture 1: Basics of Measure Theory File
  
  LECTURE 1: Basics of Measure Theory
  Sample problems: 4, 6, 7, 10, 13, 14
  
  256.8 KB
- Select activity Lecture 1: solutions to selected problems
  
  Lecture 1: solutions to selected problems File
  
  Lecture 1: solutions to selected problems
  
  143.3 KB
- Select activity Lecture 1 Recording, 9/11/2020
  
  Lecture 1 Recording, 9/11/2020 URL
  
  Lecture 1 Recording, 9/11/2020
- Select activity MTP24, Lecture 2 slides
  
  MTP24, Lecture 2 slides File
  
  MTP24, 22/01/2024, Lecture 2 slides
  
  200.5 KB
- Select activity Lecture 2: Random variables, independence, integration and conditioning
  
  Lecture 2: Random variables, independence, integration and conditioning File
  
  LECTURE 2: Random variables, independence, integration and conditioning (printed LN)
  Sample problems: 1, 4, 5, 7
  
  242.0 KB
- Select activity MTP meeting 18/11/2022 5pm
  
  MTP meeting 18/11/2022 5pm External tool
- Select activity Zoom Lecture 18/11/22: Notes
  
  Zoom Lecture 18/11/22: Notes File
  
  Handwritten notes on Conditional Concepts
  (Zoom Lecture 18/11/22)
  
  6.6 MB
- Select activity MTP24, Lecture 3 slides
  
  MTP24, Lecture 3 slides File
  
  MTP24 - Lecture 3 slides, 29/01/24: Conditional concepts and martingales.
  
  201.3 KB
- Select activity Lecture 2: solutions to problems
  
  Lecture 2: solutions to problems File
  
  Lecture 2: solutions to problems
  
  172.5 KB
- Select activity Lecture 2 Recording 16/11/2020
  
  Lecture 2 Recording 16/11/2020 File
  
  Lecture 2 Recording 16/11/2020
  
  401.0 MB
- Select activity LECTURE 3: Convergence concepts and martingales
  
  LECTURE 3: Convergence concepts and martingales File
  
  LECTURE 3: Convergence concepts and martingales (printed LN)
  Sample problems: 1, 2, 6, 9, 11
  
  215.2 KB
- Select activity Lecture 3: solutions to selected problems
  
  Lecture 3: solutions to selected problems File
  
  Lecture 3: solutions to selected problems
  
  165.7 KB
- Select activity Lecture 3 Recording, 23/11/2020
  
  Lecture 3 Recording, 23/11/2020 File
  
  Lecture 3 Recording, 23/11/2020
  
  487.0 MB
- Select activity MTP24-Lecture 4 slides
  
  MTP24-Lecture 4 slides File
  
  MTP24-Lecture 4 slides
  
  196.4 KB
- Select activity Lecture 4: The Brownian motion
  
  Lecture 4: The Brownian motion File
  
  Lecture 4: The Brownian motion (printed LN)
  
  237.1 KB
- Select activity Handwritten notes Lecture 4, 29/11/2021
  
  Handwritten notes Lecture 4, 29/11/2021 File
  
  Handwritten notes accompanying Lecture 4, 29/11/2021
  
  13.1 MB
- Select activity Lecture 4: solutions to selected problems
  
  Lecture 4: solutions to selected problems File
  
  147.7 KB
- Select activity Lecture 4 recording, 30/11/2020
  
  Lecture 4 recording, 30/11/2020 File
  
  Lecture 4 recording, 30/11/2020, 10:30-12:30
  
  461.1 MB
- Select activity Lecture 5, printed LN
  
  Lecture 5, printed LN File
  
  Lecture 5: Weak convergence of measures and the invariance principle (printed LN)
  sample problems: 2,3,4,6
  
  274.2 KB
- Select activity Handwritten LN, Lecture 5
  
  Handwritten LN, Lecture 5 File
  
  Handwritten LN, accompanying Lecture 5, 6/12/2021
  
  11.8 MB
- Select activity Lecture 5, Recording 7/12/2020
  
  Lecture 5, Recording 7/12/2020 File
  
  Lecture 5, Recording 7/12/2020
  
  406.8 MB
- Select activity 2019/20 Exam "Measure-Theoretic Probability"
  
  2019/20 Exam "Measure-Theoretic Probability" File
  
  2019/20 Exam "Measure-Theoretic Probability"
  
  152.5 KB
- Select activity 2019/20 Exam "Measure-Theoretic Probability" (Solutions)
  
  2019/20 Exam "Measure-Theoretic Probability" (Solutions) File
  
  2019/20 Exam "Measure-Theoretic Probability" (Solutions)
  
  172.5 KB
- Select activity LTCC: MTP exam 2021-22
  
  LTCC: MTP exam 2021-22 Folder
  
  LTCC: MTP exam 2021-22
Select topic Steve Coad: Topics in the Design of Experiments

Steve Coad: Topics in the Design of Experiments
Select topic MAXIMUM ENTROPY MODELS FOR COMPLEX NETWORKS

MAXIMUM ENTROPY MODELS FOR COMPLEX NETWORKS
- Select activity Slides Lesson 1: Introdution to Complex Networks and Maximum Entropy Principle
  
  Slides Lesson 1: Introdution to Complex Networks and Maximum Entropy Principle File
  
  2.4 MB
- Select activity Slides lesson 2: Maximum entropy principle. Canonical and microcanonical ensembles.
  
  Slides lesson 2: Maximum entropy principle. Canonical and microcanonical ensembles. File
  
  478.8 KB
- Select activity Lesson 2: Handwritten notes
  
  Lesson 2: Handwritten notes File
  
  2.7 MB
- Select activity Slides Lesson 3: Random graphs, Network ensemble with given degree sequence
  
  Slides Lesson 3: Random graphs, Network ensemble with given degree sequence File
  
  1.1 MB
- Select activity Handwritten notes:Lesson 3
  
  Handwritten notes:Lesson 3 File
  
  2.8 MB
- Select activity Slides lesson 4: Correlated and uncorrelated networks, Canonical Ensembles in the Uncorrelated limit, The configuration model and the non-equivalence of ensembles, Two star and Strauss model
  
  Slides lesson 4: Correlated and uncorrelated networks, Canonical Ensembles in the Uncorrelated limit, The configuration model and the non-equivalence of ensembles, Two star and Strauss model File
  
  1.1 MB
- Select activity Slides lesson 5: Two star and the Strauss model, Block models and inference, Maximum Entropy models for multiplex networks and simplicial complexes
  
  Slides lesson 5: Two star and the Strauss model, Block models and inference, Maximum Entropy models for multiplex networks and simplicial complexes File
  
  3.6 MB
- Select activity Lesson 5 Handwritten notes
  
  Lesson 5 Handwritten notes File
  
  1.5 MB
Select topic MAXIMUM ENTROPY MODELS FOR COMPLEX NETWORKS

MAXIMUM ENTROPY MODELS FOR COMPLEX NETWORKS
- Select activity Lecture 1 Part 1 Maximum Entropy Models of Networks
  
  Lecture 1 Part 1 Maximum Entropy Models of Networks QMplus Media Video
- Select activity Lesson 1 Part 2 Maximum Entropy Models of Networks
  
  Lesson 1 Part 2 Maximum Entropy Models of Networks QMplus Media Video
Select topic Michael Farber: Morse theory, Topology & Robotics

Michael Farber: Morse theory, Topology & Robotics
Lecture 1-Topology of sublevel sets, operation of attaching cells, Morse functions,
Morse Lemma, existence of Morse functions, crossing a Morse critical value. Main
theorem of Morse theory. Morse inequalities. Examples: spheres, complex projective
spaces, etc.
Lecture 2- Smale’s solution of Generalised Poincare Conjecture.
H-cobordism theorem. Ideas and techniques of the proof.
Lecture 3- Planar linkages and their configuration spaces. Formula for their Betti
numbers. Walker’s Conjecture.
Lecture 4- Spaces of polygons in high dimensions, classification of these spaces in
combinatorial terms.
Lecture 5- Robot motion planning and topology. Schwarz genus of a fibration. Lusternik-
Schnirelmann theory. Topological complexity.
- Recommended reading:
1. J. Milnor, Morse theory. 1963
2. J. Milnor, Lectures on the h-cobordism theorem. 1965.
3. M. Farber, Invitation to topological robotics, EMS, 2008.
- Additional Optional reading:
M. Farber and V. Fromm, The topology of spaces of polygons. Trans. Amer. Math. Soc.
365 (2013), no. 6, 3097–3114.
- Prerequisites:
Basic homology theory of cell complexes, basic knowledge smooth manifolds.
Lecturer Details:
Lecturer: Professor Michael Farber
Lecturer home institution: Queen Mary University of London
Lecturer e-mail: M.Farber@qmul.ac.uk
Lecturer telephone number: 07906345551

Topic outline

General

Shengwen Wang: Introduction to Mean Curvature Flow

Ginestra Bianconi: Maximum Entropy Models for Complex Networks

Alexander Sodin: Introduction to Harmonic Analysis

Juan Valiente Kroon: Mathematical Topics in General Relativity

Alexander Gnedin: Measure Theoretic Probability

Steve Coad: Topics in the Design of Experiments

MAXIMUM ENTROPY MODELS FOR COMPLEX NETWORKS

MAXIMUM ENTROPY MODELS FOR COMPLEX NETWORKS

Michael Farber: Morse theory, Topology & Robotics