FIRST WEEK
(7/3 – 11/3)
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Hours |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
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8:30 AM - 10 AM |
Tran NT 1 |
Tran NT 2 |
Kersting GK 1 |
Winter AW 2 |
Neeman JN 3, JN 4 |
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10 AM – 10:30 AM |
TEA BREAK |
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10:30 AM – 12:00 PM |
Neeman JN 1 |
Neeman JN 2 |
Winter AW 1 |
Kersting GK 2 |
Kersting GK 3 |
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12:00 PM – 2:00 PM |
LUNCH BREAK |
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2:00 PM – 3:00 PM |
Geldhauser Tutorial Session |
Geldhauser Tutorial Session |
DAAD guided tour |
Geldhauser Tutorial Session |
DAAD: interactive session (in Vietnamese) |
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3:00 PM – 3:30 PM |
TEA BREAK |
DAAD study in Germany Information Session |
TEA BREAK |
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3:30 PM – 4:30 PM |
Problem Session |
Problem Session |
Problem Session |
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SECOND WEEK
(14/3 – 18/3)
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Hours |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
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8:30 AM - 10 AM |
Tran NT 3
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Tran NT 4 |
Rizzolo DR 2 |
Kersting GK 4 |
Rizzolo DR 4 |
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10 AM – 10:30 AM |
TEA BREAK |
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10:30 AM – 12:00 PM |
Winter AW 3 |
Rizzolo DR 1 |
Winter AW 4 |
Rizzolo DR 3 |
Kersting GK 5 |
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12:00 PM – 2:00 PM |
LUNCH BREAK |
Museum + lunch excursion |
LUNCH BREAK |
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2:00 PM – 3:00 PM |
Geldhauser Tutorial Session |
Geldhauser Tutorial Session |
Geldhauser Tutorial Session |
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|
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3:00 PM – 3:30 PM |
TEA BREAK |
TEA BREAK |
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3:30 PM – 4:30 PM |
Problem Session |
Problem Session |
Problem Session |
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Lectures by Tran: A size-biased introduction to Kingman's theory of random partitions
These lectures introduce the building blocks of combinatorial stochastic processes, namely random partitions. We focus on Kingman's theory and important running examples, such as the Poisson-Dirichlet family of partitions which have enjoyed applications in Bayesian statistics and machine learning.
NT 1, NT 2: Random partitions from an i.i.d sequence.
NT 3, NT 4: Exchangeable random partitions. Kingman's theorem and applications.
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Lectures by Neeman: Multi-type branching processes and stochastic block models
Multi-type branching processes has applications in population genetics and graph clustering. In these lectures we will discuss the Kesten and Stigum reconstruction problem for inferring the type of the root. Then we will introduce the stochastic block model and use the above results to prove a threshold for detectability.
JN 1: Random trees, Galton-Watson trees
JN 2: Multi-type branching processes
JN 3, JN 4: Stochastic block model and the reconstruction theorem
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Lectures by Rizzolo: Asymptotic properties of random trees
In this series we will look at asymptotic properties of random trees. The primary model we will focus on are Galton-Watson trees conditioned on their number of vertices. Our goal will be to investigate the structure of these trees in the limit as the number of vertices go to infinity. We will look at both local properties such as the degree of the root, or of a uniformly random vertex, and global properties such as the diameter of the graph. In both cases we will show that there is a limiting tree that captures the corresponding properties of a large Galton-Watson tree. Time permitting, we will discuss applications of these results to topics such as random planar structures and pattern-avoiding permutations as well as extensions to other models of random trees.
DR 1: Conditioned Galton-Watson trees
DR 2, DR 3: Limit of conditioned Galton-Watson trees
DR 4: Applications
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Lectures by Kersting: Coalescents and their shapes
These lectures introduce topics from the theory of coalescents and their relations to population genealogies. It also examines recent results on the special class of Beta-coalescents and their shape with emphasis on total length, total external length and related quantities.
GK 1, GK 2: Coalescent theory and population genetics applications
GK 3, GK 4, GK5: Beta coalescents
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Lectures by Winter: Pruning procedures on trees
In this lecture we start with considering dynamic edge percolation (also called pruning) of Galton-Watson trees. An interesting question to ask is about how many cuts does it need to isolate the root. We will follow Jansen's proof to show that the suitable rescaled number converges weakly to a Rayleigh distribution. The latter is known as the distribution of the random height of a Brownian CRT, which is the scaling limit of suitably rescaled Galton-Watson trees. We therefore next introduce pruning procedures on the Brownian CRT and establish the convergence of the corresponding pruning processes. For that purpose we introduce notions of convergence of trees equipped with sampling and pruning measures. Finally we consider dynamic vertex percolation of Galton-Watson trees, where the pruning intensity depends of the degree of an vertex, and discuss once more the convergence to the pruning process on the continuum limit. We will close with open problems concerning such non-homogeneous pruning procedures
AW1, AW2: The discrete picture: The tree-valued Markov chain arising from pruning Galton-Watson trees.
AW3: The continuous picture: Pruning of random continuum trees.
AW4: Convergence of the discrete to the continuous picture: Leaf sampling weak vague topology and the pruning process