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This will be a follow-up of the March 2019 workshop and the 2021 online workshop. As before, the program lies at the juncture of three areas:(1) Probability theory of random processes on negatively curved spaces.(2) Ergodic theory and hyperbolic dynamics (3) hyperbolic geometry.1. Probability:The 2019 workshop laid stress on random walks, while the 2021 workshop emphasized  Bernoulli percolation among topics allied with probability. While random walks on hyperbolic groups have received some attention, other random processes, such as first and last passage percolation, are in a barely nascent state. This is not due to a dearth of problems but rather that people with a dual expertise in both the relevant probabilistic methods and a feel for the geometry of negatively curved spaces, are rare.The 2021 workshop addressed this lacuna by having a set of talks on Bernoulli percolation. The 2023 workshop will deal with more advanced themes like Liouville quantum gravity.2. Ergodic theory: Invar...

This will be a follow-up of the March 2019 workshop and the 2021 online workshop. As before, the program lies at the juncture of three areas:(1) Probability theory of random processes on negatively curved spaces.(2) Ergodic theory and hyperbolic dynamics (3) hyperbolic geometry.1. Probability:The 2019 workshop laid stress on random walks, while the 2021 workshop emphasized  Bernoulli percolation among topics allied with probability. While random walks on hyperbolic groups have received some attention, other random processes, such as first and last passage percolation, are in a barely nascent state. This is not due to a dearth of problems but rather that people with a dual expertise in both the relevant probabilistic methods and a feel for the geometry of negatively curved spaces, are rare.The 2021 workshop addressed this lacuna by having a set of talks on Bernoulli percolation. The 2023 workshop will deal with more advanced themes like Liouville quantum gravity.2. Ergodic theory: Invar...

This is a followup discussion meeting on complex and algebraic geometry involving the below speakers.1. Jose Ignacio Butgos GilArakelov theory, equidistribution and algebraic dynamics: The famous Bogomolov conjecture states that, given a curve C of genus bigger or equal than 2 and defined over a number field, then there exists a number ε > 0 such that the set of algebraic points of C whose N eron–Tate height is smaller that ε is finite. This conjecture was proved by Ullmo and Zhang at the end of last century, based on a pioneering work of Szpiro, Ullmo and Zhang on equidistribution of points of small height. Arakelov theory brings geometric intuition to arithmetic and is a natural framework where to study heights and many questions related to equidistribution. In this course we will give an introduction to heights using Arakelov theory, we will discuss classical equidistribution results and their applications, putting on equal foot the arithmetic and the geometric setting. Finally we w...

We plan an intensive 1-week preparatory school, where participants interested in but new to population genetics can learn key mathematical concepts and tools (for students from a biology background), and important concepts and basic knowledge of biology and genetics (for students from a non-biology background). Scheduled a year before the next main ICTS population genetics school in 2024, the preparatory school will allow participants to strengthen their basic skills and understanding, allowing them to make the most of advanced lectures from experts in the main school. Participants will be asked to come prepared with a basic understanding of biology and computer programming and mathematics (based on suggested reading and other resources provided by email), and lectures during school will help them solidify their understanding and use it to solve simple but interesting problems in population genetics and evolution. The lectures will cover topics such as basic evolutionary forces, neutra...

This is a followup discussion meeting on complex and algebraic geometry involving the below speakers.1. Jose Ignacio Butgos GilArakelov theory, equidistribution and algebraic dynamics: The famous Bogomolov conjecture states that, given a curve C of genus bigger or equal than 2 and defined over a number field, then there exists a number ε > 0 such that the set of algebraic points of C whose N eron–Tate height is smaller that ε is finite. This conjecture was proved by Ullmo and Zhang at the end of last century, based on a pioneering work of Szpiro, Ullmo and Zhang on equidistribution of points of small height. Arakelov theory brings geometric intuition to arithmetic and is a natural framework where to study heights and many questions related to equidistribution. In this course we will give an introduction to heights using Arakelov theory, we will discuss classical equidistribution results and their applications, putting on equal foot the arithmetic and the geometric setting. Finally we w...

We plan an intensive 1-week preparatory school, where participants interested in but new to population genetics can learn key mathematical concepts and tools (for students from a biology background), and important concepts and basic knowledge of biology and genetics (for students from a non-biology background). Scheduled a year before the next main ICTS population genetics school in 2024, the preparatory school will allow participants to strengthen their basic skills and understanding, allowing them to make the most of advanced lectures from experts in the main school. Participants will be asked to come prepared with a basic understanding of biology and computer programming and mathematics (based on suggested reading and other resources provided by email), and lectures during school will help them solidify their understanding and use it to solve simple but interesting problems in population genetics and evolution. The lectures will cover topics such as basic evolutionary forces, neutra...