| Friday 29 November 2024 | |
| Events for day: Wednesday 11 September 2024 |
| 10:00 - 12:00 Geometry and Topology Short Course Pointwise Ergodic Theorem Along the Primes School MATHEMATICS This talk focuses on pointwise ergodic theorems and their connection to Bourgain's path to his Fields Medal. We aim to cover four key milestones: Part One: We investigate the norm convergence of ergodic averages, concluding with an explanation of the Baby Spectral Theorem. Part Two: We examine the pointwise ergodic theorem established by Birkhoff in 1931. Depending on the time available, we will cover at least one proof, exploring Calderon's transference in the process. Part Three: This section delves into the circle method and its comparison to the continuous Fourier Transform. We will also discuss several properties of pri ... 14:00 - 16:00 Geometry and Topology Short Course Pointwise Ergodic Theorem Along the Primes School MATHEMATICS This talk focuses on pointwise ergodic theorems and their connection to Bourgain's path to his Fields Medal. We aim to cover four key milestones: Part One: We investigate the norm convergence of ergodic averages, concluding with an explanation of the Baby Spectral Theorem. Part Two: We examine the pointwise ergodic theorem established by Birkhoff in 1931. Depending on the time available, we will cover at least one proof, exploring Calderon's transference in the process. Part Three: This section delves into the circle method and its comparison to the continuous Fourier Transform. We will also discuss several properties of pri ... 16:00 - 17:30 Lecture Mathematical Approaches to Genome Rearrangements and Evolutionary Dynamics in Structured Populations School MATHEMATICS In this talk, I will present probabilistic and statistical models addressing problems in population genetics and genome rearrangements. Population models can be classified into two types: those with a constant population size, like the Moran process, and those with a stochastically varying population size, as in branching processes. I will begin by focusing on the structured Moran process, where populations reside on geometric structures (vertices of graphs). These models capture the effects of population geometry on evolutionary dynamics by incorporating frequency-dependent fitness and spatial constraints. I will demonstrate methods for appr ... 18:00 - 19:30 Lecture Measure-valued diffusions, random walks, and medians in genetics and genomics School MATHEMATICS In this talk, I explore the evolution of types or species in populations from both genetic and genomic perspectives. I first discuss the Fleming-Viot (FV) process in random environment, a measure-valued diffusion modeling the evolution of type-frequencies in countable populations subject to genetic drift, mutation, and selection. The random environment introduces fluctuating fitness among types, meaning their relative strength compared to each other varies stochastically over time. This makes the model significantly more complex than the classical version. I then briefly describe a more general model where multiple FV processes coexist, with ... |