| Wednesday 22 January 2025 | |
| Events for day: Wednesday 22 January 2025 |
| 11:00 - 12:00 Wednesday Weekly Seminar - Virtual Format Krylov Complexity as a Probe for Chaos School PARTICLES AND ACCELERATORS Abstract: In this talk, I will explore the use of Krylov complexity as a diagnostic tool for understanding the chaotic nature of quantum systems. The concept of Krylov complexity is introduced within the framework of the Lanczos algorithm, allowing us to study the system's dynamics in a finite Krylov subspace. By analyzing the time evolution and saturation of complexity, it is possible to demonstrate how it distinguishes between chaotic and integrable many-body systems. These distinctions will be illustrated with numerical results from spin models, providing insights into the interplay between Krylov complexity and quantum chao ... 14:00 - 15:00 Weekly Seminar Advancements in Computational Microbiome Research: From Network Construction to Disease Prediction School BIOLOGICAL SCIENCES The topic of my presentation is about four different projects that have recently been completed and include three computational packages. The first package was designed for constructing microbial networks, which can model complex interactions among microbial species. In the second project, a package was developed for aligning and comparing two different networks, with applications in areas such as genetic data analysis and comparing biological networks between individuals or environments. The third package was designed for penalized high-dimensional models, enabling the analysis of various biological data and extracting complex patterns. This ... 16:00 - 17:00 Mathematics Colloquium Boundedness Results in Algebraic Geometry through Moduli and Hodge Theory School MATHEMATICS Thanks to Faltings, Arakelov and Parshin's solution to Mordell's conjecture we know that smooth complex projective curves of genus at least equal to 2 have finite number of rational points. A key input in the proof of this fundamental result is the boundedness of families of smooth projective curves of a fixed genus (greater than 1) over a fixed base scheme. The latter was generalized by the combined spectacular results of Kovacs-Lieblich and Bedulev-Viehweg to higher dimensional analogues of such curves; the so-called canonically polarized projective manifolds. In this talk I will discuss our recent extension of this boundedness result to th ... |