Math Calendar
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
Speakers:
1. Soumya Sankar: Overview of seminar
2. Justin Uhlemann: Introduction to higher dimensional Arakelov theory - I
3. Robin de Jong: Introduction to higher dimensional Arakelov theory - II
See https://www.rationalpoints.nl/events-2/learning-seminar-on-arakelov-theory/ for more details.
UGC colloquium webpage https://utrechtgeometrycentre.nl/ugc-seminar/
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
A Stochastic Reaction Network (SRN) is a continuous-time, discrete-space Markov chain, which models the random interaction of d species through reactions, commonly applied in (bio-)chemical systems. Our special interest lays in estimating statistical quantities and filtering in high dimensional SRNs (i.e., in systems with many species, in which d >> 1). Traditional methods like Monte Carlo estimators, solving filtering equations, solving the chemical master equations or the Kolmogorov backward equations become computationally expensive in such scenarios. To address the curse of dimensionality, we propose the Markovian Projection (MP) technique [1] to reduce the SRN to a lower-dimensional SRN (called MP-SRN) while preserving the marginal distribution of the original high-dimensional system. In this talk, we explore how MP can be used to derive an efficient importance sampling scheme for estimating rare event probabilities. We also explore how MP can be applied in filtering for deriving the distribution of unobserved species conditioned on a sample path of observed species.
[1] Ben Hammouda, C., Ben Rached, N., Tempone, R., & Wiechert, S. (2024). Automated importance sampling via optimal control for stochastic reaction networks: A Markovian projection-based approach. Journal of Computational and Applied Mathematics, 446, 115853.
Abstract: Up to affine transformations over Z there are 18 different 3D Fano polytopes. The set of vertices of such a polytope is a subset V of Z^3 which can be used as exponents for a Laurent polynomial. The surface in P^3 defined by the homogenization of such a Laurent polynomial is a quartic K3 surface. Varying the coefficients of the Laurent polynomial yields a family of K3 surfaces. The aim of the talk is to demonstrate how the Gelfand-Kapranov-Zelevinsky hypergeometric system associated with V and results on Mirror Symmetry for lattice polarized K3 surfaces lead to simple elegant expressions for the transcendental periods as functions of the coefficients of the Laurent polynomial.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.
Title:
Extremes in dynamical systems: max-stable and max-semistable laws
Abstract:
Extreme value theory for chaotic, deterministic dynamical systems is a rapidly expanding area of research. Given a dynamical system and a real-valued observable defined on its state space, extreme value theory studies the limit probabilistic laws for asymptotically large values attained by the observable along orbits of the system. Under suitable mixing conditions the extreme value laws are the same as those for stochastic processes of i.i.d. random variables.
Max-stable laws typically arise for probability distributions with regularly varying tails. However, in the context of dynamical systems, where the underlying invariant measure can be irregular, max-semistable distributions also have a natural place in studying extremal behaviour. In this talk I will first discuss a family of autoregressive processes with marginal distributions resembling the Cantor function. The resulting extreme value law can be proven to be a max-semistable distribution. Alternatively, we can describe the autoregressive process in terms of an iterated map with an invariant measure. Further examples of extreme value laws in dynamical systems are discussed as well.