Events

The workshop gathers experts working on elliptic and parabolic equations, singular analysis, and geometric aspects of pdes, and applications.

International Conference on Analysis and Applied Mathematics (ICAAM) aims to bring mathematicians working in the area of analysis and applied mathematics together to share new trends of applications of mathematics. In mathematics, the developments in the field of applied mathematics open new research areas in analysis and vice versa. That is why we planned the conference series to provide a forum for researchers and scientists to communicate their recent developments and present their original results in various fields of analysis and applied mathematics. The main organizers of the conference are: Bahcesehir University, Türkiye, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan Analysis & PDE Center, Ghent University, Ghent, Belgium

Scientific Directors: - Albert Cohen, Sorbonne Univ., France - Domenico Marinucci, Univ. Roma Tor Vergata, Italy - Hendrik Speleers, Univ. Roma Tor Vergata, Italy Lectures: - Holger Rauhut, RWTH Aachen University, Germany - Compressive Sensing - Gitta Kutyniok, Ludwig Maximilian Univ. Munich, Germany - High-Dimensional Approximation in Machine Learning - Francis Bach, INRIA Ecole Normale Supérieure Paris, France - Adaptivity in High-Dimensional Statistical Learning - Dirk Nuyens, KU Leuven, Belgium - High-Dimensional Integration - Markus Bachmayr, RWTH Aachen University, Germany - Numerics of High-Dimensional PDEs

A joint event of the School of Mathematics, IAS, the International Academy for the History of Science, and the International Commission for the History of Mathematics Talk abstract: The Classification of Finite Simple Groups (CFSG), also known as the enormous theorem, is a highlight of 20th-century mathematics, both with respect to its mathematical content and to the complex process of proving the result. From a historical perspective, it offers an excellent opportunity to focus on more general developments in the history of 20th-century mathematics, such as changing perceptions of what a mathematical proof is, the character and the many contexts of mathematics as an intergenerational and international collaborative enterprise, and the impact of Cold War research policies on CFSG/pure mathematics. We consider the CFSG as (possibly) the first instant of what we tentatively call big mathematics in this project. The existing proof of the CFSG is estimated to be spread on somewhere between 10.000 and 15.000 journal pages in ca. 500 separate articles written by more than 100 mathematicians. The unprecedented nature of this enterprise from the 1950s until the 1980s is quite tangible: the extraordinarily large number of mathematicians involved internationally (working as a team), the difficulty and complexity of the problem, the use of computers within the proof, the effect of the Cold War on CFSG/pure mathematics (e.g. via new funding possibilities by both civil and military agencies). The history of CFSG has to be studied as a key example of the impact of politics on research in pure mathematics in the Cold War, namely via new possibilities of funding research in general and of mathematical research in particular, a largely unexplored territory, but crucial for CFSG. The historical analysis will be guided by three themes: suitability of big mathematics as an analytical concept, the role of self-historicization in CFSG, and the changing nature of proof in mathematics in the second half of the 20th century. About the panel discussion: There is much opportunity for collaboration between mathematicians and historians to examine together the recent history of mathematics. The practice of mathematics has changed greatly over the course of the twentieth century, and even more rapidly in recent years with the rise of computing and the internet. A deeper understanding of how cultural, intellectual, political, and social factors have interacted with and shaped the recent evolution of the discipline would be valuable both as intellectual history, and to inform the way mathematicians themselves think about their subject and anticipate to its future. This panel will look at the difficulties and possibilities of such collaborative historical work.

Computational phylogenetic methods have become essential tools for understanding the evolutionary relationships that underlie much life science research. Motivated by biological questions and insights, built on a broad spectrum of mathematical and statistical ideas and approaches, and implemented through novel and sophisticated algorithmic design, their development draws from multiple fields. Bringing together researchers spanning disciplinary perspectives and techniques, this workshop will present a diverse sample of work addressing current challenges in phylogenetics, with an eye toward future progress.

The program will explore different perspectives on uncertainty quantification, efficient simulation, and the analysis of complex stochastic systems. The topics covered will include exciting recent developments on efficient methods for approximating quasi-stationary distributions, simulation of equilibrium distributions, information divergences in sensitivity analysis of rare events, large deviations methods for efficient importance sampling, accelerated Monte Carlo via nonlinear PDE, and complex probabilistic models including reflected diffusions and high-dimensional dynamics arising in chemistry and physics.

Inverse problems are widespread in many varied fields such as medical and satellite imaging, biology, astronomy, geophysics, environmental sciences, computer vision, energy, finance, and defence. These problems are inverse in the sense that they arise from seeking to use a mathematical or physical model “backwards” to indirectly determine a quantity of interest from the effect that this quantity causes on some observed data. A main challenge resulting from using models “backwards” to measure causes from their effects is that solutions are often not well posed, i.e., not unique and/or unstable with respect to small perturbations in the data. This difficulty has stimulated an important amount of research and innovation at the interface of applied mathematics, statistics, engineering, physics, and other fields, leading to great social and economic benefit through impact on science, medicine, and engineering.

The event will especially focus on the recent connections of the Fourier transform of fractal measures, Fractal Uncertainty Principles and discretised sum-product theory appearing in these topics (mixing rates / spectral gaps, Diophantine approximation problems, quantum chaos such as scattering resonance distribution and eigenstate delocalisation in high energy) and bringing dialogue between these communities to solve some of the current challenges.

Invited Speakers: Alberto Enciso (ICMAT) Simon Chandler-Wilde (Reading) Lyonell Boulton (Heriot-Watt) Fioralba Cakoni (Rutgers) Chris Judge (Bloomington) Emily Dryden (Bucknell) Cristina Trombetti (Naples) Michael Magee (Durham) Maciej Zworski (Berkeley) Wilhelm Schlag (Yale) Public Lecture: Dmitri Vassiliev (UCL)

GAP is a series of summer schools, each devoted to a topic related to geometry and mathematical physics. Traditionally, the emphasis is on interaction between speakers and participants rather than on an intensive schedule of talks. This time there will be three mini-courses, a number of invited talks, and a poster session for young participants.