Carlos Kenig’s talk delved into the topic of nonlinear wave equations, specifically focusing on the long-time behaviour of large solutions to the energy-critical focusing nonlinear wave equation. Over the last fifteen years, remarkable strides have been made in unravelling the intricacies of these equations. His lecture provided insights into the asymptotic simplification of these equations, demonstrating their transformation into sums of modulated static solutions plus a linear term in all dimensions, particularly in the radial case.
Carlos Kenig is an Argentine-American mathematician and the Louis Block Distinguished Service Professor at the University of Chicago’s Department of Mathematics. His work in harmonic analysis and partial differential equations is well recognized.
A meeting for the Catalan mathematical community
The CRM Colloquium 2023 was not just a platform for mathematical knowledge dissemination; it was a testament to the power of collaboration and networking within the mathematical community in Barcelona. The event attracted over fifty researchers and students from diverse mathematical backgrounds, offering them a unique opportunity to connect, exchange ideas, and cultivate collaborations that can lead to future work.
The new format of the CRM Colloquium emphasizes the importance of fostering these connections. By encouraging interdisciplinary interactions and interdisciplinary thinking, the event aimed to create an environment where mathematical insights could transcend traditional boundaries.
The Centre de Recerca Matemàtica has long been an international referent of mathematical research excellence, bringing every year renowned mathematicians from all over the world to collaborate with local researchers and participate in the scientific activities organized by the center. The new CRM Colloquium further solidifies its reputation as a hub for cutting-edge mathematical inquiry. As the world of mathematics continues to evolve and expand, events like these serve as a reminder of the boundless possibilities that emerge when brilliant minds unite to unravel the mysteries of the mathematical universe.
You can watch the colloquium by Professor Kenig here:
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Almost every automaton can be reset with a short word
Guillaume Chapuy (Université Paris Cité, CNRS) and Guillem Perarnau (UPC, CRM) have shown that a random finite automaton with n states can, with high probability, be reset by a word of length of order √n log n. The result, published in ACM Transactions on Algorithms, pins the exponent at 1/2, the lower end of a decade of numerical estimates, and addresses the random version of the synchronization problem behind a conjecture Ján Černý posed in 1964 and which still remains open.
Exposició ‘Les matemàtiques de Gaudí’
CRM quod erat demonstrandum | 48
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