Abstract: It is commonly known that the interplay of linear and nonlinear effects gives rise to solitons, i.e., self-trapped localized structures, in a wide range of physical settings, including optics, Bose-Einstein condensates (BECs), hydrodynamics, plasmas, condensed-matter physics, etc. Nowadays, solitons are considered as an interdisciplinary class of modes, which feature diverse internal structures. While most experimental realizations and theoretical models of solitons have been elaborated in one-dimensional (1D) settings, a challenging issue is prediction of stable solitons in 2D and 3D media. In particular, multidimensional solitons may carry an intrinsic topological structure in the form of vorticity. In addition to the "simple" vortex solitons, fascinating objects featuring complex structures, such as hopfions, i.e., vortex rings with internal twist, have been predicted too. A fundamental problem is the propensity of multidimensional solitons to be unstable (naturally, solitons with a more sophisticated structure, such as vortex solitons, are more vulnerable to instabilities). Recently, novel perspectives for the creation of stable 2D and 3D solitons were brought to the attention of researchers inoptics and BEC. The present talk aims to provide an overview of the main results and ongoing developments in this vast field. An essential conclusion is the benefit offered by the exchange of concepts between different areas, such as optics, BEC, and hydrodynamics. Recent review articles and a book on the subject of the talk: Y. Kartashov, G. Astrakharchik, B. Malomed, and L. Torner, Frontiers in multidimensional self-trapping of nonlinear fields and matter, Nature Reviews Physics 1, 185-197 (2019) https://doi.org/10.1038/s42254-019-0025-7. B. A. Malomed, (INVITED) Vortex solitons: Old results and new perspectives, Physica D 399, 108-137 (2019) https://doi.org/10.1016/j.physd.2019.04.009; free access: https://authors.elsevier.com/a/1ZXATc2Eea3QG Z. Luo, W. Pang, B. Liu, Y. Li, and B. A. Malomed, A new form of liquid matter: quantum droplets, Front. Phys. 16, 32501 (2021) https://link.springer.com/article/10.1007/s11467-020-1020-2. B. A. Malomed, Multidimensional dissipative solitons and solitary vortices, Chaos, Solitons & Fractals 163, 112526 (2022) https://doi.org/10.1016/j.chaos.2022.112526. B. A. Malomed, Multidimensional Soliton Systems, Advances in Physics X 9:1, 2301592 (2024). G. Li, Z. Zhao, B. Liu, Y. Li, Y. V. Kartashov, and B. A. Malomed, Can vortex quantum droplets be realized experimentally? Frontiers of Phys. 20, 013401 (2025). B. A. Malomed, Prediction and observation of topological modes in fractal nonlinear optics, Light: Science & Applications 14, 29 (2025). B. A. Malomed, Multidimensional solitons (a book), AIP (American Institute of Physics) Publishing, Melville, NY, 2022. Co-sponsored by: Prof. Nicolas Quesada Speaker(s): Boris J. Armand Bombardier J-2074, Polytechnique Montréal, Montréal, Quebec, Canada, J3X 1P7

Abstract: Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that basic interference phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a Jekyll-and-Hyde sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by basic interference phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the ‘toy field theory’) that reproduces the relevant phenomenology of quantum interference while rejecting these radical interpretational claims. It also reproduces a number of related interference experiments that are thought to support these interpretational claims, such as the Elitzur-Vaidman bomb tester, Wheeler’s delayed-choice experiment, and the quantum eraser experiment. The systems in the toy field theory are field modes, each of which possesses, at all times, both a particle-like property (a discrete occupation number) and a wave-like property (a discrete phase). Although these two properties are jointly possessed, the theory stipulates that they cannot be jointly known. The phenomenology that is generally cited in favour of nonlocal or backwards-in-time causal influences ends up being explained in terms of inferences about distant or past systems, and all that is observer-dependent is the observer’s knowledge of reality, not reality itself. Co-sponsored by: Prof. Nicolas Quesada Speaker(s): David Schmid J. Armand Bombardier J-2074, Polytechnique Montréal, Montréal, Quebec, Canada, J3X 1P7