Symmetries and fluctuations are integral features of nature. We explore their role across three different physical systems. First, we will examine the validity of the geodesic rule, a key postulate of the Kibble-Zurek mechanism, which describes topological defect formation during second-order phase transitions. Through equilibrium Monte Carlo simulations of the XY model and a complex scalar field theory, we find that thermal fluctuations cause a breakdown of the geodesic rule, leading to a higher defect density than standard predictions. In the second case, we analyze how spacetime oscillations influence fluctuations in non-Abelian SU(2) gauge fields. While linearized gauge field analysis reveals parametric resonance arising from oscillatory metric components, the emergence of non-Abelian interactions produces amplified growth in SU(2) gauge fields, leading to increased energy density and tr(FF̃). Finally, we will discuss Z3 symmetry in 2+1 flavor QCD. Dynamical fermion contributions explicitly break the Z3 symmetry, resulting in two metastable states within the deconfined phase at sufficiently high temperatures. Our results suggest that these states may be present at temperature scales(∼446 MeV) achieved in Heavy-ion collision experiments.

A key challenge in development is to understand how complex organisms physically coordinate the morphogenesis of multiple tissues. Here, using biophysical approaches, we investigate how muscles located under the epidermis specifically stimulate the extension of anterior-posterior (AP-oriented) epidermal adherens junctions during late C. elegans embryonic elongation. First, light-sheet imaging shows that asynchronous patterns of muscle contractions drive embryo rotations. In turn, junctions between the lateral and dorso-ventral epidermis repeatedly oscillate between a folded, hypotensed state, and an extended, hypertensed state. Second, FRAP (Fluorescence Recovery After Photobleaching) analysis of an E-cadherin::GFP construct shows that muscle contractions stimulate E-cadherin turnover. Moreover, a mechano-chemical model recapitulating in vivo observations predicts that enhanced accumulation of E-cadherin along AP-oriented junctions lowers their line tension and further favors their elongation. It also allows us to quantify mechanical forces without any disruption of embryo anatomy. Altogether, our results illustrate how muscle contractions fluidize epidermal adherens junctions, which, combined with anisotropic tension within the epidermis, drives their polarized extension.

Understanding the nature of dark matter, such as its intrinsic spin, mass, interaction strengths, whether it is single- or multi-component, and its origin in the early universe, remains an unresolved mystery in particle physics. In this seminar, I will discuss a minimal two-component dark matter framework, constructed by extending the Standard Model with a scalar and a fermionic SU(2)L​ doublet. The interplay of both components enables the model to naturally accommodate the observed relic abundance, even in regions that would otherwise predict under-abundance. Finally, I will outline potential signals at the upcoming Large Hadron Collider (LHC) that could help distinguish such a two-component dark matter scenario. In the second part of the seminar, I will discuss possible connections among dark matter, the matter–antimatter asymmetry, and the origin of neutrino masses. An extension of the Standard Model with a complex scalar and right-handed neutrinos can simultaneously address these issues while also realising a first-order phase transition that may leave detectable imprints as stochastic gravitational waves. Finally, I will briefly outline some of my ongoing and future projects. Refs: (1) arXiv:2505.02816 (communicated to PRD) (2) arXiv:2409.17067 (communicated to EPJC)

Forecasting chaotic dynamical systems is a central challenge across science and engineering. In this talk, we will explore how random feature maps can be adapted to deliver remarkably strong performance on this task. A key ingredient for successful forecasting is ensuring that the features produced by the model lie in the nonlinear region of the activation function. We will see how this can be achieved through careful selection of the internal weights in a data-driven way using a hit-and-run algorithm. With a few additional modifications, such as increasing the depth of the model and introducing localization, we can achieve state-of-the-art forecasting results on a variety of high-dimensional chaotic systems, reaching up to 512 dimensions. Our method produces accurate short-term trajectory predictions, as well as reliable estimates of long-term statistical behavior in the test cases.

Peptide conformations underpin cell signaling, drug design, and protein-structure prediction, yet distributions for longer peptides are hard to obtain because experimental resources (e.g., PDB) are sparse beyond di-/tripeptides. This thesis uses optimal transport to build conformational distributions for longer chains: starting from dipeptide statistics, we construct tetrapeptide distributions by minimizing expected interaction energies and then extend the procedure recursively. Applied to alanine/glycine tetrapeptides, the method captures right-handed α-helix preferences in alanine-rich sequences (AAAA, AAAG) and β-turn tendencies in glycine-rich ones (GGGG, GAGG). The framework yields scalable conformational probabilities for longer peptides, enabling efficient prediction of flexibility and bioactive low-energy states.