Talks

Mathematicians have trained themselves to see objects from many points of view. When considering the real numbers, we can as easily see them as equivalence classes of Cauchy sequences, or Dedekind cuts, or the unique uniformly complete Archimedean field. The computer is not as forgiving and forces us to pick a particular definition that we must stick with. Using examples from the Lean mathematical library, Mathlib, I investigate why it is so important to choose the right definition when formalizing, what makes formal definitions look different from pen and paper definitions, and how we can design our definitions to make proofs flow smoothly.

We study some of the properties of non-equilibrium phase transitions of an interacting system that is in a state with large deviation from equilibrium. We consider a field theoretical model of scalar particles interacting with vector gauge fields with local U (1) gauge symmetry. We show that the evolution of this system towards an equilbrium state can be described using the principle of emergence of global gauge invariance. As a toy model we consider a scalar-vector model with local U (1) gauge invariance. Invoking the assumption of local U (1) gauge invariance breaking we evaluate time evolution of some of the observables of this system. To make our calculations explicit we calculate the time evolution of order parameter of this sytem and evaluate its scaling behaviour near transition region. In the mean-field approximation we show that, for the unperturbed case, that correspond to no external driving the order parameter has a universal algebriac decay m(t) ∼ t −1/2 . However for time-dependent diffusion coefficient, it is found that order parametr has a universal algabriac decay m(t) ∼ t −1/3 . The results are in total agreement with the recent findings using stochastic models of non-equilibrium system

In this work, we studied the three-dimensional random field Potts model (RFPM), focusing on its phase transition, which is governed by a random fixed point located at zero temperature. As finding ground states in RFPM is NP-hard, we employed our recently developed quasi-exact scheme based on graph cuts to determine approximate ground states and analyze critical behavior. We evaluated various key observables, such as magnetization, Binder and energy cumulants, specific heat, and susceptibilities, which we extrapolated to the quasi-exact ground state limit. Their finite-size scaling analyses revealed strong evidence for a continuous transition induced by disorder, in contrast to the first-order transition seen in the pure case. Our results suggest a new universality class for q-state RFPM, distinct from the RFIM.

As natural environments are not static, the model parameters in biologically realistic problems are not constant in time, and such situations in population biology are often described in terms of effective parameters that subsume some of the details of the problem; however, it is not always possible to define an effective parameter. I will describe a simple solvable model to address when and why an effective parameter can not be defined, and the implications thereof.

Phase ordering driven by nonequilibrium fluctuations is a hallmark of both living and synthetic active matter. Unlike equilibrium systems, where ordered states arise from the minimisation of free energy, active systems are fueled by the constant injection of energy at the microscopic scale. The emergence of ordered phases in such driven systems challenges our conventional views of domain growth and interfacial structure. In this talk, I will present results on the investigation of coarsening of colloidal clusters in active liquids containing E. coli, highlighting the nature of ordering in systems dominated by strong fluctuations. Our experiments reveal that uniform dispersions of colloids and swimmers are inherently unstable, resulting in spontaneous phase separation characterised by fractal interfaces and unconventional domain growth kinetics.

Fundamental laws of physics are symmetric under time reversal (T) symmetry, hence we are tempted to deduce that the evolution of the world may be T-symmetric. On the other end, there is an important conjecture that a conservative system with many particles becomes randomized. The latter process, called thermalization, is related to the second law of thermodynamics that makes the macroscopic world asymmetric. In addition to these two divergent topics, I will cover additional T-breaking frameworks: multiscale energy transfer, open systems, and asymmetric objects. In driven dissipative nonequilibrium systems, including turbulence, the multiscale energy flux from large scales to small scales helps determine the arrow of time. In addition, open systems are often irreversible due to particle and energy exchanges between the system and the environment.

Discrepancies between Lorentzian and Euclidean calculations of quantum corrections to de Sitter horizon thermodynamics revealed the existence of ‘edge’ degrees of freedom on the horizon. In this talk, I will review these calculations and present updates on understanding the physics of such edge modes in both gauge theories and (higher-spin) gravity. For Einstein gravity, I will discuss a plausible interpretation involving an embedded spherical brane. Finally, I will comment on how these ideas extend to more general black hole spacetimes.