Talks

In this talk, I will discuss a birational realization of King's conjecture which is indeed true, and its connections with noncommutative algebraic geometry and mirror symmetry. In particular, I will also establish the A-side analog of this result using constructible sheaves and promote the celebrated Coherent-Constructible Correspondence to a global family. The talk is based on recent joint work https://arxiv.org/abs/2501.00130 and work in preparation with David Favero.

Concentrated electrolytes have the potential to improve the mechanical stability of rechargeable batteries. Using molecular dynamics simulations, we calculated the ionic conductivity of highly concentrated EC-LiTFSI electrolytes at varying salt concentrations ranging between 0.005 M and 2.5 M and examined the ion transport mechanisms. Ionic conductivity is found to increase at low salt concentrations before declining at higher salt concentrations beyond 0.6 M. Our extensive simulations and analyses suggest a universal relationship between the ionic conductivity and c as σ(c)~c^α e^(-c/c_0 ) The proposed relationship convincingly explains the ionic conductivity over a wide range of c, where the term c^α accounts for the uncorrelated motion of ions and e^(-c/c_0 ) captures the salt-induced changes in shear viscosity. Our simulations suggest vehicular mechanism to be dominant at low c regimes, which transition into a Grotthuss mechanism at high c regime, where structural relaxation is the dominant form of ion transport mechanism.

Two dimensional elastic tethered membranes (ball-and-spring model) with finite bending rigidity and no self-avoidance are known to exist in a flat/crumpled phase for small/large temperatures. The change in phase is mediated by a second order phase transition. Once self-avoidance is introduced, the tethered membranes do not exhibit a crumpled phase and remain flat for all temperatures. By considering the nodes of the membrane as active Brownian particles, we observe that membranes without self-avoidance retain the crumpling transition with activity as the tuning parameter. We find evidence of a crumpled phase with Flory dimensions of 2.4 in spherical self-avoiding active membranes.

We present PIC-VIC, a novel computational framework for simulating collective behavior of self-propelled particles on curved surfaces. Building upon the Particle-in-Cell (PIC) method, widely used in plasma physics, we track individual particles (Lagrangian description) while employing a static Eulerian mesh for interaction calculations. Using mesh with arbitrary geometries we extend the Vicsek model to study flocking dynamics on curved manifolds. Crucially, we incorporate Laplace-Beltrami based vector diffusion to ensure geometrically consistent averaging of particle velocities, effectively implementing parallel transport on the curved surface. This particle-based PIC-VIC method complements continuum active-hydrodynamics approaches and allows for the investigation of curvature-induced fluctuations. We demonstrate the capabilities of PIC-VIC and discuss its potential for uncovering novel collective phenomena, emergent patterns, and geometry-driven interactions in biological, physical, and artificial systems constrained to non-Euclidean spaces.

We study the nonequilibrium stationary state (NESS) induced by quantum resetting of a system of N noninteracting bosons in a harmonic trap. Under repeated resetting, the system reaches a NESS where the positions of bosons get strongly correlated due to simultaneous resetting induced by the trap. We fully characterize the steady state by analytically computing several physical observables such as the average density, extreme value statistics, order and gap statistics, and also the distribution of the number of particles in a region [−L,L], known as the full counting statistics (FCS). This is a rare example of a strongly correlated quantum many-body NESS where various observables can be exactly computed.

Emergence of different interesting phenomena in different scale is the heart of different physical system in mother nature. In this presentation, we show explicitly how the strong correlation appears in double frequency sine-Gordon field theory. Our study is the detail quantum field theoretical derivation of strongly correlated quantum Ising model.