RESEARCH

A. Stochastic and nonequilibrium processes

1. Boundary conditions for stochastic differential equations (SDEs): Encounter-based models of absorption; semi-permeable interfaces and snapping out BM; sticky boundaries; stochastically gated boundaries.

2. Diffusion in singularly perturbed domains: narrow capture problems; accumulation-times; encounter-based models; semi-permeable interfaces; applications to synaptic receptor trafficking and bacterial quorum sensing

3. Stochastic resetting: nonequilibrium stationary states; first-passage time problems; stochastic thermodynamics; randomly switching potentials; accumulation times; encounter-based models and semipermeable membranes; applications to cellular transport processes

4. Stochastic interacting particle systems: mean field theory; generalized McKean-Vlasov equations; effects of stochastic resetting, absorbing boundaries and switching potentials; applications to colloids, coupled phase oscillators, spiking neural networks

5. Cellular self-organisation: active phase separation and biological condensates; protein aggregation in membranes; cellular length control; cell polarisation

6. Active particles: trapping of active particles at partially absorbing or sticky walls; mean field theory; effects of stochastic resetting

7. Stochastically switching (hybrid) systems: environmental vs particle switching; stochastic hybrid path integrals and large deviations

B. Stochastic models of cellular transport

1 .Cytoneme-based morphogenesis and viral spread,

2. Axonal motor transport

3. Queuing theory of target resource accumulation

4. Stochastically switching diffusion processes: applications to gap junctions, ion channels, nuclear transport, protein concentration gradients

5. Protein receptor trafficking and synaptic plasticity

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