### Mathematics of Diffusive transport with applications to chemoreception and nuclear scaling

Alan Lindsay

Department of Applied & Computational Math & Statistics

University of Notre Dame

Cells grow, divide, and move based on chemical signals received at localized surface receptors. Receptors occupy only a small fraction of the cell surface area, yet cells exhibit exquisite sensory capacity. In this talk I will describe mathematical tools that can be used to analyze the role that receptor organization or clustering plays in biophysical phenomena. This involves a wide array of techniques from asymptotic analysis, homogenization theory, computational PDEs and Bayesian statistical methodologies. I will also describe some recent work on scaling problems with particular focus on the nucleus. In this work, we aim to combine the above mentioned mathematical methods with experimental data to isolate the mechanisms controlling organelle dynamics and equilibrium size.