# Mathematics

## Random Maps 1

## Interacting Particle Systems 1

## Balanced self-interacting random walks

N.B. Due to microphone problems, the audio at the beginning of this recording is poor.

It is well known that a random walk in d>2 dimensions where the steps are i.i.d. mean zero and fully supported (not restricted to a hyperplane), is transient. Benjamini, Kozma and Schapira asked if we still must have transience when each step is chosen from either μ1 or μ2 based on the past, where μ1 and μ2 are fully supported mean zero distributions. (e.g. we could use μ1 if the current state has been visited before, and μ2 otherwise). We answer their question, and show the answer can change when we have three measures instead of two. To prove this, we will adapt the classical techniques of Lyapunov functions and excessive measures to this setting. No prior familiarity with these methods will be assumed, and they will be introduced in the talk. Many open problems remain in this area, even in two dimensions. Lecture based on joint work with Serguei Popov (Campinas) and Perla Sousi (Cambridge).

## Asymptotic dimension

## Second Bounded Cohomology

## On growth and form: geometry, physics and biology

## Mathematical Cell Biology Summer Course Lecture 36

## Mathematical Cell Biology Summer Course Lecture 35

- Regulatory circuits in Bacterial Chemotaxis and motility
- Introduction to molecular motors, porters vs rowers and cooperativity of myosin in muscle
- Microtubule dynamics
- Cytokinesis
- FRAP studies of microtubule dynamics in the mitotic spindle