# Scientific

## 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).

## Mathematical Cell Biology Summer Course Student Lecture 9

Size regulation in cell organelles

## Mathematical Cell Biology Summer Course Student Lecture 8

Mechanics of invadopods

## Asymptotic dimension

Most of the talk will be an introduction to (second) bounded cohomology of a discrete group. I will explain classical constructions of bounded cocycles and recent results (joint with Bromberg and Fujiwara) regarding mapping class groups and a construction of bounded cocycles with coefficients in an arbitrary unitary representation.

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## Second Bounded Cohomology

Most of the talk will be an introduction to (second) bounded cohomology of a discrete group. I will explain classical constructions of bounded cocycles and recent results (joint with Bromberg and Fujiwara) regarding mapping class groups and a construction of bounded cocycles with coefficients in an arbitrary unitary representation.

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## Mathematical Cell Biology Summer Course Student Lecture 7

Transport of early endosomes on microtubules

## Mathematical Cell Biology Summer Course Student Lecture 6

Reaction diffusion patterns

## Mathematical Cell Biology Summer Course Student Lecture 5

Glucose, Insulin, and beta cell dynamics

## Mathematical Cell Biology Summer Course Student Lecture 4

Positional information and gradients

## Mathematical Cell Biology Summer Course Student Lecture 3

Local Pulse Analysis applied to polarization models