**Distinguished lectures**

**Talk 1: Interpolation of data by smooth functions // Talk 2: Mathematical problems on graphene**

**Speaker:** Charles Fefferman (Princeton University)**Date:** Friday, 15 October 2021 - 15:00 - 17:30**Online:** youtu.be/VER3NzEGLd0

**Abstract:**

**Talk 1: "Interpolation of data by smooth functions"**

Let X be your favorite Banach space of continuous functions on R^n. Given a real-valued function f on a (possibly awful) subset E of R^n, how can we decide whether f extends to a function F:R^n->R in the space X? If such an F exists, then how small can we take its norm in X? What can we say about derivatives of F? Can we take F to depend linearly on f?

Suppose E is finite. Can we compute an F whose norm in X has the least possible order of magnitude? How many computer operations does it take? What if we demand merely that F agree approximately with f on E? What if we are allowed to discard a few data points as "outliers"? Which data points should we discard?

**Talk 2: "Mathematical problems on graphene"**

The talk presents two standard models used by physicists to study the propagation of electrons in graphene. The lecture presents theorems that relate those models to each other, then derive from them some well-known phenomena along with another phenomenon that's not so well known.

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