# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Friday, November 22, 2013, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G11

**Speaker**: Uli Wagner (Institute of Science and Technology Austria)

## Can a balloon be shrunk to a point in the presence of obstacles? --- An Introduction to Computational Homotopy Theory

A classical result on the computational complexity of topological problems is that there is no algorithm to decide whether a given closed loop inside a given "shape" can be contracted to a single point without ever leaving the shape (more formally, it is undecidable whether a given element of the fundamental group of a given space is trivial).

In this talk, we will give a gentle introduction to a family of algorithmic questions of the same flavor, namely concerning the classification, up to continuous deformation, of continuous maps from one space into another. It turns out that for these questions there is a sharp "phase transition" between polynomiality and undecidability: on the one hand, under suitable hypothesis these questions can be solved in polynomial time, but if these hypotheses are slightly relaxed, the questions become undecidable.

This will be a survey on recent joint with Čadek, Krčál, Matoušek, Sergeraert, and Vokřínek.

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