Algebraic topology and homotopy theory constitute central areas of contemporary mathematics, exploring spaces through algebraic invariants and continuous deformations. Techniques in this field ...

When students are genuinely curious about new concepts and ideas, they develop their own study skills, says Professor Pekka Pankka. Geometry, Algebra, and Topology are pure mathematics and essential ...

In the computer vision field of object detection, deep learning models are trained to identify objects of interest within an image of a scene. For example, such models can be trained to detect viruses ...

We consider when it is possible to bound the Lipschitz constant a priori in a homotopy between Lipschitz maps. If one wants uniform bounds, this is essentially a finiteness condition on homotopy. This ...

The Earth's climate system seems to have shifted abruptly between colder and warmer modes in the past. Do we risk the same today from anthropogenic climate change? Frankly, climate models cannot ...

Arunas Liulevicius taught mathematics for 50 years at the University of Chicago, where he twice earned the school’s Llewellyn John and Harriet Manchester Quantrell Award for Excellence in ...

Bartels, Bellissard (until 2021), Böhm, Courtney (2022-2023), Cuntz, Ebert, Echterhoff, Gardam (2022-2023), Gardella (until 2021), Geffen (since 2022), Hein (since ...

In this course we will consider the structure of (infinite) groups. For this, we will study actions of groups on interesting topological and metric spaces. The geometry of these spaces can be used to ...