Geometric Group Theory

Students of the "Introduction to Geometric Group Theory" course at Prishtina International Summer University 2022, tweeting about cool math stuff.

[Geometric Group Theory @GroupGeometric]

The Nielsen–Schreier theorem states that if H is a subgroup of a free group G, then H is itself isomorphic to a free group. So, there exists a set S of elements which generate H, with no nontrivial relations among the elements of S. Read this for more: https://t.co/tqzkW75kRp

[Geometric Group Theory @GroupGeometric]

#Inverse #mathematics
This would have been life if we lived in inverse world

[Geometric Group Theory @GroupGeometric]

#geometry #FunFacts
DID YOU KNOW?

“Geometric group theory study the finitely of generated groups via exploring the connections between algebraic properties of groups,topological and geometric properties of spaces on which these groups act.”

[Geometric Group Theory @GroupGeometric]

When you want to take a break and go to holiday, but everything reminds you of math😂. #treegraph #geometry #algebra

[Geometric Group Theory @GroupGeometric]

Daily reminder🤣:

[Geometric Group Theory @GroupGeometric]

#amenability #maths #geometricgrouptheory

[Geometric Group Theory @GroupGeometric]

Construct an oriented graph on the sidewalk pattern in the photo such that the graph will have minimal number of edges and will go through the points P I S U, in that order.

#maths #graphs #geometricgrouptheory

[Geometric Group Theory @GroupGeometric]

A mess it is 😩

#geometricgrouptheory #groups #maths

[Quanta Magazine @QuantaMagazine]

As the quartet of mathematicians dove in to the near 50-year-old problem, they found roadblocks everywhere. “It became pretty clear pretty quickly why this problem had not been solved,” said one of the four. https://t.co/1xvEzOlrIJ

[Geometric Group Theory @GroupGeometric]

➡️🛏🌙

#geometricgrouptheory #maths

[Geometric Group Theory @GroupGeometric]

Did you know that it is possible to cut a solid ball into 5 pieces, and by re-assembling them, using rigid motions only, form TWO solid balls, EACH THE SAME SIZE AND SHAPE as the original? 

Read this! https://t.co/xkZH5RHO2X

[Geometric Group Theory @GroupGeometric]

#graphs #geometricgrouptheory 😅

[Geometric Group Theory @GroupGeometric]

Here's the Cayley graph for (G, •) = (Z^2, +), S = {(1, 0), (0, 1)} 😅

[Geometric Group Theory @GroupGeometric]

Ehh normal groups 🤣🤣
#normalgroups #abstractalgebra #PISU

[Geometric Group Theory @GroupGeometric]

Walking through Skënderbeu square we noticed this cube. Just so you know this cube has 48 isometries (symmetry elements) and that set forms a group in relation to composition of functions.

[Geometric Group Theory @GroupGeometric]

When the professor assigns you some exercises with groups but he is too generous that he says that the given group is an…

[Geometric Group Theory @GroupGeometric]

Did you know that we use graphs euphemistically even in astronomy?

Since in astronomy, we always need to locate any distant planet, star, constellation and many more, we use graphs and graph theory to determine them, or at least just to locate them.
Here, it is an example:

[Geometric Group Theory @GroupGeometric]

When you are on your trip but you are a math student and now even trees looks like trees🌳🪵
#math #summerschool2022

[Geometric Group Theory @GroupGeometric]

- When you start working for a Corporate after studying Graph Theory for a semester😅

[Geometric Group Theory @GroupGeometric]

In the mathematical subject of geometric group theory, a train track map is a continuous map f from a finite connected graph to itself which is a homotopy equivalence and which has particularly nice cancellation properties with respect to iterations.
#geometricgrouptheory