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Archives
Tag Archives: Lattices
Lattice parametrization
We came to the point where we have already seen how lattices appear naturally in problems arising from number theory. In this post we construct a nice space which parametrize the set of all lattices of a certain dimension, with … Continue reading
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Tagged Homogeneous spaces, Hyperbolic space, Lattices, SL_2(Z)
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The rise of algebraic extensions
In the post about number theory and lattices, we tried to determine when is the Euclidean distance in is actually a Euclidean norm and we were led to study the embeddings of rings such as as lattices in . As mentioned … Continue reading
From number theory to geometry of lattices
Number theory can mean a lot of thing to a lot of people. This is a very big part of mathematics, and it contains many areas starting with the elementary number theory (“simple” congruence like arguments), algebraic number theory (e.g. … Continue reading
From Diophantine approximation to geometry of numbers
We all know about Pythagoras and his obsession with triangles. Usually when we first learn about the rational and real numbers, we are also told about the Pythagoreans, a 6th century BCE cult that started with the followers of Pythagoras and … Continue reading
A wild lattice appears
A couple of years ago I began doing some research in a new mathematical area (at least new for me) and suddenly lattices began to appear everywhere. The thing that makes these lattices interesting is how they are connected to … Continue reading