I have recently stumbled upon two amazing paper by D.W Roeder which aim to view Pontryagin Duality categorically. Before going into detail, let’s formulate what we’re dealing with. 325 more words

## Tags » Group Theory

#### I have Raman pouring out of my ears!

I again spent most of today reading about Raman spectroscopy of graphene for my talk. I’m actually starting to understand and make some progress though. Of course I started this morning with two basic questions. 458 more words

#### Today is his birthday. He had only 20 of them.

French mathematician Evariste Galois was born on this day in 1811.

His life was full of promise…and turmoil. He made major contributions to math while still a teenager, and his work was fundamental for several different fields of math including… 42 more words

#### Isomorphic groups from linear algebra

Although algebraic structures (such that groups, rings, fields, etc.) are generally difficult to classify, surprisingly linear algebra tells us that vector spaces (over a fixed field) are classified up to isomorphism by only one number: the dimension! 299 more words

#### a poem, a strategic lemma

Lemma

,

such that .

Proof:

By employing the **Double Coset Counting Formula** we have , and since then such that .

But so , hence, having , this implies that , where .

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