### Is Galois theory a lousy lover?

Pure Mathematics Postgraduate Seminar

24th November 2017, 4:30 pm – 5:40 pm

Howard House, 4th Floor Seminar Room

We've all noticed it, and frankly, we're not impressed. Group theory has just about put its back out for Galois theory, and what has it done in return? Well, as far as most of us see, just about nothing! But the two were born foreach other! So Galois theory must have surely done something for Group theory in return, but what?

On Friday, we'll have a glimpse at what the two have been getting up to while no one's been looking.

What?! You're still reading this? You mean the above wasn't enough to convince you already? Oh, what's that? You're actually just super interested and just want to know more? Okay well, I suppose I'm feeling generous, so here's a rough idea:

We'll be experiencing two tales about Galois theory and Group theory. The first revolves around a result of Schur, which under a few conditions gives an explicit bound on the order of a finite subgroup of the general linear group. The second will feature Schur indices, and here we'll have a glimpse at their role in a generalisation of the BSD conjecture.

I will assume very little background - Anyone who knows what groups and vector spaces are should be fine. We'll see many examples throughout the talk, which illustrate any definitions that are given.

*Biography:*

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