BMS scolloquium

Probability, Geometry, and algorithms ,[object Object]

How do we make a simple object ,[object Object],[object Object],[object Object]

Why is linear good? ,[object Object],hard

Why is continuous good? ,[object Object],[object Object]

Abelian is good ,[object Object]

Now, apply the above to groups: ,[object Object],[object Object],[object Object]

How easy is ,[object Object],is known as harmonic analysis

Obviously too easy. ,[object Object],[object Object]

The Prime Number Theorem ,[object Object],[object Object]

(Some confusion) ,[object Object]

Another continuous, linear, abelian group ,[object Object],[object Object]

Analogue of prime number theorem? ,[object Object],[object Object],[object Object]

The study of Z n ,[object Object]

Now, let’s remove commutativity ,[object Object]

What is a lattice? ,[object Object],[object Object]

Geometry of lattices: examples ,[object Object]

Everyone’s favorite lattice ,[object Object]

More generally ,[object Object]

More favorites ,[object Object],[object Object]

Why “principal”? ,[object Object]

(Hard) exercises ,[object Object],[object Object],[object Object],[object Object]

Congruence subgroup property (CSP) ,[object Object]

Is a random matrix in SL(n, Z ) irreducible? ,[object Object],[object Object]

Second question first... ,[object Object]

First question is harder: ,[object Object],[object Object]

[object Object],[object Object]

[object Object],[object Object],Luckily, in both cases the answer is the same

Generating sets ,[object Object],[object Object]

How are results like this proved? ,[object Object],[object Object]

To get convergence rates ,[object Object],[object Object],[object Object]

Property T, continued ,[object Object]

Going even further from continuous ,[object Object],[object Object]

Is a group Zariski dense? ,[object Object],[object Object]

Unlike for lattices ,[object Object],[object Object],[object Object]

Why undecidable? ,[object Object],[object Object]

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