We explain our proof of the unbounded denominators conjecture.
This talk will require the main theorem of the lecture on Nov. 17,
2021, as a “black box” but otherwise be logically
independent of that talk.
Let f=?anxn??[x] be a power series which is also a meromorphic
function in some neighborhood of the origin. The subject of the
talk will be how certain conditions on f(x) as a meromorphic
function actually guarantee that f(x) is an algebraic...
Somehow, despite the title, SL(2,Z) is the poster child for
arithmetic groups not satisfying the congruence subgroup property,
which is to say that it has finite index subgroups which can not be
defined by congruence conditions on their coefficients...
After surveying some important consequences of the property of
bounded generation (BG) dealing with SS-rigidity, the congruence
subgroup problem, etc., we will focus on examples of boundedly
generated groups. We will prove that every unimodular
I'll describe a method for analyzing the first-order theory of
an arithmetic group using its congruence quotients. When this
method works, it gives a strong form of first-order rigidity
together with a complete description of the collection of...