Alternatively have a look at the program.

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We will discuss an equidistribution problem concerning rational planes in four-space. Due to an accidental isomorphism this problem relates in a natural manner to the simultaneous study of four CM-points on the modular surface and two points on the two-dimensional sphere. Using Duke's theorem and a joining classification we obtain joint equidistribution under suitable congruence conditions on the covolume of the planes.

This is joint work with Menny Aka and Andreas Wieser, and relies on a joint theorem with Elon Lindenstrauss.

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## Life and Mathematics of Sergiy Kolyada

## Audience recollections of Sergiy Kolyada

## Special alpha-limit sets

This is an unfinished work, started last year with Sergiy Kolyada and

Lubomir Snoha. I hoped all three of us would complete it during this

meeting...

We investigate the notion of the special alpha-limit set of a point.

For a given map of a compact space to itself, it is defined as the

union of the sets of accumulation points over all backward branches of

the map. We consider mainly the case of interval maps. We give many

examples showing how those sets may look like. The main question is

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## Teichmuller curves mod $p$

A Teichmuller curve is a totally geodesic curve in the moduli space of Riemann surfaces. These curves are defined by polynomials with integer coefficients which are irreducible over $\mathbb C$. We will show that these polynomials have surprising factorizations mod $p$. This is joint work with Keerthi Madapusi Pera.

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