Be'eri Greenfeld (Bar-Ilan University) Residual Girth of Groups and Algebras (01/11/2017) A conjugacy limit group is the limit of a sequence of conjugates of the positive diagonal Cartan subgroup, C of SL(n) in the Chabauty topology. Over R, the group C is naturally associated to a projective n-1 simplex. We can compute the conjugacy limits of C by collapsing the n-1 simplex in different ways. In low dimensions, we enumerate all possible ways of doing this. In higher dimensions, we show there are infinitely many non-conjugate limits of C. In the Q_p case, SL(n) has an associated p+1 regular affine building. (We'll give a gentle introduction to buildings in the talk). The group C stabilizes an apartment in this building, and limits are contained in the parabolic subgroups stabilizing the facets in the spherical building at infinity. There is a strong interplay between the conjugacy limit groups and the geometry of the building, which we exploit to extend some of the results above. The Q_p part is joint work in progress with Corina Ciobotaru. Residual Girth of Groups and Algebras (01/11/2017) Be'eri Greenfeld (Bar-Ilan University) Residual girth of finitely generated (residually finite) groups measures how large are finite quotients into which the n-ball of the Cayley graph injects. While for a general group the residual girth may grow arbitrarily fast, bounds are known for special classes of groups (e.g. nilpotent, linear etc.) . We study an analogous notion for algebras. We compare the residual girth of a group with that of its group algebra, showing they need not coincide. We prove that for special classes of algebras (e.g. representable algebras) the residual girth is asymptotically equivalent to the growth in the sense of the GK-dimension. Examples are constructed to show that without special assumptions on the algebra, its residual girth can be arbitrarily fast.