Title: Some recent results on arboreal Galois groups [POSTPONED] Speaker: Robert Benedetto (Amherst College)
Time: Wednesday, January 17, 2018 at 11:15 am Place: MONT 313Abstract: Let $K$ be a number field, let $f\in K(x)$ be a rational function of degree $d$, and let $a\in K$. The roots of $f^n(z)-a$ are the $n$-th preimages of $a$ under $f$, and they have the natural structure of a $d$-ary rooted tree $T$. There is a natural Galois action on the tree, inducing a representation of the absolute Galois group of $K$ in the automorphism group of $T$. In many cases, it is expected that the image of this arboreal Galois representation has finite index in the automorphism group, but in some cases, such as when f is postcritically finite (PCF), the image is known to have infinite index. In this talk, I'll describe some recent results on arboreal Galois groups of certain polynomials, in both the PCF and non-PCF cases.Comments: This talk has been canceled due to weather and will be rescheduled later.

Title: Spring Semester Meet and Greet Speaker: All Graduate Students (University of Connecticut)
Time: Friday, January 19, 2018 at 12:20 pm Place: MONT 214Abstract: This is an opportunity to meet new graduate students and reintroduce returning graduate students to the SIGMA seminar series.

Title: Embeddings of the Heisenberg group and the Sparsest Cut problem Speaker: Robert Young (Courant Institute)
Time: Friday, January 19, 2018 at 1:30 pm Place: MONT 414Abstract: The Heisenberg group $\mathbb{H}$ is a sub-Riemannian manifold that is hard to embed in $\mathbb{R}^n$. Cheeger and Kleiner introduced a new notion of differentiation that they used to show that it does not embed nicely into $L_1$. This notion is based on surfaces in $\mathbb{H}$, and in this talk, we will describe new techniques that let us quantify the "roughness" of such surfaces, find sharp bounds on the distortion of embeddings of $\mathbb{H}$, and estimate the accuracy of an approximate algorithm for the Sparsest Cut Problem. (Joint work with Assaf Naor)