Department of

# Mathematics

Seminar Calendar
for Geometry, Groups, and Dynamics/GEAR Seminar events the year of Tuesday, February 19, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2019          February 2019            March 2019
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5                   1  2                   1  2
6  7  8  9 10 11 12    3  4  5  6  7  8  9    3  4  5  6  7  8  9
13 14 15 16 17 18 19   10 11 12 13 14 15 16   10 11 12 13 14 15 16
20 21 22 23 24 25 26   17 18 19 20 21 22 23   17 18 19 20 21 22 23
27 28 29 30 31         24 25 26 27 28         24 25 26 27 28 29 30
31


Thursday, January 17, 2019

12:00 pm in 243 Altgeld Hall,Thursday, January 17, 2019

#### Index properties of random automorphisms of free groups.

###### Ilya Kapovich (Hunter College)

Abstract: For automorphisms of the free group $F_r$, being "fully irreducible" is the main analog of the property of being a pseudo-Anosov element of the mapping class group. It has been known, because of general results about random walks on groups acting on Gromov-hyperbolic spaces, that a "random" (in the sense of being generated by a long random walk) element $\phi$ of $Out(F_r)$ is fully irreducible and atoroidal. But finer structural properties of such random fully irreducibles $\phi\in Out(F_r)$ have not been understood. We prove that for a "random" $\phi\in Out(F_r)$ (where $r\ge 3$), the attracting and repelling $\mathbb R$-trees of $\phi$ are trivalent, that is all of their branch points have valency three, and that these trees are non-geometric (and thus have index $<2r-2$). The talk is based on a joint paper with Joseph Maher, Samuel Taylor and Catherine Pfaff.

Thursday, January 24, 2019

12:00 pm in 243 Altgeld Hall,Thursday, January 24, 2019

#### Stretch Factors Coming From Thurston's Construction

###### Joshua Pankau (U Iowa)

Abstract: Associated to every pseudo-Anosov map is a real number called its stretch factor. Thurston proved that stretch factors are algebraic units, but it is unknown exactly which algebraic units are stretch factors. In this talk I will discuss a construction of pseudo-Anosov maps due to Thurston, and discuss my recent results where I classified (up to power) the stretch factors coming from this construction. We will primarily focus on a specific class of algebraic units known as Salem numbers. This talk is intended to be accessible to everyone.

Tuesday, January 29, 2019

12:00 pm in 243 Altgeld Hall,Tuesday, January 29, 2019

#### The Farey Sequence Next-Term Algorithm, and the Boca-Cobeli-Zaharescu Map Analogue for Hecke Triangle Groups G_q

###### Diaaeldin Taha (University of Washington)

Abstract: The Farey sequence is a famous enumeration of the rationals that permeates number theory. In the early 2000s, F. Boca, C. Cobeli, and A. Zaharescu encoded a surprisingly simple algorithm for generating--in increasing order--the elements of each level of the Farey sequence as what grew to be known as the BCZ map, and demonstrated how that map can be used to study the statistics of subsets of the Farey fractions. In this talk, we present a generalization of the BCZ map to all Hekce triangle groups G_q, q \geq 3, with the G_3 = SL(2, \mathbb{Z}) case being the "classical" BCZ map. If time permits, we will present some applications of the G_q-BCZ maps to the statistics of the discrete G_q linear orbits in the plane \mathbb{R}^2 (i.e. the discrete sets \Lambda_q = G_q (1, 0)^T).

Tuesday, February 5, 2019

12:00 pm in 243 Altgeld Hall,Tuesday, February 5, 2019

#### Asymptotics of the expected diameter of translation surfaces

###### Anja Randecker (U Toronto)

Abstract: For the hyperbolic structure on a Riemann surface, Mirzakhani has proven asymptotics of the expected diameter for large genus surfaces. An abelian differential equips a Riemann surface with a translation structure. In joint work with Howard Masur and Kasra Rafi, we prove asymptotics for large genus translation surfaces of area 1. Unlike in the case of hyperbolic surfaces, the expected diameter goes to zero as the genus goes to infinity.

Tuesday, February 26, 2019

12:00 pm in 243 Altgeld Hall,Tuesday, February 26, 2019

#### Congruence subgroups in genus one

###### Autumn Kent (U Wisconsin)

Abstract: I’ll discuss a proof of Asada’s theorem that mapping class groups of punctured tori have the congruence subgroup property.

Thursday, March 14, 2019

12:00 pm in 243 Altgeld Hall,Thursday, March 14, 2019

###### Pierre Will (Institut Fourier)

Abstract: In this talk, I will explain how it is possible to construct interesting geometric structures modelled on the boundary at infinity of the complex hyperbolic 2-space. In particular, I will describe examples of hyperbolic 3-manifolds that appear this way. This talk is based on joint works with Antonin Guilloux, and John Parker.

Thursday, March 28, 2019

12:00 pm in 243 Altgeld Hall,Thursday, March 28, 2019

#### To Be Announced

###### Sunny Xiao (Brown U)

Abstract: TBA

Thursday, April 25, 2019

12:00 pm in 243 Altgeld Hall,Thursday, April 25, 2019

Abstract: TBA