Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 3, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, September 3, 2015

11:00 am in 241 Altgeld Hall,Thursday, September 3, 2015

#### Finiteness of unramified deformation rings

###### Patrick Allen (UIUC Math)

Abstract: Class field theory allows one to precisely understand ramification in abelian extensions of number fields. A consequence is that infinite pro-p abelian extensions of a number field are infinitely ramified above p. Boston conjectured a nonabelian analogue of this fact, predicting that certain pro-p representations that are unramified at p act via a finite quotient, and this conjecture strengthens the unramified version of the Fontaine-Mazur conjecture. We show in many cases that one can deduce Boston's conjecture from the unramified Fontaine-Mazur conjecture, which allows us to deduce (unconditionally) Boston's conjecture in many two-dimensional cases. This is joint work with F. Calegari.

1:00 pm in Altgeld Hall 243,Thursday, September 3, 2015

#### On purely loxodromic actions

###### Ilya Kapovich (UIUC Math)

Abstract: Purely loxodromic isometric actions of finitely generated groups on Gromov-hyperbolic spaces (that is, actions where every element of infinite order in the group acts as a loxodromic isometry) appear naturally in many contexts, such as in the theories of hyperbolic, relatively hyperbolic and acylindrically hyperbolic groups, the study of convex cocompact subgroups of mapping class groups, etc. Often one needs to consider non-proper actions, and in that context the notion of an acylindrical action serves as an important substitute of being proper. We construct an example of an isometric action of the free group $F(a,b)$ on a $\delta$--hyperbolic graph $Y$, such that this action is acylindrical, free, purely loxodromic, has asymptotic translation lengths of nontrivial elements of $F(a,b)$ separated away from $0$, has quasiconvex orbits in $Y$, but such that the orbit map $F(a,b)\to Y$ is not a quasi-isometric embedding. View talk at https://youtu.be/y5eXM5Nst0U

2:00 pm in 241 Altgeld Hall,Thursday, September 3, 2015

#### Asymptotics of relative cubic function fields

###### Ravi Kiran Donepudi (UIUC Math)

Abstract: Fix a function field $k$. By Galois theory, every cubic extension of $k$ with Galois group $S_3$ has a unique quadratic sub-extension. So we fix a quadratic extension $K_2/k$ and count the number of cubic extensions of $k$ whose Galois closure contains $K_2$ up to a bounded discriminant. Following a result for number fields by Cohen and Morra (2010), we have an asymptotic formula for this count. Our main tools are Kummer theory and a tauberian theorem. This is joint work with Stefan Erickson and Colin Weir.

2:00 pm in 347 Altgeld Hall,Thursday, September 3, 2015

#### Organizational Meeting

3:00 pm in 243 Altgeld Hall,Thursday, September 3, 2015

#### Organizational Meeting

4:00 pm in 245 Altgeld Hall,Thursday, September 3, 2015