Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, October 28, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2014          October 2014          November 2014
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  6             1  2  3  4                      1
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30


Tuesday, October 28, 2014

11:00 am in 243 Altgeld Hall,Tuesday, October 28, 2014

#### Representation stability for homotopy groups of configuration spaces

###### Jeremy Miller (Stanford University)

Abstract: In the 1970s, McDuff proved that configuration spaces of distinct unordered particles in an open manifold exhibit homological stability. That is, H_i(Conf_k(M)) is independent of k for k>>i. A natural follow up question is: Do the homotopy groups also stabilize? From explicit calculations, one can show that this is not the case. However, in joint work with Alexander Kupers, I have shown that the rational homotopy groups of configuration spaces of particles in simply connected manifolds of dimension at least 3 exhibit representation stability in the sense of Church and Farb. This follows from a more general theorem we prove relating the homotopy groups and cohomology groups of co-FI-spaces and from the work of Church on representation stability for the cohomology of ordered configuration spaces. This result on homotopy groups suggests that in situations with homological stability, one should not expect classical stability for homotopy groups. Instead, one should try to incorporate the fundamental group into one's definition of stability.

1:00 pm in Altgeld Hall 243,Tuesday, October 28, 2014

#### Gap distribution for saddle connections on the octagon

###### Grace Work (UIUC Math)

Abstract: We will describe the strategy used to explicitly compute the limiting gap distribution for slopes of saddle connections on the octagon. This is the first such computation where the Veech group of the translation surface has multiple cusps. This is joint work with Caglar Uyanik. View talk at http://youtu.be/9ui5dm5n5KU

1:00 pm in Altgeld Hall,Tuesday, October 28, 2014

#### No seminar

Abstract: No seminar---Midwest Model Theory Day in Chicago

1:00 pm in 347 Altgeld Hall,Tuesday, October 28, 2014

#### CANCELLED

###### Chanwoo Kim (Wisconsin-Madison)

2:00 pm in 347 Altgeld Hall,Tuesday, October 28, 2014

#### Coalescence in branching trees with application to branching random walks.

###### Krishna Athreya (Iowa State University)

Abstract: Consider a single type Galton Watson branching tree that is super critical with no extinction. Pick two individuals at random by srswor from the nth generation and trace their lines of descent back in time till they meet.Call that generation number the coalescence time Xn. This talk will address the problem of determining the limit behavior of Xn as n goes to infinity for both supercritical and explosive cases. An application to branching random walks will also be discussed.

3:00 pm in 241 Altgeld Hall,Tuesday, October 28, 2014

#### Extending factorizations of complete uniform hypergraphs

###### Amin Bhamanian   [email] (Illinois State Math)

Abstract: We consider when a given $r$-factorization of the complete uniform hypergraph on $m$ vertices $K_m^h$ can be extended to an $s$-factorization of $K_n^h$. The case of $r=s=1$ was first posed by Cameron in terms of parallelisms, and solved by Häagkvist and Hellgren. We extend these results, which themselves can be seen as extensions of Baranyai's Theorem. For $r=s$, we show that the "obvious" necessary conditions, together with the condition that $\gcd(m,n,h)=\gcd(n,h)$ are sufficient. For $r < s$ we show that the obvious necessary conditions, augmented by $\gcd(m,n,h)=\gcd(n,h)$, $n\geq2m$, and $1 \leq \frac{s}{r} \leq \frac{m}{k} \left(1 -\binom{m-k}{h}/\binom{m}{h}\right)$ are sufficient, where $k=\gcd(m,n,h)$. Joint work with Mike Newman.