Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, August 27, 2013.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2013             August 2013           September 2013
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1  2  3  4  5  6                1  2  3    1  2  3  4  5  6  7
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Tuesday, August 27, 2013

11:00 am in 243 Altgeld Hall,Tuesday, August 27, 2013

#### Always-Cartesian Cubes

###### Rosona Eldred (Hamburg)

Abstract: Homotopy limits are well-modeled by mapping spaces; a map of diagrams induces a map the other direction on homotopy limits. To map from larger to smaller homotopy limits is very natural, but to build a "wrong way" map, and to get that map for all homotopy functors applied to your diagram -- this is where always cartesian cubes come in. In this talk I will give a classification of square diagrams which are homotopy pullbacks (i.e. cartesian) and which retain this property when any equivalence-preserving functor is applied, as well as discuss work towards a classification for higher dimensional cubes.

1:00 pm in 345 Altgeld Hall,Tuesday, August 27, 2013

#### The Asymptotic Couple of the Field of Purely Logarithmic Transseries

###### Allen Gehret (UIUC Math)

Abstract: We will define the valued differential fi eld of purely logarithmic transseries. Next we will define the asymptotic couple for this fi eld, which is the value group with additional structure induced by the field derivation. Finally we will discuss a quantifier elimination result for this asymptotic couple and some corollaries.

2:00 pm in Altgeld Hall 347,Tuesday, August 27, 2013

#### Estimates on the transition densities of symmetric Markov processes dominated by stable-like processes in $C^{1,\gamma}$ open sets

###### Panki Kim (Seoul National University)

Abstract: In this talk, we discuss the behavior of transition density (Dirichlet heat kernel) for a large class of symmetric pure jump Markov processes in open subset. The jumping kernels of symmetric Markov processes we consider are dominated by the one of stable like processes. We present a recent result on the sharp Dirichlet heat kernel estimates on $C^{1, \gamma}$-open sets. This talk is based on a joint work with Kyung-Youn Kim.

3:00 pm in 241 Altgeld Hall,Tuesday, August 27, 2013

#### On the number of $K_4$-saturating edges

###### Hong Liu   [email] (UIUC Math)

Abstract: Let $G$ be a $K_4$-free graph, an edge in its complement is a $K_4$-saturating edge if the addition of this edge to $G$ creates a copy of $K_4$. Erdős and Tuza conjectured that for any $n$-vertex $K_4$-free graph $G$ with $\lfloor n^2/4\rfloor+1$ edges, one can find at least $(1+o(1))\frac{n^2}{16}$ $K_4$-saturating edges. We construct a graph with only $\frac{2n^2}{33}$ $K_4$-saturating edges. Furthermore, we prove that it is best possible, i.e., one can always find at least $(1+o(1))\frac{2n^2}{33}$ $K_4$-saturating edges in an $n$-vertex $K_4$-free graph with $\lfloor n^2/4\rfloor+1$ edges.
This is a joint work with Jozsef Balogh.

3:00 pm in 243 Altgeld Hall,Tuesday, August 27, 2013

#### Organizational Meeting

###### friends of A. Coble (UIUC)

4:00 pm in 243 Altgeld Hall,Tuesday, August 27, 2013

#### Organizational Meeting

Abstract: We will discuss the structure and schedule of the seminar. We'll be taking speakers slots too, so if you'd like to give a talk or know someone who would, please come. There will be cookies.