Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, February 21, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2017          February 2017            March 2017
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  7             1  2  3  4             1  2  3  4
8  9 10 11 12 13 14    5  6  7  8  9 10 11    5  6  7  8  9 10 11
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Tuesday, February 21, 2017

12:00 pm in 243 Altgeld Hall,Tuesday, February 21, 2017

#### Groups Associated with Rational Proper Maps

###### John P. D'Angelo (Illinois Math)

Abstract: Given a rational proper map $f$ between balls of typically different dimensions, we define a subgroup $\Gamma_f$ of the source automorphism group. We prove that this group is noncompact if and only if $f$ is linear. We show how these groups behave under certain constructions such as juxtaposition and partial tensor products. We then sketch a proof of the following result. If $G$ is an arbitrary finite subgroup of the source automorphism group, then there is a rational map $f$ for which $\Gamma_f = G$. We provide many examples and, if time permits, discuss the degree estimate conjecture. This work is joint with Ming Xiao.

1:00 pm in 345 Altgeld Hall,Tuesday, February 21, 2017

#### "Strong theories of ordered abelian groups" by A. Dolich and J. Goodrick (2nd talk)

###### Erik Walsberg (UIUC Math)

2:00 pm in 243 Altgeld Hall,Tuesday, February 21, 2017

#### L^2 extension of d-bar closed forms from hypersurfaces

###### Jeffery McNeal (The Ohio State University)

Abstract: Extending holomorphic functions off of hypersurfaces, with L^2 control, was initiated by pioneering work of Ohsawa and Takegoshi in the late 80s. The original extension results have been greatly generalized, as there are numerous application of such results to problems in analytic geometry. Less is known about extending higher order forms. I will discuss some new results about extension of d-bar closed forms with L^2 estimates. The talk will start with the simplest extension set-up -- a domain in C^n, a hyperplane and functions -- then add apparatus slowly-- moving to manifolds, bundle-valued forms, and curvature conditions. The results discussed were obtained in collaboration with Dror Varolin.

3:00 pm in 241 Altgeld Hall,Tuesday, February 21, 2017

#### Reconstruction from the deck of $k$-vertex induced subgraphs

###### Douglas B. West (Illinois Math and Zhejiang Normal University)

Abstract: The $k$-deck of a graph is its multiset of subgraphs induced by $k$ vertices; we ask whether the $k$-deck determines the graph. We show that a complete $r$-partite graph is determined by its $(r+1)$-deck. Letting $n=|V(G)|$, we generalize a result of Bollobás by showing that for $l=(1-o(1))n/2$, almost every graph $G$ is determined by various sets of ${l+2\choose 2}$ subgraphs with $n-l$ vertices. However, when $l=n/2$, the entire $(n-l)$-deck does not always determine whether $G$ is connected (it fails for $n$-vertex paths). We strengthen a result of Manvel by proving for each $l$ that when $n$ is sufficiently large (at least $l^{l^2}$), the $(n-l)$-deck determines whether $G$ is connected ($n\ge25$ suffices when $l=3$, and $n\le 2l$ cannot suffice). Finally, for every graph $G$ with maximum degree $2$, we determine the least $k$ such that $G$ is reconstructible from its $k$-deck, which involves extending a result of Stanley. This is joint work with Hannah Spinoza.

4:00 pm in 245 Altgeld Hall,Tuesday, February 21, 2017

#### From Computational Algebra to Quantitative Medicine

###### Reinhard Laubenbacher and Anna Konstorum   [email] (Center for Quantitative Medicine, University of Connecticut)

Abstract: In this informal discussion conducted by Skype, the panelists from the Center for Quantitative Medicine at the University of Connecticut will describe their career paths from mathematics into medicine, and then take questions from the audience. Background: Prof. Laubenbacher spent most of his career working in computational algebra and discrete mathematics. Dr. Konstorum's thesis work was in differential equations. All are welcome to participate in this career event!