Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, March 19, 2014.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, March 19, 2014

4:00 pm in 241 Altgeld Hall,Wednesday, March 19, 2014

#### Fool's Solitaire on Graph Joins

###### Sarah Loeb (UIUC Math)

Abstract: The talk will be targeted at an undergraduate audience, but anyone is welcome! No prior knowledge will be expected.

Peg solitaire is a table game people may have played at Cracker Barrel. Beeler and Hoilman generalized the game to connected graphs. A graph is a collection of vertices and edges. In the graph game, pegs are placed on all but one vertex. If $xyz$ form a 3-vertex path and $x$ and $y$ each have a peg but $z$ does not, then we can remove the pegs at $x$ and $y$ and place a peg at $z$. By analogy with the moves in the original game, this is called a jump. The goal of the peg solitaire game on graphs is to find jumps that reduce the number of pegs on the graph to 1.

Beeler and Rodriguez proposed a variant where we instead want to maximize the number of pegs remaining when no more jumps can be made. Maximizing over all initial locations of a single hole, the maximum number of pegs left on a graph $G$ when no jumps remain is the fool's solitaire number $F(G)$. The join of two graphs $G$ and $H$ consists of disjoint copies of $G$ and $H$ and all possible edges between them. We determine the fool's solitaire number for the join of any graphs $G$ and $H$.

4:00 pm in 245 Altgeld Hall,Wednesday, March 19, 2014

#### Informational meeting about a new grant from NSF

###### Professors Baryshnikov, DeVille, and Laugesen (Dept of Mathematics, Univ of Illinois)

Abstract: All U.S. graduate students in Mathematics are invited to this informational meeting about a new grant from NSF. The grant aims to prepare Mathematics graduate students for research outside the Mathematics Department, in interdisciplinary scientific settings, national labs, and industry. The grant will fund students for a mix of on-campus summer activities and off-campus internships, beginning Summer 2014. No previous experience is required in interdisciplinary or industrial mathematics. Please come and explore the possibilities!