UIUC Dept. of Mathematics Seminar Calendar

     August 2011           September 2011          October 2011    
 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                      1
  7  8  9 10 11 12 13    4  5  6  7  8  9 10    2  3  4  5  6  7  8
 14 15 16 17 18 19 20   11 12 13 14 15 16 17    9 10 11 12 13 14 15
 21 22 23 24 25 26 27   18 19 20 21 22 23 24   16 17 18 19 20 21 22
 28 29 30 31            25 26 27 28 29 30      23 24 25 26 27 28 29
                                               30 31

Tuesday, September 6, 2011

Topology Seminar
11:00 am in 241 Altgeld Hall, Tuesday, September 6, 2011

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Submitted by franklan.

Matthew Ando (UIUC)
Equivariant elliptic cohomology and the Tate curve

Number Theory
1:00 pm in 241 Altgeld Hall, Tuesday, September 6, 2011

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Bruce Berndt (UIUC)
A Lattice Sum from a Monthly Problem
Abstract: Three of the American Mathematical Monthly Problems Editors contacted the speaker over three years ago about a conjecture made by George Lamb in connection with his attempt to solve a problem proposed in the Monthly. The problem concerned the evaluation of a certain doubly infinite lattice sum. In joint work with recent Illinois postdoc Mat Rogers, the Monthly problem and Lamb's conjecture were solved. We observed that our ideas could be extended to evaluate many more lattice sums. Keys to our evaluations are theorems of Jacobi and Ramanujan on theta functions, and the Jacobian elliptic functions.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, September 6, 2011

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Bernard Lidicky (UIUC Math)
6-critical graphs with small crossing number
Abstract: A graph $G$ is $k$-critical if it has chromatic number $k$ and every proper subgraph has chromatic number less than $k$. Knowledge of the complete list of $k$-critical graphs in a family yields a polynomial time algorithm for deciding $(k-1)$-colorability in that family if the list is finite. Results of Dirac, Gallai, and Thomassen imply that for any fixed surface $\Sigma$ and $k \geq 6$, there are only finitely many $k$-critical graphs embeddable in $\Sigma$. This also implies that there are only finitely many such graphs with bounded crossing number when $k \geq 6$. Oporowski and Zhao showed that no $6$-critical graphs have crossing number at most $2$ and that $K_6$ is the only $6$-critical graph with crossing number $3$. They conjectured that $K_6$ is the only $6$-critical graph up to five crossings. It turned out that this conjecture is false, but their result can be pushed further to show that $K_6$ is the only 6-critical graph with crossing number at most 4. (This is joint work with Rok Erman, Frederic Havet, and Ondrej Pangrac.)