For more information about this meeting, contact Robert Vaughan, Mihran Papikian, Ae Ja Yee, Kirsten Eisentraeger.

Title: | The Erdos-Heilbronn Problem for Finite Groups |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Jeffrey Paul Wheeler, University of Pittsburgh |

Abstract: |

Additive Number Theory can be best described as the study of sums of sets of integers. A simple example is given two subsets A and B of a set of integers, what facts can we determine about A+B where A+B := { a+b | a \in A andb \in B }? Note that Lagrange's Four Square Theorem can be expressed as N_0 = S + S +
S + S where N_0 is the set of nonnegative integers and S the set of all perfect squares. As well the binary version of Goldbach's Conjecture can stated E \subseteq P + P where E be the set of even integers greater than 2 and P the primes,
A classic problem in Additive Number Theory was a conjecture of Paul Erdos and Hans Heilbronn which stood as an open problem for over 30 years until proved in 1994 by Dias da Silva and Hamidounne. The conjecture had its roots in the Cauchy-Davenport Theorem, namely if A and B are nonempty subsets of Z/pZ with p prime, then |A+B| >= min{p,|A|+|B|-1\}, where A+B := {a+b | a \in A and b \in B}. Erdos and Heilbronn conjecture in the early 1960s that if the operation is changed to a restricted sum A \dot{+} B := {a+b | a \in A and b \in B, a \ne b}, then |A \dot{+} B| >=
min{p,|A|+|B|-3\}. We extend these results from Z/pZ to finite groups. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 01 / 15 / 2015 |

Time: | 11:15am - 12:05pm |