This seminar runs every Monday during the semester at 2PM in Hill 705. The current organizers are Jeff Kahn, Bhargav Narayanan, Swee Hong Chan, and Natalya Ter-Saakov.
If you wish to join our listserv, please email Natalya Ter-Saakov at nt399@math.rutgers.edu.
Click here for the abstract archive for this semester, and here for older abstracts.
Next Talk:
Date: September 22, 2025 at 2:00pm
Speaker: John Byrne (University of Delaware)
Title: New constructions and bounds for nonabelian Sidon sets with applications to Turán-type problems
Abstract: An Sk-set is a subset of a group whose k-tuples have distinct products. An Sk'-set is a subset of a group whose bipartite Cayley graph has no cycle of length 2k. We give explicit constructions of large Sk-sets in the symmetric and alternating groups and of S2-sets in direct powers of these groups. We give probabilistic constructions for 'nice' groups which obtain large S2'-sets in the symmetric group. We also give upper bounds on the size of Sk-sets in certain groups, improving the trivial bound by a constant multiplicative factor. We describe some connections between Sk-sets and extremal graph theory. In particular, we determine up to a constant factor the minimum outdegree of a digraph which guarantees even cycles with certain orientations. As applications, we improve the upper bound on Hamilton paths which pairwise create a two-part cycle of given length, and we show that a directed version of the Erdős-Simonovits compactness conjecture is false. This talk is based on joint work with Michael Tait.
September 22 --- John Byrne (University of Delaware)
October 13 --- Doron Puder (Tel Aviv University)
October 20 --- Boris Buch (Carnegie Mellon University)
October 27 --- Lior Gishboliner (University of Toronto)
November 3 --- Jonathan Tidor (Princeton University)