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Seminar Details

Product Free Sets in the Alternating Group

  • Start Date: October 31, 2022
  • Event Start Time: 2:00 PM
  • Event End Time: 3:00 PM
  • Seminar Series: Rutgers Discrete Mathematics Seminar
  • Presenter(s): Noam Lifshitz - Institute for Advanced Study
  • Event Location: Hill Center-Room 705
  • Event Additional Info: <p>See:&nbsp;<a href="https://sites.google.com/view/rutgersdmseminar">https://sites.google.com/view/rutgersdmseminar</a></p>
  • Presentation Type: Stand Alone Presentation
  • Abstract:

    A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of $A_n$ be?

    In the talk we will completely solve the problem by determining the largest product free subset of $A_n$.

    Our proof combines a representation theoretic argument due to Gowers, with an analytic tool called hypercontractivity for global functions. We also make use of a dichotomy between structure and a pseudorandomness notion of functions over the symmetric group known as globalness.

    Based on a joint work with Peter Keevash and Dor Minzer.