Title: An algorithm for computing Brauer groups of cubic surfaces via reduction mod p

Abstract:

For arithmetic geometers, the Brauer group of a variety can give us insight into the existence of rational points. In fact, it is conjectured that a Brauer-Manin obstruction is the only possible obstruction to the Hasse principle for del Pezzo surfaces. Unfortunately for us, the Brauer group is rather sneaky and direct computation can be extremely difficult and time consuming. In this talk, we present an algorithm for computing the Brauer group of cubic surfaces indirectly, via reduction mod p at many primes. Along the way, we will dip our toes into the world of Bayesian statistics and debate the merits of certainty versus efficiency!

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Contact Information

**Tel** (713) 348-4829

**Mailing Address:**

Rice University

Math Department -- MS 136

P.O. Box 1892

Houston, TX 77005-1892

**Physical Address:**

Rice University

Herman Brown Hall for Mathematical Sciences

6100 Main Street

Houston, TX 77005