| Description: | [DMS Seminar] Dr. Pankaj Vishe (Durham University) -- Quartic Forms in 37 Variables |
| Date: | Wednesday, Sep 07, 2016 |
| Time: | 3 p.m. - 4 p.m. |
| Venue: | 108, Lecture Hall Complex |
| Details: | A projective variety X defined over the rational numbers is said to satisfy the Hasse principle if the presence of an adelic point on X guarantees the presence of a rational point. We prove that a smooth quartic hypersurface over Q satisfies Hasse Principle as long as the number of variables are greater than or equal to 37. The key ingredient is Kloosterman type extra averaging in conjunction with the van der Corput differencing applied to estimate the ''minor arc contribution'' in the Hardy-Littlewood circle method. This is a joint work with Oscar Marmon. |
| Calendar: | Seminar Calendar (entered by saugata.bandyopadhyay) |