- Series
- Student Algebraic Geometry Seminar
- Time
- Friday, February 12, 2021 - 9:00am for 1 hour (actually 50 minutes)
- Location
- Online
- Speaker
- Jaewoo Jung – Georgia Tech – jaewoojung@gatech.edu – https://sites.google.com/view/jaewoojung/home
- Organizer
- Marc Harkonen
Please Note: URL: https://teams.microsoft.com/l/meetup-join/19%3a3a9d7f9d1fca4f5b991b4029b09c69a1%40thread.tacv2/1612989014268?context=%7b%22Tid%22%3a%22482198bb-ae7b-4b25-8b7a-6d7f32faa083%22%2c%22Oid%22%3a%2206706002-23ff-4989-8721-b078835bae91%22%7d
Even though it is not easy to determine global non-negativity of a polynomial, if the polynomial can be written as a sum of squares(SOS), we certainly see that it must be non-negative(PSD). Representability of polynomials in terms of sums of squares is a good certification for global non-negativity in the sense that any non-negative polynomials is just a sum of squares in some cases. However, there are some non-negative polynomials which cannot be written as sum of squares in general. So, one can ask about when the set of sums of squares is same as the set of non-negative polynomials or describing gap between set of sums of squares and non-negative polynomials if they are different.
In this talk, we will introduce an algebraic invariant (of variety) which can tell us when the two sets are same (or not). Moreover, we will discuss about cases that we can exactly describe structural gaps between the two sets.
URL: Microsoft Teams