Seminars and Colloquia by Series

Friday, April 26, 2019 - 12:00 , Location: Skiles 006 , Jaewoo Jung , Georgia Institute of Technology , jjung325@gatech.edu , Organizer: Trevor Gunn

It is known that non-negative homogeneous polynomials(forms) over $\mathbb{R}$ are same as sums of squares if it is bivariate, quadratic forms, or ternary quartic by Hilbert. Once we know a form is a sum of squares, next natural question would be how many forms are needed to represent it as sums of squares. We denote the minimal number of summands in the sums of squares by rank (of the sum of squares). Ranks of some class of forms are known. For example, any bivariate forms (allowing all monomials) can be written as sum of $2$ squares.(i.e. its rank is $2$) and every nonnegative ternary quartic can be written as a sum of $3$ squares.(i.e. its rank is $3$). Our question is that "if we do not allow some monomials in a bivariate form, how its rank will be?". In the talk, we will introduce this problem in algebraic geometry flavor and provide some notions and tools to deal with.

Friday, April 19, 2019 - 12:00 , Location: Skiles 006 , Marc Härkönen , Georgia Tech , harkonen@gatech.edu , Organizer:
Friday, April 12, 2019 - 12:00 , Location: Skiles 006 , Stephen McKean , Georgia Tech , mckean@math.gatech.edu , Organizer:

Milnor K-theory is a field invariant that originated as an attempt to study algebraic K-theory. Instead, Milnor K-theory has proved to have many other applications, including Galois cohomology computations, Voevodsky's proof of the Bloch-Kato conjecture, and Kato's higher class field theory. In this talk, we will go over the basic definitions and theorems of Milnor K-theory. We will also discuss some of these applications.

Friday, April 5, 2019 - 12:00 , Location: Skiles 006 , Justin Chen , Georgia Tech , jchen646@gatech.edu , Organizer: Cvetelina Hill
Friday, March 15, 2019 - 12:00 , Location: Skiles 006 , Trevor Gunn , Georgia Tech , Organizer: Trevor Gunn

I will introduce briefly the notion of Berkovich analytic spaces and certain metric graphs associated to them called the skeleton. Then we will describe divisors on metric graphs and a lifting theorem that allows us to find tropicalizations of curves in P^3. This is joint work with Philipp Jell.

Friday, February 22, 2019 - 12:00 , Location: Skile 006 , Cvetelina Hill , Georgia Tech , cvetelina.hill@gatech.edu , Organizer: Cvetelina Hill
Friday, February 1, 2019 - 12:00 , Location: Skiles 006 , Tianyi Zhang , Georgia Tech , Organizer: Trevor Gunn
Friday, January 25, 2019 - 12:00 , Location: Skiles 005 , Tim Duff , Georgia Tech , Organizer: Trevor Gunn

Bring a laptop with Macaulay 2 installed.

Thursday, November 15, 2018 - 13:30 , Location: Skiles 006 , Marcel Celaya , Georgia Tech , Organizer: Trevor Gunn
Thursday, November 8, 2018 - 13:30 , Location: Skiles 006 , Stephen McKean , Georgia Tech , Organizer: Trevor Gunn

In 1986, Herb Clemens conjectured that on a general quintic threefold, there are finitely many rational curves of any given degree. In this talk, we will give a survey of what is known about this conjecture. We will also highlight the connections between enumerative geometry and physics that arise in studying the quintic threefold.

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