Friday September 01, 2017 2:30 PM  3:30 PM Math Tower 5127

Organizational MeetingWe will decide on the topic(s), speakers and meeting time for the seminar going forward.

Friday September 08, 2017 2:30 PM  3:30 PM Math Tower 5127
 Nathan Chen, Stony Brook University
Introduction to abelian varietiesIn this talk we will introduce abelian varieties, take a first look at their basic properties and discuss some examples.

Friday September 15, 2017 2:30 PM  3:30 PM Math Tower 5127
 Dahye Cho, Stony Brook University
Introduction to singularities in algebraic geometryWe will give a basic introduction to the notion of singular points on an algebraic variety and begin investigating the local structure of the variety near such points. For today, we will focus on a number of examples of hypersurface singularities and some of their fundamental invariants.

Friday September 22, 2017 2:30 PM  3:30 PM Math Tower 5127
 Marlon de Oliveira Gomes, Stony Brook University
Puiseux series for plane curve singularitiesGiven a singular, plane algebraic curve, we will describe a method to find a holomorphic parametrization of a neighborhood of a singular point, the Puiseux expansion of the curve near the singularity. I will describe examples of formal computations of Puiseux series, and prove that such series converge. Time permitting, we will describe the relation between Puiseux expansions and resolutions of plane curve singularities.

Friday September 29, 2017 2:30 PM  3:30 PM Math Tower 5127
 Ying Hong Tham, Stony Brook University
Puiseux pairs with a view to topological invariantsEe will recall some of the definitions from last week and continue our study of Puiseux series of plane curves. We will introduce Puiseux pairs, compute some examples and, time allowing, investigate their relation to the topology near the singularity.

Friday October 06, 2017 2:30 PM  3:30 PM Math Tower 5127
 Charlie Cifarelli, Stony Brook University
Facts on curves and a view towards surface singularitiesHaving now spent some time investigating singularities of curves in the plane, we will discuss some other important facts about algebraic curves and group actions on them that will set the scene for our study of quotients of the affine plane  the model for our first nice class of surface singularities.

