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.

Friday October 20, 2017 2:30 PM  3:30 PM Math Tower 5127
 John Sheridan, Stony Brook University
Examples of surface singularitiesIn this talk we will introduce some more algebraic terminology and study a number of examples of surface singularities that will be useful comparisons to keep in mind as we focus more on rational singularities in the coming weeks.

Friday October 27, 2017 2:30 PM  3:30 PM Math Tower 5127
 Frederik Benirschke, Stony Brook University
Kleinian SingularitiesWe will continue with our study of rational singularities on surfaces, indicating the construction of Kleinian singularities via group quotients of the affine plane.

Friday November 03, 2017 2:30 PM  3:30 PM Math Tower 5127
 Yoonjoo Kim, Stony Brook University
Resolutions of rational double point singularitiesContinuing the discussion of the previous talk, we keep studying rational double points (RDP) on complex surfaces. This time, we will talk about the resolution of RDPs. More specifically, we will discuss the minimal resolution of RDPs, blowup of curves and surfaces, and the configuration of their exceptional divisors.

Friday November 10, 2017 2:30 PM  3:30 PM Math Tower 5127
 Ruijie Yang, Stony Brook University
Minimal resolution of A_n singularitiesWe learned from last week that minimal resolutions of rational double points can be obtained from the embedded resolution of a suitable hyperplane section. We will examine the case of an A_n singularity carefully and also give another way of constructing minimal resolutions.

Friday November 17, 2017 2:30 PM  3:30 PM Math Tower 5127
 Tim Ryan, Stony Brook University
Rational singularities in generalIn this talk, we will study one more example of resolving a rational double point  the E_6 resolution. This will conclude our study of Rational Double Points (RDPs) and we finally graduate to rational singularities in general. We will give the definition of a rational singularity and set up the necessary tools to prove the first main theorem on surface quotient singularities.

