Student Algebraic Geometry Seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Friday
September 01, 2017

2:30 PM - 3:30 PM
Math Tower 5-127

Organizational Meeting

We 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 5-127
Nathan Chen, Stony Brook University
Introduction to abelian varieties

In 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 5-127
Dahye Cho, Stony Brook University
Introduction to singularities in algebraic geometry

We 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 5-127
Marlon de Oliveira Gomes, Stony Brook University
Puiseux series for plane curve singularities

Given 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 5-127
Ying Hong Tham, Stony Brook University
Puiseux pairs with a view to topological invariants

Ee 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 5-127
Charlie Cifarelli, Stony Brook University
Facts on curves and a view towards surface singularities

Having 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 5-127
John Sheridan, Stony Brook University
Examples of surface singularities

In 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 5-127
Frederik Benirschke, Stony Brook University
Kleinian Singularities

We 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 5-127
Yoonjoo Kim, Stony Brook University
Resolutions of rational double point singularities

Continuing 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 5-127
Ruijie Yang, Stony Brook University
Minimal resolution of A_n singularities

We 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 5-127
Tim Ryan, Stony Brook University
Rational singularities in general

In 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.


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Instructions for subscribing to Stony Brook Math Department Calendars