The Algebraic Geometry Pre-Seminar takes place on Wednesdays 3:00–3:25PM in STON 215. Graduate students are particularly encouraged to attend. Note that when there is no external speaker, we may schedule pre-print seminar at 3:00–4:30PM in the same location.
September 24: Hannah Larson (University of California, Berkeley)
Location: Zoom (https://purdue-edu.zoom.us/j/97786675764?pwd=ZUxkQzFsck5IaFBBZnhiOVNTZys4UT09)
Title: Linear series on curves
Abstract: I will explain the correspondence between maps to projective space and linear series. Then, we'll discuss some concrete examples in low genus.
August 27: Takumi Murayama (Purdue University)
Location: STON 215
Title: Embeddings of projective varieties and Fujita's conjecture
Abstract: All smooth projective curves (which, over the complex numbers, are the same thing as Riemann surfaces) can be embedded into a projective space. However, it is difficult to find an explicit embedding of a given smooth projective curve into a projective space.
In this talk, I will discuss how to find embeddings of smooth projective curves into projective spaces. This motivates Fujita's very ampleness conjecture, which predicts there is a uniform way to use an ample divisor on a smooth projective variety X to find an embedding of X into a projective space. Fujita's very ampleness conjecture is known in dimensions at most 2 over the complex numbers. It remains a difficult open problem even in dimension 3.
September 3: Zhiyuan Jiang (Purdue University)
Location: STON 215
Title: Complex analytic geometry and positivity
Abstract: I will review some basic concepts in analytic geometry with a focus on the comparison between algebraic geometry and analytic geometry. I will also introduce the concept of positivity in complex analytic geometry and the role they play in birational geometry, bimeromorphic geometry, and the minimal model program.
September 10: Donu Arapura (Purdue University)
Location: STON 215
Title: Perverse Sheaves
Abstract: Perverse sheaves were invented by Beilinson, Bernstein and Deligne a bit over 40 years ago. The first thing to point out (as the inventors do) is that they aren’t perverse and they aren’t sheaves. What they are are really nice objects of the constructible derived category of a variety.
September 17: Fanjun Meng (UC San Diego)
Location: STON 215
Title: Wall crossing for moduli of weighted pointed stable curves
Abstract: I will review Hassett’s classical result on wall crossing for moduli of weighted pointed stable curves.
September 24: Hannah Larson (University of California, Berkeley)
Location: Zoom (https://purdue-edu.zoom.us/j/97786675764?pwd=ZUxkQzFsck5IaFBBZnhiOVNTZys4UT09)
Title: Linear series on curves
Abstract: I will explain the correspondence between maps to projective space and linear series. Then, we'll discuss some concrete examples in low genus.
October 29: Florin Ambro (Simion Stoilow Institute of Mathematics of the Romanian Academy)
Location: Zoom (https://purdue-edu.zoom.us/j/97786675764?pwd=ZUxkQzFsck5IaFBBZnhiOVNTZys4UT09)
Title: An invitation to toric varieties
Abstract: Toric varieties provide a bridge between algebraic geometry and combinatorics. From a lattice and a cone or polytope, one constructs a toric singularity or polarized variety, whose invariants are controlled by combinatorics. Such explicit examples can be used to test open problems in algebraic geometry, and gain intuition for the general case. Conversely, combinatorial problems can be solved by using the geometry of the associated toric variety. The aim of this short talk is to present some basic examples of toric varieties, and their corresponding combinatorial data.