Algebraic Geometry

Organizer: Ravi Vakil

Upcoming Events

May
31
Date12:00 PM
Location
383N
Speaker
Joaquin Moraga (UCLA)

Fano varieties are one of the three building blocks of algebraic varieties.In this talk, we will discuss how to describe a general n-dimensional Fano variety.Although there is no consensus on how to answer to this question, we will explore some new invariants motivated by…

May
31
Date2:30 PM
Location
383N
Speaker
Dori Bejleri (University of Maryland)

The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau…

Past Events

May
24
Date2:30 PM
Location
380-X (notice unusual location!)
Speaker
Daniel Halpern-Leistner (Cornell)

Harder-Narasimhan (HN) theory gives a structure theorem for principal G bundles on a smooth projective curve. A bundle is either semistable, or it admits a canonical filtration whose associated graded bundle is semistable in a graded sense. After reviewing recent advances in extending HN theory…

May
24
Date12:30 PM
Location
383N
Speaker
Hannah Larson (UC Berkeley, Clay)

I'll start by defining the Chow ring, which is an important invariant of a scheme (or stack). Next, I will define the Picard variety and Picard stack of a curve, and then introduce their universal versions $J^d_g$ and $\mathscr{J}^d_g$ over the moduli space of curves $M_g$. Recently, progress…

May
03
Date2:30 PM
Location
383-N
Speaker
Matt Kerr (Washington University St. Louis)

I will describe the construction of motivic cohomology classes on hypergeometric families of Calabi-Yau 3-folds using Hadamard convolutions.  One can view this as a “higher” version of the Mordell-Weil group for families of elliptic curves, giving rise to sections of “higher” Jacobian…

May
03
Date12:00 PM
Location
383N
Speaker
Matt Kerr (Washington University in St. Louis)

I will describe the construction of motivic cohomology classes on hypergeometric families of Calabi-Yau 3-folds using Hadamard convolutions.  One can view this as a “higher” version of the Mordell-Weil group for families of elliptic curves, giving rise to sections of “higher” Jacobian…

Apr
19
Date2:30 PM
Location
383-N
Speaker
Mura Yakerson (Oxford)

The well-known Adams conjecture in topology is a theorem about compactifications of real vector bundles on CW-complexes, which has important implications for analyzing stable homotopy groups of spheres. In the talk we will discuss an algebro-geometric version of this statement, which tackles…

Apr
19
Date12:00 PM
Location
383N
Speaker
Jakub Witaszek (Princeton)

In my talk, I will start by reviewing how various properties of characteristic zero singularities can be understood topologically by ways of the Riemann-Hilbert correspondence. After that, I will explain how similar ideas can be applied in the study of mixed characteristic singularities.…

Apr
12
Date12:00 PM
Location
383N
Speaker
Weite Pi (Yale)

The moduli spaces of one-dimensional sheaves on the projective plane have been studied through their connections to enumerative geometry and representation theory. In this talk, I will explain a systematic approach to study their cohomology rings, using notably tautological relations of…

Apr
05
Date12:00 PM
Location
383N
Speaker
Matt Baker (Georgia Tech)

We give a new proof, along with some generalizations, of a folklore theorem - attributed to Laurent Lafforgue - that a rigid matroid (i.e., a matroid whose base polytope is indecomposable) has only finitely many projective equivalence classes of representations over any given field. A key…

Mar
15
Date2:30 PM
Location
380-W
Speaker
Hunter Spink (Toronto)

I will talk about a new algebra of operations on polynomials which has the property

$T_iT_j=T_jT_{i+1}$ for $i>j$ and a family of polynomials dual to them called forest polynomials. This family of operations plays the exact role for quasisymmetric polynomials and forest polynomials as…

Mar
15
Date12:00 PM
Location
383N
Speaker
Rosie Shen (Harvard)

We survey some extensions of the classical notions of Du Bois and rational singularities, known as the k-Du Bois and k-rational singularities. By now, these notions are well-understood for local complete intersections (lci). We explain the difficulties beyond the lci case, and propose new…