Overview
The Midwest Algebraic Geometry Graduate Conference (MAGGC) aims to gather graduate students who are interested in algebraic geometry and related areas to share their research and knowledge. The event will happen on August 10-11 at the University of Illinois at Chicago (UIC), Department of Mathematics, Statistics, and Computer Science.
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Speakers, Titles, and Abstracts
Faculty Talk: Noncommutative algebraic geometry
Speaker: Alex Perry
Abstract: I will explain an enlargement of classical algebraic geometry based on a more flexible notion of a space, called a noncommutative algebraic variety. The focus will be on examples and applications to questions in birational geometry, Hodge theory, and hyperkahler geometry.
Postdoc Talk: ACC for mlds for terminal threefolds
Speaker: Jihao Liu
Abstract: Shokurov’s ascending chain condition (ACC) conjecture for minimal log discrepancies (mlds) is a major conjecture in birational geometry and has important application towards the termination of flips. Recently, the speaker, J. Han, and Y. Luo confirm this conjecture for terminal threefolds. In this talk, I will discuss this result and investigate its related corollaries and applications.
Topological Abel-Jacobi map and Mixed Hodge Structures
Speaker: Yilong Zhang
Abstract: The Abel-Jacobi map on a smooth projective curve is a group homomorphism which sends divisors of degree zero to the Jacobian of the curve. In fact, the Abel-Jacobi image can be also extracted from the mixed Hodge structure on the H^1 of the complement of the support of the divisor. Similar argument holds in higher dimensions for Griffiths' Abel-Jacobi map. In 2015, Xiaolei Zhao defined a notion called Topological Abel-Jacobi map, which is a generalization of Griffiths' Abel-Jacobi map to topological cycles. We will show it coincides with an alternative definition using R-splitting properties of certain mixed Hodge structures. This answers a question of Christian Schnell.
Well-definedness and continuity of global F-signature on the ample cone
Speaker: Seungsu Lee
Abstract: F-signature plays a crucial role when measuring singularities of varieties in positive characteristics. For example, if R is a local ring, s(R) = 1 implies R is regular, and 0<s(R)<1 implies R is strongly F-regular which is a char p analog of klt singularities. For a globally F-regular variety $X$, we define the global F-signature as the F-signature of the section along an invertible sheaf $L$ over X. In this talk, we will discuss the global F-signature is well-defined and is continuous on the ample cone. This is joint work with Swaraj Pande.
Decompostion of diagonal in Chow-Witt ring: rational case
speaker: Haoyang Liu
Abstract: The decomposition of diagonal class in the rational Chow ring of an abelian variety over a field k is a well-known result of Deninger and Murre. We want to extend this decomposition to the "quadratic refinement" of Chow ring, which we call it Chow-Witt ring. With a strong result by Jacobson, we can do this decomposition in rational case. If time permits, we can do elliptic curve case as an example.
V-filtrations on D-modules
Speaker: Bradley Dirks
Abstract: "The V-filtration of Kashiwara and Malgrange is the D-module theoretic incarnation of the nearby and vanishing cycles functors on perverse sheaves. I will define D-modules on smooth complex varieties, V-filtrations, and b-functions, with some examples. Time permitting, I will describe a construction relating V-filtrations along a hypersurface to those along a higher codimension subvariety."
Why the (p-adic completion of the) absolute integral closure has uncountable krull dimension
Speaker: Jack J Garzella
Abstract: The absolute integral closure, and it's p-adic completion, are very important in mixed characteristic algebraic geometry. It's applications include singularity theory, the minimal model program, and even the direct summand conjecture from commutative algebra. This ring has many nice properties, but I'd like to highlight an ugly one: it has uncountable krull dimension. We'll talk about what this means, and how one can use ideas from Number Theory to prove it (in the simplest case).
The infinite-variable polynomial ring in positive characteristic
Speaker: Karthik Ganapathy
Abstract: GL-equivariant modules over infinite-variable polynomial rings have found applications in topology, algebraic statistics and combinatorics. The structure theory of such modules is well understood in characteristic zero by the work of Sam–Snowden and others. I will talk about ongoing work to extend their results to positive characteristic emphasizing the key differences.
Hilbert Schemes and Newton-Okounkov Bodies
Speaker: Ian Cavey
Abstract: The Hilbert scheme of n points in the (affine) plane parametrizes finite, length n subschemes of C^2. In this talk I will discuss the combinatorics of the “Newton-Okounkov bodies” of these Hilbert schemes. These Newton-Okounkov bodies are (unbounded) polyhedra which encode geometric information about the Hilbert schemes. If time permits I will also discuss some partial results and conjectures for Hilbert schemes of points on complete toric surfaces.
Acknowledgement
We would like to thank Izzet Coskun and Benjamin Bakker for sponsoring this event.
Questions?
Please contact any one of the organizers for questions/concerns: