UPDATE -- Feedback Form:  All participants are requested to fill out the feedback form.  Thanks!

Registration: Please fill out the registration form by February 7.   

Speakers: 

• Hamid Abban (University of Nottingham)

• Hülya Argüz (University of Georgia)

• Kristin DeVleming (University of Massachusetts Amherst)

• Christopher Hacon (University of Utah) 

• Felix Janda (University of Illinois Urbana-Champaign)

• Lena Ji (University of Michigan)

• Sara Torelli (University of Texas at Austin)

Location: All talks will be held in the auditorium at the Schiller Institute on the Boston College Chestnut Hill campus:

107 Auditorium 

The Schiller Institute for Integrated Science and Society

245 Beacon St

Chestnut Hill, MA 02467

The Saturday banquet will be at My Happy Hunan Kitchen, 1926 Beacon St, Brighton. 

Hotel: All participants who are provided with housing will be staying at the AC Hotel By Marriott Cleveland Circle. The address is:

395 Chestnut Hill Ave

Boston, MA 02135

The hotel is a 25 minute walk from the BC campus.  Alternatively, with a bit more time and preparation one can take the campus shuttle (Commonwealth Ave route, hotel: Reservoir T stop, BC: Conte Forum stop).

Transportation and Parking: Here is the Boston College Chestnut Hill campus map.  (The Schiller Institute is in the building marked 245 Beacon.)  Detailed directions can be found here. 

Titles and abstracts:

Hamid Abban (University of Nottingham): K-moduli of Fano hypersurfaces

Beyond detecting the existence of Kähler-Einstein metrics on Fano manifolds, K-stability also provides a natural framework for compactifying the moduli spaces of Fano varieties. A good playground for testing the theory is the case of Fano hypersurfaces. In the pretalk I present some general aspects and lay out the (conjectural) picture for cubic hypersurfaces. The main talk concentrates on quartic 3-folds, where I highlight the progress so far which shows the complexity of the general picture.

Hülya Argüz (University of Georgia): The KSBA moduli space of log Calabi-Yau surfaces

The KSBA moduli space, introduced by Kollár--Shepherd-Barron, and Alexeev, is a natural generalization of "the moduli space of stable curves" to higher dimensions. It parametrizes stable pairs (X,B), where X is a projective algebraic variety satisfying certain conditions and B is a divisor such that K_X+B is ample. This moduli space is described concretely only in a handful of situations: for instance, if X is a toric variety and B=D+\epsilon C, where D is the toric boundary divisor and C is an ample divisor, it is shown by Alexeev that the KSBA moduli space is a toric variety. Generally, for a log Calabi-Yau variety (X,D) consisting of a projective variety X and an anticanonical divisor D, with B=D+\epsilon C where C is an ample divisor, it was conjectured by Hacking--Keel--Yu that the KSBA moduli space is still toric (up to passing to a finite cover). In joint work with Alexeev and Bousseau, we prove this conjecture for all log Calabi-Yau surfaces. This uses tools from the minimal model program, log smooth deformation theory and mirror symmetry.

Kristin DeVleming (University of Massachusetts Amherst): The Hassett-Keel program in genus 4

Studying the minimal model program with scaling on the moduli space of genus g curves and interpreting the steps in a modular way is known as the Hassett-Keel program. The first few steps are well-understood yet the program remains incomplete in general. We complete the Hassett-Keel program in genus 4 using wall-crossing in K-moduli and modular interpretations. This is joint work with Kenneth Ascher, Yuchen Liu, and Xiaowei Wang.

Christopher Hacon (University of Utah): Recent progress in the Kahler minimal model program

The minimal model program is an ambitious program that aims to understand the geometry of complex projective varieties (eg. manifolds defined by polynomial equations). After reviewing some of the highlights of the minimal model program for complex projective varieties (in the pretalk), we will discuss some recent results and challenges encountered trying to extend the minimal model program to the context of Kahler varieties.

Felix Janda (University of Illinois Urbana-Champaign): Techniques for computing higher genus Gromov-Witten invariants and a connection to birational invariants

I will discuss the new machinery "log GLSM" for computing higher genus Gromov-Witten invariants of complete intersections. As part of this program, we construct a new moduli space of "punctured R-maps". I will describe these spaces and highlight new connections to invariants in birational geometry.  This is joint work with Q. Chen and Y. Ruan.

Lena Ji (University of Michigan): The K-moduli space of a family of conic bundles

In this talk, we study the moduli space of a family of Fano threefolds, and we construct a compactification using K-stability. These threefolds admit a conic bundle structure—we relate the K-moduli space of the threefolds to the GIT moduli space of the discriminant curves, and we study the behavior of the conic bundle structure on the boundary. The technique we use is wall-crossings in K-moduli for certain log Fano pairs (X, cD) as the coefficient c varies. Our work is the first to systematically study these K-moduli spaces when D is not proportional to the anticanonical divisor of X, and we find surprising wall-crossing behavior in this setting. This work is joint with Kristin DeVleming, Patrick Kennedy-Hunt, and Ming Hao Quek.

Sara Torelli (University of Texas at Austin): Holomorphic forms on moduli spaces of curves

In the last years holomorphic forms on the moduli space $\overline{\mathcal{M}}_{g,n}$ of stable curves with $n$-marked points have been intensively studied in accordance with some predictions provided by the Langland program. On the other hand, on the moduli space $\mathcal{M}_{g,n}$ of smooth curves with $n$-marked points holomorphic forms are much less understood and the question whether the restriction map of holomorphic forms from $\overline{\mathcal{M}}_{g,n}$ to $\mathcal{M}_{g,n}$ is surjective is widely open, with the exception of holomorphic functions. The result I will present states that all holomorphic one forms vanish on $\mathcal{M}_{g,n}$, for $g\geq 4$, and in particular proves that the restriction map of holomorphic forms is an isomorphism in this case. The work is joint with F.F. Favale and G.P. Pirola.

Short talks:

Miguel Prado (Boston College): Counting isoresidual differentials on CP^1

Ruoxi Li (UIUC): A Geometric Construction for Cosection and Reduced Perfect Obstruction Theory

Qitong Jiang (Penn State): Degeneration of Dynamics of Surface Maps

Wanchun Shen (Harvard): Du Bois complexes of moduli spaces

Weite Pi (Yale): On a compact analogue of the P = W conjecture

James Austin Myer (CUNY): (Toward) an(other) algorithm for resolution of singularities (for curves) in positive characteristic

Zhijia Zhang (NYU): Equivariant Birational Geometry of Singular Cubic Threefolds (with two A_n singularities)

Fernando Figueroa (Princeton/UCLA): Fundamental groups of low coregularity pairs

Andrei Ionov (Boston College): Tilting sheaves in real stratifications and Koszul duality

Dmitry Kubrak (IAS): Singular Z-cohomology of log schemes

D. Zack Garza (University of Georgia): Compact moduli of degree two polarized Enriques surfaces

Yidi Wang (University of Pennsylvania): Local-global principles for integral points on stacky curves

Yuze Luan (UC Davis): Irreducible components of the Hilbert scheme of points on non-reduced plane curves

The Boston College Organizers: Dawei Chen, Qile Chen, Maksym Fedorchuk, Brian Lehmann 

We gratefully acknowledge the support of the NSF and the host institutions. 

We are dedicated to upholding the principles and practices of equal opportunity, affirmative action, and nondiscrimination. Our commitment extends to fostering an inclusive environment for all AGNES participants. Boston College's related policies and compliance are applicable to all AGNES participants. If there are any concerns or requests for assistance related to discrimination or harassment, please reach out to one of the organizers.