Locations
Posters
Posters will be hung in groups of 15 (or so) right outside the LSC Grand Ballroom, on the days below. Each group of posters will be displayed for a full day, so you may peruse them during coffee break, or at your leisure. Poster presenters will be by their posters happy to talk to you between 11:30 and 12:15.
Tuesday 7/15
Haggai Liu: Moduli Spaces of Weighted Stable Curves and their Fundamental Groups
Ryo Ishizuka: On the derived deformation functor of Frobenius liftings
Sophie Kriz: Interpolated equivariant schemes
Jack Garzella: High performance computing in F-singularities and characteristic p algebraic geometry
Lycka Drakengren: A self-intersection of the Torelli map
Doyoung Choi: Singularities and syzygies of secant varieties of smooth projective varieties
Erik Barinaga: On Chow groups of Deligne--Lusztig varieties
Dzoara Nunez: Cohomology of a certain wild quotient singularity
Martina Miseri: The Prym-canonical Clifford index
Jon Kim: Moduli of (b,c)-weighted stable marked cubic surfaces
Hyunsuk Kim: Singular cohomology and local cohomology of toric varieties via mixed Hodge modules
Debjit Basu: Smoothing of Abelian carpets on elliptic ruled surfaces.
Zakaria Brahimi: cubic fourfolds and reducible OADP surfaces
Shreya Sharma: Amitsur group of G-varieties
Enhao Feng: Moduli space of genus one curves on smooth cubic threefold
Roktim Mascharak: Birational Geometry of Three-folds versus Birational Geometry of Foliations on Three-fold.
Thursday 7/17
Vivien Picard: Logarithmic Hodge numbers and weakly ordinary varieties
Shubham Saha: Rational Chow ring of the universal moduli stack of rank two bundles over genus two curves
Crislaine Kuster: Codimension one foliations on adjoint varieties
Yutaro Sugimoto: On controlling the dynamical degrees of automorphisms of complex simple abelian varieties
Zhijia Zhang: Equivariant unirationality of Fano threefolds
Juan Zuniga: Wahl singularities in degenerations of del Pezzo surfaces
Jan Lange: On the rationality problem for low degree hypersurfaces
Jaime Negrete: Classification of Horikawa surfaces with T-singularities
Will Newman: The Chow Ring of bar M_{1,n} via Higher Chow Groups
Fumiya Okamura: Moduli spaces of rational curves on Artin-Mumford double solids
Matthew Hase-Liu: Moduli spaces of curves on low degree hypersurfaces and the circle method
Xintong Jiang: Boundedness of complements for fibered Fano threefolds in positive characteristic
Shikha Bhutani: On Kawamata-Viehweg Vanishing for surfaces of del Pezzo type over imperfect fields.
Haoming Ning: Higher Du Bois and Higher Rational Pairs
Javier Reyes: Classification of Singular Fibers in Hyperelliptic Fibrations
Longke Tang: The P^1-motivic Gysin map
Tuesday 7/22
Alexandra Sonina: Finite subgroups of automorphism groups of Severi–Brauer varieties
Alex Villaro Krüger: Fano threefolds of type 4-1: Moduli, derived categories (and rationality?)
Tomoki Yoshida: A simple derived categorical generalization of Ulrich bunldes
Alessandro Frassineti: Modular vector bundles on hyperkähler manifolds of Debarre–Voisin type
Dhruv Goel: Chow Ring Classes of Varieties of Secant and Tangent Lines to Smooth Projective Varieties
Darragh Glynn: Boundary stratifications of Hurwitz spaces
Terry Song: Cohomology of Vakil--Zinger mapping spaces
Natasha Crepeau: Constructing fine V-compactified Jacobians from triangulations
Siao Chi Mok: Logarithmic Fulton--MacPherson configuration spaces
Amy Li: Vanishing H^1 of low-degree Hurwitz spaces
Naufil Sakran: Enumerating Log Rational Curves on some Toric Variety
Erin Dawson: Tropical Tevelev degrees
Hao Zhang: Gopakumar--Vafa invariants associated to $cA_n$ singularities
Feiyang Lin: Resolving the singularities of splitting loci
Sayan Chattopadhyay: The Mirror to the Logarithmic Hilbert Scheme of Points on P^2
Giusi Capobianco: hyperelliptic double covers and the Abel-Prym map
Francesca Rizzo: On the fixed locus of the antisymplectic involution of an EPW cube
María Abad Aldonza and Florent Dupont: Chern character of the multilayer quantum Hall bundle
Flash talks schedule
Monday 7/14, 5:30-6:45pm
Session A (ENGRG 100 chaired by C. Hacon)
Miguel Prado Isoresidual curves
Abstract: Fixing the residues of differentials forms over the Riemann Sphere for a given strata determines an "isoresidual" variety that can be described via intersection theory on the multiscale compactification. In particular I'll adress the case when this locus is a curve.
Fanjun Meng Wall crossing for moduli of stable pairs
Abstract: Hassett showed that there are natural reduction morphisms between moduli spaces of weighted pointed stable curves when we reduce weights. I will discuss some joint work with Ziquan Zhuang which constructs similar morphisms between moduli of stable pairs in higher dimension.
Jaeho Shin Birational Geometry of Matroids and Abstract Hyperplane Arrangements
Abstract: The geometry of abstract hyperplane arrangements goes beyond the lattice geometry of flat lattices, incorporating the polyhedral geometry of matroids. Studying how a matroid tiling extends to a larger one leads to the question of whether reduction morphisms between moduli spaces of weighted stable hyperplane arrangements are surjective. In this talk, I will introduce the development of the theory and outline the above mentioned surjectivity problem.
Richard Haburcak Brill--Noether loci in low genus
Abstract: A refined Brill--Noether theory studies the linear systems on curves with a given Brill--Noether special linear system, which can be rephrased as understanding the relative positions of (components of) Brill--Noether loci, which parameterize curves with a particular projective embedding. Using recent and classical results, we identify the relative positions of Brill--Noether loci in low genus and find new expectations in general.
Dario Weißmann Distinguishing algebraic spaces from schemes
Abstract: We introduce local invariants of algebraic spaces which measure how far they are from being a scheme. In the setting of a stack admitting a separated (good) moduli space this also yields a criterion for when the moduli space is a scheme. As an application we identify all separated good moduli spaces of vector bundles over a smooth projective curve which are schemes. This is joint work with Andres Fernandez Herrero and Xucheng Zhang.
Soham Karwa K-affine structures on skeleta
Abstract: TBD
Livia Campo K-stability of Fano 3-fold hypersurfaces of index 1
Abstract: The existence of Kaehler-Einstein metrics on Fano 3-folds can be determined by studying lower bounds of stability thresholds. In this talk I will discuss the K-stability of Fano 3-fold hypersurfaces via Abban-Zhuang Theory. This is a joint work with Takuzo Okada.
Fernando Figueroa: Algebraic Tori in the complement of Quartic Surfaces
Abstract: TBD
Jose Yanez: Calabi-Yau pairs of low complexity
Abstract: The complexity of a Calabi-Yau pair (X,B) is an invariant that relates the dimension of X, the Picard rank of X, and the coefficients of B. It was proven by Brown, McKernan, Svaldi and Zong that the complexity of a Calabi-Yau pair is nonnegative, and a variety X admits a Calabi-Yau pair of complexity 0 if and only if X is toric. In this talk we will discuss the geometry of Calabi-Yau pairs of index one and complexity one or two. Both descriptions are done in terms of cluster type varieties, a generalization of toric varieties. This is joint work with Joshua Enwright, Jennifer Li and Joaquin Moraga.
Eric Jovinelly Free curves on klt Fano varieties
Abstract: We prove the smooth locus of any klt Fano variety contains higher genus free curves. We then use the existence of such free curves to get some applications: we prove the existence of free rational curves in terminal Fano threefolds; obtain an optimal upper bound on the length of extremal rays in the Kleiman-Mori cone of any klt pair; and study the fundamental group of the smooth locus of a Fano variety. This is joint work with Brian Lehmann and Eric Riedl.
Session B (Nutrien 140 chaired by R. Cavalieri)
Wern Yeong A hyperbolicity conjecture for adjoint bundles
Abstract: We propose a conjecture, inspired by Fujita’s freeness conjecture, on the algebraic hyperbolicity of generic sections of adjoint bundles on smooth projective varieties. We give some new and old evidence in support. Based on joint work with J. Moraga.
Theo Papazachariou On products of K-moduli spaces
Abstract: In recent years, K-stability has made extraordinary progress in constructing moduli spaces of Fano varieties and log Fano pairs. This construction, however, is not explicit, and needs to be studied in a case-by-case basis to explicitly describe specific examples of moduli spaces for Fano varieties. In this talk I will describe the local and global structures of the K-moduli space of products of Fano varieties and provide a method to study K-moduli spaces of products of Fano varieties. I will demonstrate that a connected component of the K-moduli stack that contains a product, must only contain product Fano varieties. I will also demonstrate that there exists a well-defined morphism from the product of K-moduli stacks of Fano varieties to the K-moduli stack of their product and show that it is an isomorphism under specific conditions. Using this I will present some explicit examples of reduced connected components of the K-moduli stack of Fano threefolds, and log Fano pairs.
Nikolaos Tsakanikas Primitive Enriques varieties
Abstract: I will introduce the class of primitive Enriques varieties and I will outline the basic properties of these geometric objects. The talk is based on joint work with
Francesco Denisi, Ángel David Rios Ortiz and Zhixin Xie.
Eduardo Alves da Silva Classification of log Calabi-Yau pairs (P^3,D) of coregularity 2
Abstract: The problem of classifying log Calabi-Yau pairs up to volume preserving (or crepant) equivalence is very challenging. Recently, some progress was made by Ducat for pairs of the form (P^3,D) and of coregularity ≤ 1. Whilst invariants and refinements in the classification have been studied especially in the coregularity 0 case, the high coregularity one is the hardest to analyze. In this talk, I will illustrate such a statement by addressing the missing case of coregularity 2 for pairs of the form (P^3,D) and sharing some interesting findings. This is a joint work in progress with Daniela Paiva, Sokratis Zikas & Felipe Zingali Meira.
Carolina Tamborini Hodge theory and projective structures on compact Riemann surfaces
Abstract: We discuss properties and open questions concerning families of projective structures on the moduli space of curves.
Aline Zanardini
Abstract: TBD
Shiji Lyu Singularities of excellent rings and schemes
Abstract: TBD
Alapan Mukhopadhyay Frobenius, Singularities and Homological Algebra.
Abstract: The Frobenius endomorphism appears in the definitions of the prime characteristic analogues of the singularities of complex varieties-- appearing in the Minimal Model Programme. We aim to provide an explanation of the appearance of Frobenius, in the characterization of these prime characterisitc singularity classes. We prove that the bounded derived category of a prime characteristic variety can be generated from the perfect complexes using the Frobenius pushforward functor. Our result generalizes earlier characterization of homological properties using Frobenius, notably Kunz's theorem. The talk reports a joint work with Ballard, Lank, Iyengar and Pollitz.
Yuta Takada Automorphisms of K3 surfaces
Abstract: TBD
Michele Pernice Moduli stacks of genus one Gorenstein curves with projective good moduli spaces
Abstract: The search for alternative compactifications of the moduli space of smooth curves has been central in the panorama of moduli spaces. A possible way to construct such compactifications is allowing curves with worse-than-nodal singularities in the moduli problem and imposing some stability conditions using the combinatorics of the curves to get the desired moduli space. We classify the open substacks inside the moduli stack $\mathcal{G}_{1,n}$ of $n$-pointed Gorenstein curves of genus one which admits a proper good moduli space. They agree with those defined by Bozlee, Kuo and Neff. Moreover, we will prove that these spaces are actually projective and we will explain why the classification is a consequence of a wall-crossing phenomenon. This is a on-going project with Luca Battistella and Andrea Di Lorenzo.
Quentin Posva MMP singularities of infinitesimal quotient singularities
Abstract: TBD
Monday 7/21, 5:30-6:45pm
Session A (ENGRG 100 chaired by A. Gibney)
Grisha Taroyan De Rham Theory in Derived Differential Geometry
Abstract: I will explain how two different notions of the de Rham stack arising in derived differential geometry lead to a version of the de Rham isomorphism and a Riemann--Hilbert correspondence. The talk is based on a recent preprint arXiv:2505.03978.
Sridhar Venkatesh Local cohomology of toric varieties
Abstract: Based on joint work with Hyunsuk Kim, I will present some new results on the local cohomological dimension of toric varieties. In particular, we show that it is not a combinatorial invariant.
Donggun Lee Representations on the cohomology of the moduli space of pointed rational curves
Abstract: The moduli space of pointed rational curves has a natural action of the symmetric group permuting the marked points. I will present combinatorial and recursive formulas for the induced representation on its cohomology and discuss various log-concavity phenomena. Based on joint works with Jinwon Choi and Young-Hoon Kiem.
Yiyu Wang Local Euler obstruction of matroid Schubert varieties
Abstract: The local Euler obstruction number of a matroid Schubert variety is given by the characteristic polynomial of the matroid evaluating at 2.
Evan Sundbo A Decomposition Theorem for Broken Toric Varieties
Abstract: I'll show you a decomposition statement that works for broken toric varieties and explain how we use it.
Ruoxi Li (cancelled) Motivic Classes of Stacks with Applications to Higgs Bundles
Abstract: I will focus on the motivic classes of stacks in finite characteristic and give the explicit formulas for the motivic classes of moduli of Higgs bundles.
Yilong Zhang Invariant Cycle Theorem over Integers
Abstract: We show in an explict example that the Local Invariant Cycle Theorem fails with integer cofficients.
Amal Mattoo Objects of a Phantom on a Rational Surface
Abstract: We construct families of objects in Johannes Krah’s phantom on a rational surface and show that they recover some of the geometry of the underlying surface.
Eduardo de Lorenzo Poza Contact loci and the arc-Floer conjecture
Abstract: The arc-Floer conjecture predicts a relationship between the topology of the arc space of an isolated hypersurface singularity, and the symplectic geometry of the associated Milnor fibration. Here we will explain this conjecture and its solution in the one-dimensional case, the only known case up to this date.
Jas Singh Smooth Calabi-Yau varieties with large index and Betti numbers
Abstract: "A normal variety X is called Calabi-Yau if its canonical divisor is Q-linearly equivalent to 0. The index of X is the smallest positive integer m so that mK_X~0. We construct smooth, projective Calabi-Yau varieties in every dimension with doubly exponentially growing index, which we conjecture to be maximal in every dimension. We also construct smooth, projective Calabi-Yau varieties with extreme topological invariants; namely, their Euler characteristics and the sums of their Betti numbers grow doubly exponentially. These are conjecturally extremal in every dimension. The varieties we construct are known in small dimensions but we believe them to be new in general. This work builds off of the singular Calabi-Yau varieties found by Esser, Totaro, and Wang."
Haohua Deng New progress on completing period mappings
Abstract: I will summary recent breakthroughs in completing general period mappings.
Giusi Capobianco The tropical Martens' theorem
Abstract: We study the conjecture stated by Jensen and Len on the tropical version of Martens' theorem. We recall Coppens' counterexample and generalize the construction to anothe class of graphs and prove that these are the only counterexamples to the conjecture.
Yuki Mizuno: Bondal-Orlov’s reconstruction theorem in noncommutative projective geometry
Abstract: I will explain Bondal-Orlov's renconstruction theorem holds in the setting of noncommutative projective geometry
Cancelled -- Daniel Brogan Hodge theory of secant varieties
Abstract: We will discuss some results about the constant mixed Hodge module on secant varieties of curves, paying special attention to the case of a rational normal curve.
Monday 7/28, 5:30-6:45pm
Session A (ENGRG 100 chaired by B. Poonen)
Sjoerd de Vries Hecke operators on Drinfeld modular forms
Abstract: The properties of the Hecke action on Drinfeld modular forms are still largely mysterious. What is known can be said in four minutes. In the last minute I will show some suggestive pictures.
Jakub Löwit On equivariant K-theory, affine Grassmannians and perfection
Abstract: We study the trace from equivariant algebraic K-theory to functions on certain fixed point schemes modeling Hochschild homology. We show that this is an equivalence in interesting examples after perfection in characteristic p, in particular for Schubert varieties in the perfect affine Grassmannian of GL_n.
Connor Stewart Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers
Abstract: We prove an inequality between the conductor and discriminant of a Z/nZ cover of P^1 defined over a discretely valued field with perfect residue field of characteristic prime to n. (Joint work with Andrew Obus and Padmavathi Srinivasan.)
Divyasree C Ramachandran Severi-Brauer bundles violating Hasse principle
Abstract: We study Severi–Brauer bundles and their Brauer groups. We answer a question posed by Bjorn Poonen in a more general setting by constructing Severi–Brauer bundles that fails the Hasse principle for rational points, without requiring explicit calculations. Based on a joint work with B. Samanta and M. Biswas.
Pankaj Singh Classifying torsors of tori with Brauer groups
Abstract: Using Mackey functors, we provide a general framework for classifying torsors of algebraic tori in terms of Brauer groups of finite field extensions of the base field. This generalizes Blunk's description of the tori associated to del Pezzo surfaces of degree 6 to all retract rational tori, essentially the largest class for which this is possible.
Zachary Gardner Moduli of prismatic (G,mu)-apertures
Abstract: Let G be a smooth affine Z_p-group scheme and mu a cocharacter with 1-bounded weights. Given this data, I will define prismatic (G,mu)-apertures and describe the key properties of their moduli. Such objects serve as group theoretic generalizations of p-divisible groups, complete with their own Dieudonne theory and Grothendieck-Messing theory. (Joint work with Keerthi Madapusi)
Cancelled -- Murat Uyar The Brauer-Manin Obstruction on a K3 Surface
Abstract: We study the Brauer–Manin obstruction on a K3 surface that appears in Shigeru Mukai's classification and admits a finite subgroup of symplectic automorphisms embeddable in the Mathieu group M_20. (Joint work with Colin Ingalls and Adam Logan)
Casimir Kothari Dieudonné Theory and Moduli of Finite Group Schemes
Abstract: Dieudonné theory classifies finite group schemes over a perfect field of positive characteristic in terms of the linear-algebraic data of Dieudonné modules. In this talk I will discuss extensions of Dieudonné theory to more general bases, and state a classification theorem for certain connected group schemes over arbitrary bases. This is joint work with Joshua Mundinger.
Sidhanth Raman Hilbert's 13th Problem for Braid Groups
Abstract: How hard is it to solve a polynomial? It can be pretty difficult, and in the sense of resolvent problems, this question is unanswered and wide open. In this talk, I'll share some joint work with Claudio Gomez-Gonzales and Jesse Wolfson on a slightly more general problem: how hard is it to write down a section of a G-torsor? When G is the braid group, we can say a lot.
James Austin Myer Topological Obstructions to the Existence of a Resolution of the Singularities of a Variety
Abstract: We discuss the construction of topological obstructions to the existence of a resolution
of the singularities of a variety à la René Thom.
Jake Huryn On the "tautological" local systems on Shimura varieties
The formalism of canonical models allows one to build local systems on arbitrary Shimura varieties. They arise from the cohomology of Abelian varieties in many cases, but are otherwise not known to be of geometric origin. I will describe some recent results on the properties of these local systems in the general case. (Based on joint work with Kiran Kedlaya, Christian Klevdal, and Stefan Patrikis and joint work with Yifei Zhang)
18:36
Alice Lin A Northcott property for heights of isogenous motives
Koshikawa defines a generalization of the Faltings height to motives defined over a number field. Assuming the Mumford-Tate conjecture, we prove a Northcott property for this height in the isogeny class of a motive, where the isogenous motives are not required to be defined over the same number field.