Publications (42)
Algebraic K-theory of toric hypersurfaces
Matt Kerr, Charles Doran
We construct classes in the motivic cohomology of certain 1-parameter families of Calabi-Yau hypersurfaces in toric Fano n-folds, with applications to local mirror symmetry (growth…
Hodge adjacency conditions for singularities
RJ Acuna, Matt Kerr
We prove compatibility relations between mixed Hodge numbers of -Du Bois fibers in flat projective families and versal deformations of isolated -Du Bois singularities. These…
Higher Abel-Jacobi maps for 0-cycles
Matt Kerr
Starting from the candidate Bloch-Beilinson filtration on Chow groups of 0-cycles constructed by J. Lewis, we develop and describe geometrically a series of Hodge-theoretic invaria…
Motivic irrationality proofs
Matt Kerr
We exhibit geometric conditions on a family of toric hypersurfaces under which the value of a canonical normal function at a point of maximal unipotent monodromy is irrational.
Hodge theory of degenerations, (I): Consequences of the decomposition theorem
Matt Kerr, Radu Laza
We use the Decomposition Theorem to derive several generalizations of the Clemens-Schmid sequence, relating asymptotic Hodge theory of a degeneration to the mixed Hodge theory of i…
The Abel-Jacobi map for higher Chow groups
Matt Kerr, James Lewis, Stefan Müller-Stach
We construct a map between Bloch's higher Chow groups and Deligne homology for smooth, complex quasiprojective varieties on the level of complexes. For complex projective varieties…
Reciprocity Laws on Algebraic Surfaces via Iterated Integrals
Ivan Horozov, Matt Kerr
This paper presents a proof of reciprocity laws for the Parshin symbol and for two new local symbols, defined here, which we call 4-function local symbols. The reciprocity laws for…
Apéry extensions
Vasily Golyshev, Matt Kerr, Tokio Sasaki
The Apéry numbers of Fano varieties are asymptotic invariants of their quantum differential equations. In this paper, we initiate a program to exhibit these invariants as (mirror…
Exterior products of 0-cycles
Matt Kerr
We study the exterior product on 0-cycles modulo rational equivalence, and prove some nonvanishing results. The main tools used are higher cycle- and Abel-Jacobi- classes developed…
The 2-part of the Bloch-Kato conjecture, and indivisibility results, for of some elliptic curves
Neil Dummigan, Vasily Golyshev, Rob de Jeu +1
For certain integers , we investigate the 2-part of the Bloch-Kato conjecture for , where is part of a (twisted) Legendre family that is 2-iso…
Non-vanishing of Ceresa and Gross--Kudla--Schoen cycles associated to modular curves
Matt Kerr, Wanlin Li, Congling Qiu +1
Associated to an algebraic curve , there are two canonically constructed homologically trivial algebraic -cycles, the Ceresa cycle in the Jacobian of , and the Gross-Kudla…
Algebraic cycles and local quantum cohomology
Charles F. Doran, Matt Kerr
We review the Hodge theory of some classic examples from mirror symmetry, with an emphasis on what is intrinsic to the A-model, and on interesting open questions and problems. In p…
Local mirror symmetry and the sunset Feynman integral
Spencer Bloch, Matt Kerr, Pierre Vanhove
We study the sunset Feynman integral defined as the scalar two-point self-energy at two-loop order in a two dimensional space-time. We firstly compute the Feynman integral, for arb…
Classification of smooth horizontal Schubert varieties
Matt Kerr, Colleen Robles
We show that the smooth horizontal Schubert subvarieties of a rational homogeneous variety are homogeneously embedded cominuscule , and are classified by subdiagrams o…
A note on higher Green's functions
Charles F. Doran, Matt Kerr
We give a cycle-theoretic proof of the Gross-Zagier conjecture in weight four for several modular curves of genus zero.
An Exponential History of Functions with Logarithmic Growth
Matt Kerr, Gregory Pearlstein
We survey recent work on normal functions, including limits and singularities of admissible normal functions, the Griffiths-Green approach to the Hodge conjecture, algebraicity of…
The Abel-Jacobi Map for Higher Chow Groups, II
Matt Kerr, James D. Lewis
We explicitly describe cycle-class maps c_H from motivic cohomology to absolute Hodge cohomology, for smooth quasi-projective and (some) proper singular varieties, and compute spec…
Two applications of the integral regulator
Matt Kerr, Muxi Li
We review Li's refinement of the KLM regulator map, and use it to detect torsion phenomena in higher Chow groups.
Polarized relations on horizontal SL(2)s
Matt Kerr, Gregory Pearlstein, Colleen Robles
We introduce a relation on real conjugacy classes of SL(2)-orbits in a Mumford-Tate domain D which is compatible with natural partial orders on the sets of nilpotent orbits in the…
An explicit basis for the rational higher Chow groups of abelian number fields
Matt Kerr, Yu Yang
We review and simplify A. Beilinson's construction of a basis for the motivic cohomology of a point over a cyclotomic field, then promote the basis elements to higher Chow cycles a…
Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution
Genival da Silva, Matt Kerr, Gregory Pearlstein
We collect evidence in support of a conjecture of Griffiths, Green and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degene…
Specialization of cycles and the K-theory elevator
Pedro Luis del Angel, Charles Doran, Jaya Iyer +4
A general specialization map is constructed for higher Chow groups and used to prove a "going-up" theorem for algebraic cycles and their regulators. The results are applied to stud…
Simplicial Abel-Jacobi maps and reciprocity laws
Jose Ignacio Burgos Gil, Matt Kerr, James D. Lewis +1
We describe an explicit morphism of complexes that induces the cycle-class maps from (simplicially described) higher Chow groups to rational Deligne cohomology. The reciprocity law…
Normal functions, Picard-Fuchs equations, and elliptic fibrations on K3 surfaces
Xi Chen, Charles Doran, Matt Kerr +1
Using Gauss-Manin derivatives of normal functions, we arrive at some remarkable results on the non-triviality of the transcendental regulator for of a very general projective…
Three vignettes on hypergeometric normal functions
Matt Kerr
We use Hodge-theoretic methods to (i) explain number-theoretic identities of a type recently considered by Guillera and Zudilin, (ii) describe the Frobenius dual of Abel-Jacobi per…
Hodge theory of degenerations, (III): a vanishing-cycle calculus for non-isolated singularities
Matt Kerr, Radu Laza
We continue our study of the Hodge theory of degenerations, Part I of which covered consequences of the Decomposition Theorem and Part II of which concerned geometric applications…
A Feynman integral via higher normal functions
Spencer Bloch, Matt Kerr, Pierre Vanhove
We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical intern…
Deformation of rational singularities and Hodge structure
Matt Kerr, Radu Laza, Morihiko Saito
For a one-parameter degeneration of reduced compact complex analytic spaces of dimension , we prove the invariance of the frontier Hodge numbers (that is, with $pq(n{-…
The arithmetic of Calabi-Yau motives and mobile higher regulators
Vasily Golyshev, Matt Kerr
We construct elements in the motivic cohomology of certain rank 4 weight 3 Calabi--Yau motives, and write down explicit expressions for the regulators of these elements in the cont…
Geometric interpretation of toroidal compactifications of moduli of points in the line and cubic surfaces
Patricio Gallardo, Matt Kerr, Luca Schaffler
It is known that some GIT compactifications associated to moduli spaces of either points in the projective line or cubic surfaces are isomorphic to Baily-Borel compactifications of…
On the isomorphism question for complete Pick multiplier algebras
Matt Kerr, John E. McCarthy, Orr Shalit
Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra $\mv = \{f\big|_V : f \in \cM_d\}$, where is some integer or , $\cM_d$…
Naive boundary strata and nilpotent orbits
Matt Kerr, Gregory Pearlstein
We study certain real Lie-group orbits in the compact duals of Mumford-Tate domains, verifying a prediction made in [Green, Griffiths, Kerr; Mumford-Tate domains: their geometry an…
Unipotent extensions and differential equations (after Bloch-Vlasenko)
Matt Kerr
S. Bloch and M. Vlasenko recently introduced a theory of \emph{motivic Gamma functions}, given by periods of the Mellin transform of a geometric variation of Hodge structure, which…
Remarks on eigenspectra of isolated singularities
Ben Castor, Haohua Deng, Matt Kerr +1
We introduce a simple calculus, extending a variant of the Steenbrink spectrum, for describing Hodge-theoretic invariants of (smoothings of) isolated singularities with (relative)…
Boundary Components of Mumford-Tate Domains
Matt Kerr, Gregory Pearlstein
We study certain spaces of nilpotent orbits in Hodge domains, and treat a number of examples. More precisely, we compute the Mumford-Tate group of the limit mixed Hodge structure o…
Real regulator maps with finite 0-locus
RJ Acuna, Devin Akman, Matt Kerr
A Laurent polynomial in two variables is tempered if its edge polynomials are cyclotomic. Variation of coefficients leads to a family of smooth complete genus curves carrying a…
Hodge theory of degenerations, (II): vanishing cohomology and geometric applications
Matt Kerr, Radu Laza
We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of…
and quantum curves
Charles F. Doran, Matt Kerr, Soumya Sinha Babu
A 2015 conjecture of Codesido-Grassi-Mariño in topological string theory relates the enumerative invariants of toric CY 3-folds to the spectra of operators attached to their mirro…
Algebraic and analytic compactifications of moduli spaces
Patricio Gallardo, Matt Kerr
In this expository note, we offer an overview of the relationship between Hodge-theoretic and geometric compactifications of moduli spaces of algebraic varieties.
Variations of Hodge structure and orbits in flag varieties
Matt Kerr, Colleen Robles
Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford-Tate domains, arise as open --orbits in flag varieties $G/…
On the torsion locus of the Ceresa normal function
Matt Kerr, Salim Tayou
We prove that the positive-dimensional part of the torsion locus of the Ceresa normal function in is not Zariski dense when . Moreover, it has only finitel…
Normal Functions over Locally Symmetric Varieties
Ryan Keast, Matt Kerr
We classify the irreducible Hermitian real variations of Hodge structure admitting an infinitesimal normal function, and draw conclusions for cycle-class maps on families of abelia…