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Top Papers in Holomorphic methods

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Identities between Modular Graph Forms

This paper investigates the relations between modular graph forms, which are
generalizations of the modular graph functions that were introduced in earlier
papers motivated by the structure of the low

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Geometric methods in holomorphic dynamics

In this note we review a selection of contemporary research themes in
holomorphic dynamics. The main topics that will be discussed are: geometric
(laminar and woven) currents and their applications, b

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Ffoliations in holomorphic curves

About $\mathcal{C}^\infty$ foliations by holomorphic curves on complex surfaces

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Holomorphic Density Functional Theory

Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham Density Functional Theory (KS-DFT) both have the potential to yield multiple solutions. However, the formal r

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Theta Series for Quadratic Forms of Signature $(n-1,1)$ with (Spherical) Polynomials

We construct almost holomorphic and holomorphic modular forms by considering
theta series for quadratic forms of signature $(n-1,1)$. We include homogeneous
and spherical polynomials in the definition

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On the relationship between orbitals of interior points and orbits of boundary points under iterates of holomorphic maps

The Denjoy--Wolff set for holomorphic sequences, non-autonomous dynamical systems and wandering domains

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Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups -- Arithmetic Holomorphic Structures

Let $p$ be a prime number. Let $X/E$ be a geometrically connected, smooth,
quasi-projective variety over a finite extension $E/\mathbb{Q}_p$. In this
paper I demonstrate the existence of isomorphs of

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On the holomorphic extensions of holomorphic jets associated with high tensor powers of a positive line bundle along submanifolds

The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds

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Holomorphic Floer theory and Donaldson-Thomas invariants

We present several expected properties of the holomorphic Floer theory of a
holomorphic symplectic manifold. In particular, we propose a conjecture
relating holomorphic Floer theory of Hitchin integra

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Constraints in the BV formalism: six-dimensional supersymmetry and its twists

We formulate the abelian six-dimensional $\mathcal{N}=(2,0)$ theory
perturbatively, in a generalization of the Batalin-Vilkovisky formalism. Using
this description, we compute the holomorphic and non-

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Holomorphic integer graded vertex superalgebras

In this note we study holomorphic integer graded vertex superalgebras. We
prove that all such vertex superalgebras of central charge 8 and 16 are purely
even. For the case of central charge 24 we prov

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Phase and amplitude analysis of holomorphic wavelets

Multiscale decompositions of Hardy spaces

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Holomorphic polyvector fields on toric varieties

In this paper, we give an explicit description of holomorphic polyvector
fields on smooth compact toric varieties, which generalizes Demazure's result
of holomorphic vector fields on toric varieties.

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All holomorphic operator algebras of central charge with non-trivial weight one subspaces are unitary

Unitary forms for holomorphic vertex operator algebras of central charge $24$

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First moments of Rankin-Selberg convolution of Automorphic Forms on $GL(2)$

We obtain a first moment formula for Rankin-Selberg convolution $L$-series of
holomorphic modular forms or Maass forms of arbitrary level on $GL(2)$, with an
orthonormal basis of Maass forms. One cons

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Siegel theta series for quadratic forms of signature $(m-1,1)$

We investigate Siegel theta series for quadratic forms of signature
$(m-1,1)$. On the one hand, we construct a holomorphic series that does not
transform like a modular form. On the other hand, we con

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Holomorphic Quantum Computing

We introduce a model of computing on holomorphic functions, which captures
bosonic quantum computing through the Segal-Bargmann representation of quantum
states. We argue that this holomorphic represe

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A p-adic Eisenstein measure for unitary groups

We construct a p-adic Eisenstein measure with values in the space of p-adic
automorphic forms on certain unitary groups. Using this measure, we p-adically
interpolate certain special values of both ho

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A knot Floer stable homotopy type

Given a grid diagram for a knot or link K in $S^3$, we construct a spectrum
whose homology is the knot Floer homology of K. We conjecture that the homotopy
type of the spectrum is an invariant of K. O

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Holomorphic Anomalies, Fourfolds and Fluxes

We investigate holomorphic anomalies of partition functions underlying string
compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic
fourfolds the partition functions have an a

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