131 citations · 651 across the 67 of their papers we have counts for
82 papers
The Deligne--Drinfeld conjecture after OpenAI
Thomas Willwacher
We provide a simplified and more human-friendly version of the proof of the Deligne--Drinfeld conjecture recently given by OpenAI.
The Prym-Green conjecture in even genera up to 30
Sam Payne, Thomas Willwacher
We prove the Prym-Green conjecture in every even genus from 20 to 30. The genus 24 case disproves the suggestion of Chiodo-Eisenbud-Farkas-Schreyer that the conjecture might fail i…
Polynomial point counts for moduli spaces of curves with marked points
Sam Payne, Thomas Willwacher
We prove that the number of curves of a fixed genus g with n marked points over finite fields is a polynomial function of the cardinality of the field if and only if g = 0 or 3g +…
On free generators in the Grothendieck-Teichmüller Lie Algebra
Thomas Willwacher
We prove that any homogeneous family in with nonzero coefficients of in generates a free Lie subalgebra, buildin…
The Johnson homomorphism, embedding calculus and graph complexes
Florian Naef, Thomas Willwacher
We explain how the Johnson homomorphism and the Enomoto-Satoh trace, as well as higher-loop-order generalizations, can be obtained from graph complexes originating in the Goodwilli…
FA-modules of holomorphic forms on
Samir Canning, Hannah Larson, Sam Payne +1
For fixed genus g and varying finite marking set A, the gluing and forgetful maps give the spaces of holomorphic forms on the moduli space of stable A-marked curves of genus g has…
Numerical computation of linearized KV and the Deligne-Drinfeld and Broadhurst-Kreimer conjectures
Florian Naef, Thomas Willwacher
We compute numerically the dimensions of the graded quotients of the linearized Kashiwara-Vergne Lie algebra lkv in low weight, confirming a conjecture of Raphael-Schneps in those…
The oriented graph complex revisited
Sergei Merkulov, Thomas Willwacher, Vincent Wolff
We prove that the Kontsevich graph complex and its oriented version are quasi-isomorphic as dg Lie algebras.
The motivic structures and in the cohomology of moduli spaces of curves
Samir Canning, Hannah Larson, Sam Payne +1
We study the appearances of and in the weight-graded compactly supported cohomology of moduli spaces of curves. As applications, we prove new n…
Moduli spaces of curves with polynomial point counts
Samir Canning, Hannah Larson, Sam Payne +1
We prove that the number of curves of a fixed genus g over finite fields is a polynomial function of the size of the field if and only if g is at most 8. Furthermore, we determine…
AI-assisted Automated Short Answer Grading of Handwritten University Level Mathematics Exams
Tianyi Liu, Julia Chatain, Laura Kobel-Keller +3
Effective and timely feedback in educational assessments is essential but labor-intensive, especially for complex tasks. Recent developments in automated feedback systems, ranging…
Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group
Michael Borinsky, Benjamin Brück, Thomas Willwacher
We compute the weight 2 cohomology of the Feynman transforms of the cyclic (co)operads and , and the top weight cohomology of the Feynman transfor…
Graph homology computations
Simon Brun, Thomas Willwacher
We compute numerically the homology of several graph complexes in low loop orders, extending previous results.
Models for configuration spaces of points via obstruction theory I
Thomas Willwacher
We derive rational (Sullivan) models for configuration spaces of points on manifolds purely from algebraic considerations via obstruction theory, essentially without the use of ana…
Weight 11 compactly supported cohomology of moduli spaces of curves
Sam Payne, Thomas Willwacher
We study the weight 11 part of the compactly supported cohomology of the moduli space of curves , using graph complex techniques, with particular attention to the case $n…
Stable cohomology of graph complexes in odd dimensions
Simon Brun, Thomas Willwacher
We study graph complexes related to configuration spaces and diffeomorphism groups of highly connected manifolds of odd dimension. In particular we compute the cohomology in the "h…
The weight two compactly supported Euler characteristic of moduli spaces of curves
Sam Payne, Thomas Willwacher
We derive a formula for the generating function for the weight two compactly supported -equivariant Euler characteristics of the moduli spaces of curves $\mathcal M_{g…
Weight two compactly supported cohomology of moduli spaces of curves
Sam Payne, Thomas Willwacher
We study the weight 2 graded piece of the compactly supported rational cohomology of the moduli spaces of curves and show that this can be computed as the cohomology of a…
Stable cohomology of graph complexes
Matteo Felder, Florian Naef, Thomas Willwacher
We study three graph complexes related to the higher genus Grothendieck-Teichmüller Lie algebra and diffeomorphism groups of manifolds. We show how the cohomology of these graph co…
On the homotopy type of the spaces of spherical knots in
Victor Turchin, Thomas Willwacher
We study the spaces of embeddings and those of long embeddings , i.e. embeddings of a fixed behavior outside a compact set. More pr…
On the rational homotopy type of embedding spaces of manifolds in
Benoit Fresse, Victor Turchin, Thomas Willwacher
We study the spaces of embeddings of manifolds in a Euclidean space. More precisely we look at the homotopy fiber of the inclusion of these spaces to the spaces of immersions. As a…
Oriented hairy graphs and moduli spaces of curves
Assar Andersson, Thomas Willwacher, Marko Zivkovic
We discuss a graph complex formed by directed acyclic graphs with external legs. This complex comes in particular with a map to the ribbon graph complex computing the (compactly su…
Mapping Spaces for DG Hopf Cooperads and Homotopy Automorphisms of the Rationalization of -operads
Benoit Fresse, Thomas Willwacher
We define a simplicial enrichment on the category of differential graded Hopf cooperads (the category of dg Hopf cooperads for short). We prove that our simplicial enrichment satis…
String topology and configuration spaces of two points
Florian Naef, Thomas Willwacher
Given a closed manifold . We give an algebraic model for the Chas-Sullivan product and the Goresky-Hingston coproduct. In the simply-connected case, this admits a particularly n…