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Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardness
TLDR
It is shown that, given any graph property P that is closed under the removal of vertices and edges, and that is non-trivial for bipartite graphs, the problem #IndSub(P) is #W[1]-hard and cannot be solved in time f(k)*n^{o(k)} for any computable function f, unless the Exponential Time Hypothesis fails. Expand
Multiplicativity of the double ramification cycle
The double ramification cycle satisfies a basic multiplicative relation DRC(a).DRC(b) = DRC(a).DRC(a + b) over the locus of compact-type curves, but this relation fails in the Chow ring of the moduliExpand
Intersections of loci of admissible covers with tautological classes
For a finite group $G$, let $\H_{g,G,\xi}$ be the stack of admissible $G$-covers $C\to D$ of stable curves with ramification data $\xi$, $g(C)=g$ and $g(D)=g'$. There are source and target morphismsExpand
Tevelev degrees and Hurwitz moduli spaces
We interpret the degrees which arise in Tevelev’s study of scattering amplitudes in terms of moduli spaces of Hurwitz covers. Via excess intersection theory, the boundary geometry of the HurwitzExpand
admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves.
The tautological ring of the moduli space of stable curves has been studied extensively in the last decades. We present a SageMath implementation of many core features of this ring. This includesExpand
Counting Induced Subgraphs: A Topological Approach to #W[1]-hardness
TLDR
It is proved that for monotone properties $\Phi, the problem is hard for $\#\mathsf{IndSub}(\Phi)$ if the reduced Euler characteristic of the associated simplicial (graph) complex of $\ Phi$ is non-zero. Expand
Counting Small Induced Subgraphs Satisfying Monotone Properties
TLDR
It is shown that for any non-trivial monotone property, that is subgraph-closed, properties, the problem cannot be solved in time and any significant improvement over the brute-force approach is unlikely. Expand
Dimension theory of the moduli space of twisted $k$-differentials
In this note we extend the dimension theory for the spaces $\widetilde{\mathcal H}_g^k(\mu)$ of twisted $k$-differentials defined by Farkas and Pandharipande in [FP15] to the case $k>1$. InExpand
Counting Induced Subgraphs: A Topological Approach to #W[1]-hardness
TLDR
Applying tools from the “topological approach to evasiveness” which was introduced in the seminal paper of Khan, Saks and Sturtevant [FOCS 83], it is proved that IndSub ( Φ) is hard for every monotone property ofvarPhi and can not be solved in time. Expand
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