193 citations · 494 across the 27 of their papers we have counts for
28 papers
Motivic Euler characteristics of moduli spaces of curves
Jonas Bergström, Samir Canning, Dan Petersen +1
A combination of recent results of Canning--Larson--Payne--Willwacher and Payne--Willwacher is that the motivic Euler characteristic of the moduli space of nonsingular cu…
Top weight cohomology of moduli spaces of Riemann surfaces and handlebodies
Louis Hainaut, Dan Petersen
We show that a certain locus inside the moduli space of hyperbolic surfaces, given by surfaces with "sufficiently many" short geodesics, is a classifying space of the handleb…
Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions
Jonas Bergström, Adrian Diaconu, Dan Petersen +1
We compute the stable homology of the braid group with coefficients in any Schur functor applied to the integral reduced Burau representation. This may be considered as a hyperelli…
Commutative homotopical algebra embeds into non-commutative homotopical algebra
Ricardo Campos, Dan Petersen, Daniel Robert-Nicoud +1
Over a field of characteristic zero, we show that the forgetful functor from the homotopy category of commutative dg algebras to the homotopy category of dg associative algebras is…
A remark on singular cohomology and sheaf cohomology
Dan Petersen
We prove a comparison isomorphism between singular cohomology and sheaf cohomology.
Correction to: "A spectral sequence for stratified spaces and configuration spaces of points"
Nir Gadish, Dan Petersen
We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an…
Factorization statistics and bug-eyed configuration spaces
Dan Petersen, Philip Tosteson
A recent theorem of Hyde proves that the factorizations statistics of a random polynomial over a finite field are governed by the action of the symmetric group on the configuration…
Representation stability, secondary stability, and polynomial functors
Jeremy Miller, Peter Patzt, Dan Petersen
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many fami…
A closer look at Kadeishvili's theorem
Dan Petersen
We give a proof of the Homotopy Transfer Theorem following Kadeishvili's original strategy. Although Kadeishvili originally restricted himself to transferring a dg algebra structur…
Lie, associative and commutative quasi-isomorphism
Ricardo Campos, Dan Petersen, Daniel Robert-Nicoud +1
Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg…
Cohomology of generalized configuration spaces
Dan Petersen
Let be a topological space. We consider certain generalized configuration spaces of points on , obtained from the cartesian product by removing some intersections of d…
Tautological classes with twisted coefficients
Dan Petersen, Mehdi Tavakol, Qizheng Yin
Let be the moduli space of smooth genus curves. We define a notion of Chow groups of with coefficients in a representation of , and we define a subgroup of…
A vanishing result for tautological classes on the moduli of K3 surfaces
Dan Petersen
Looijenga's vanishing theorem on the moduli space of curves says that the tautological ring vanishes above degree . We prove an analogous result for the tautological coh…
A spectral sequence for stratified spaces and configuration spaces of points
Dan Petersen
We construct a spectral sequence associated to a stratified space, which computes the compactly supported cohomology groups of an open stratum in terms of the compactly supported c…
Brown's dihedral moduli space and freedom of the gravity operad
Johan Alm, Dan Petersen
Francis Brown introduced a partial compactification of the moduli space . We prove that the gravity cooperad, given by the degree-shifted cohomologies of the s…
The Chow ring of a Fulton-MacPherson compactification
Dan Petersen
We give a short proof of a presentation of the Chow ring of the Fulton-MacPherson compactification of n points on an algebraic variety. The result can be found already in Fulton an…
Poincaré duality of wonderful compactifications and tautological rings
Dan Petersen
Let . Let be the moduli space of -pointed genus curves with rational tails. Let be the -fold fibered power of the universal curve over $M…
The tautological ring of the space of pointed genus two curves of compact type
Dan Petersen
We prove that the tautological ring of , the moduli space of n-pointed genus two curves of compact type, does not have Poincaré duality for any . This resul…
Cohomology of local systems on the moduli of principally polarized abelian surfaces
Dan Petersen
Let A_2 be the moduli stack of principally polarized abelian surfaces and V a smooth l-adic sheaf on A_2 associated to an irreducible rational finite dimensional representation of…
Minimal models, GT-action and formality of the little disk operad
Dan Petersen
We give a new proof of formality of the operad of little disks. The proof makes use of an operadic version of a simple formality criterion for commutative differential graded algeb…
The Gorenstein conjecture fails for the tautological ring of
Dan Petersen, Orsola Tommasi
Let be the smallest integer such that there is a non-tautological cohomology class of even degree on . We remark that there is such a non-tautological c…
The structure of the tautological ring in genus one
Dan Petersen
We prove Getzler's claims about the tautological ring of stable curves of genus one, i.e. that the tautological ring coincides with the even cohomology ring, and that all relations…
On the operad structure of admissible G-covers
Dan Petersen
We describe the modular operad structure on the moduli spaces of pointed stable curves equipped with an admissible -cover. To do this we are forced to introduce the notion of an…
A remark on Getzler's semi-classical approximation
Dan Petersen
Ezra Getzler notes in the proof of the main theorem of "The semi-classical approximation for modular operads" that "A proof of the theorem could no doubt be given using [a combinat…