9 citations · 24 across the 14 of their papers we have counts for
16 papers
Coexact -form spectral gaps of hyperbolic rational homology spheres
Francesco Lin, Michael Lipnowski
We discuss a construction of families of hyperbolic rational homology spheres with coexact -form spectral gap uniformly bounded below which is well-suited for explicit computati…
Dirac spectral flow and Floer theory of hyperbolic three-manifolds
Francesco Lin, Michael Lipnowski
We study the interplay between hyperbolic geometry and monopole Floer homology for a closed oriented three-manifold with equipped with a torsion spin structure $\ma…
Rigid meromorphic cocycles for orthogonal groups
Henri Darmon, Lennart Gehrmann, Michael Lipnowski
Rigid meromorphic cocycles are defined in the setting of orthogonal groups of arbitrary real signature and constructed in some instances via a -adic analogue of Borcherds' singu…
Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds
Francesco Lin, Michael Lipnowski
Froyshov invariants are numerical invariants of rational homology three-spheres derived from gradings in monopole Floer homology. In the past few years, they have been employed to…
Towards optimal spectral gaps in large genus
Michael Lipnowski, Alex Wright
We show that the Weil-Petersson probability that a random surface has first eigenvalue of the Laplacian less than goes to zero as the genus goes to infinity.
Cohen-Lenstra heuristics and bilinear pairings in the presence of roots of unity
Michael Lipnowski, Will Sawin, Jacob Tsimerman
Let be a quadratic extension of global fields. We study Cohen-Lenstra heuristics for the -part of the relative class group when contai…
Monopole Floer homology, eigenform multiplicities and the Seifert-Weber dodecahedral space
Francesco Lin, Michael Lipnowski
We show that the Seifert-Weber dodecahedral space is an -space. The proof builds on our work relating Floer homology and spectral geometry of hyperbolic three-mani…
The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds
Francesco Lin, Michael Lipnowski
We exhibit the first examples of hyperbolic three-manifolds for which the Seiberg-Witten equations do not admit any irreducible solution. Our approach relies on hyperbolic geometry…
Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds
Michael Lipnowski, Mark Stern
We relate small 1-form Laplacian eigenvalues to relative cycle complexity on closed hyperbolic manifolds: small eigenvalues correspond to closed geodesics no multiple of which boun…
Detecting large simple rational Hecke modules for via congruences
Michael Lipnowski, George J. Schaeffer
We describe a novel method for bounding the dimension of the largest simple Hecke submodule of from below. Such bounds are of interest because of their…
On Bhargava's heuristics for -number fields and the number of elliptic curves of bounded conductor
Michael Lipnowski
We propose a new model for counting -number fields having the same local properties as the splitting field of the mod -Galois representation associa…
Cohen Lenstra Heuristics for Étale Group Schemes and Symplectic Pairings
Michael Lipnowski, Jacob Tsimerman
We generalize the Cohen-Lenstra heuristics over function fields to étale group schemes (with the classical case of abelian groups corresponding to constant group schemes). By u…
How Large is ?
Michael Lipnowski, Jacob Tsimerman
Let denote the number of isomorphism classes of -dimensional abelian varieties over the finite field of size Let denote the number of isomorphism classes…
Twisted limit formula for torsion and cyclic base change
Nicolas Bergeron, Michael Lipnowski
Let be the group of complex points of a real semi-simple Lie group whose fundamental rank is equal to 1, e.g. $G= \SL_2 (\C) \times \SL_2 (\C)$ or $\SL_3 (\C)$. Then the fundam…
Equivariant Torsion and Base Change
Michael Lipnowski
What is the true order of growth of torsion in the cohomology of an arithmetic group? Let be a quaternion over an imaginary quadratic field Let be a cyclic Galois ex…
The Equivariant Cheeger-Müller Theorem on Locally Symmetric Spaces
Michael Lipnowski
In this paper, we provide a concrete interpretation of equivariant Reidemeister torsion and demonstrate that Bismut-Zhang's equivariant Cheeger-Müller theorem simplifies considerab…