Jason Semeraro

activity

20122026

most citedWeight conjectures for fusion systems

13 citations · 27 across the 24 of their papers we have counts for

collaborators

30 papers

math.GR2026

Modules with few Jordan blocks for rank $1$ groups of Lie type and related groups

Valentina Grazian, Justin Lynd, Chris Parker +2

Suppose that $p$ is a prime and $X$ is a finite group with a strongly $p$ -embedded subgroup, for example a rank $1$ group of Lie type in characteristic $p$ . Let $m$ denote the $p$ -…

math.RT2025

On character tables for fusion systems

Thomas Lawrence, Jason Semeraro

A character table $X$ for a saturated fusion system $F$ on a finite $p$ -group $S$ is the square matrix of values associated to a basis of the lattice of virtual $\mathcal…

math.RT2025

Partial character tables for $Z_{ℓ}$ -spetses

Radha Kessar, Gunter Malle, Jason Semeraro

Let $G$ be a simply connected $Z_{ℓ}$ -spets, let $q$ be a prime power, prime to $ℓ$ and let $S$ be the underlying Sylow $ℓ$ -subgroup. Firstly, motivate…

math.RT2025

Weight conjectures for fusion systems on an extraspecial group

Radha Kessar, Markus Linckelmann, Justin Lynd +1

In a previous paper, we stated and motivated counting conjectures for fusion systems that are purely local analogues of several local-to-global conjectures in the modular represent…

math.GR2025

Fusion systems related to polynomial representations of $SL_{2} (q)$

Valentina Grazian, Chris Parker, Jason Semeraro +1

Let $q$ be a power of a fixed prime $p$ . We classify up to isomorphism all simple saturated fusion systems on a certain class of $p$ -groups constructed from the polynomial represen…

math.GR2024

On $e$ -local structures for $Z_{ℓ}$ -spetses

Damiano Rossi, Jason Semeraro

Let $q$ be a prime power, $ℓ$ a prime not dividing $q$ , and $e$ the order of $q$ modulo $ℓ$ . We show that the geometric realisation of the nerve of the transporter category o…

math.RT2024

Weight conjectures for Parker--Semeraro fusion systems

Radha Kessar, Jason Semeraro, Patrick Serwene +1

We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain th…

math.GR2024

Spectra of subrings of cohomology generated by characteristic classes for fusion systems

Ian J. Leary, Jason Semeraro

If $F$ is a saturated fusion system on a finite $p$ -group $S$ , we define the Chern subring $C h (F)$ of $F$ to be the subring of the mod- $p$ cohomology…

math.RT2023

Weights for compact connected Lie groups

Radha Kessar, Gunter Malle, Jason Semeraro

Let $ℓ$ be a prime. If $G$ is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from $ℓ$ , and $ℓ$ is a good pr…

math.GR2022

Weights for $ℓ$ -local compact groups

Jason Semeraro

In this note, we initiate the study of $F$ -weights for an $ℓ$ -local compact group $F$ over a discrete $ℓ$ -toral group $S$ with discrete torus $T$ . Motivat…

math.RT2021

The principal block of a $Z_{ℓ}$ -spets and Yokonuma type algebras

Radha Kessar, Gunter Malle, Jason Semeraro

We formulate conjectures concerning the dimension of the principal block of a $Z_{ℓ}$ -spets (as defined in our earlier paper), motivated by analogous statements for fini…

math.RT2020

Weight conjectures for $ℓ$ -compact groups and spetses

Radha Kessar, Gunter Malle, Jason Semeraro

Fundamental conjectures in modular representation theory of finite groups, more precisely, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture, can be expressed i…

math.GR2020★ 2 cited

Algorithms for fusion systems with applications to $p$ -groups of small order

Chris Parker, Jason Semeraro

For a prime $p$ , we describe a protocol for handling a specific type of fusion system on a $p$ -group by computer. These fusion systems contain all saturated fusion systems. This fr…

math.RT2019

A $2$ -compact group as a spets

Jason Semeraro

In 1993, Broué, Malle and Michel initiated the study of spetses on the Greek island bearing the same name. These are mysterious objects attached to non-real Weyl groups. In algebra…

math.RT2018★ 13 cited

Weight conjectures for fusion systems

Radha Kessar, Markus Linckelmann, Justin Lynd +1

Many of the conjectures of current interest in the representation theory of finite groups in characteristic $p$ are local-to-global statements, in that they predict consequences fo…

math.GR2018

Fusion systems on maximal class $3$ -groups of rank two revisited

Chris Parker, Jason Semeraro

We complete the determination of saturated fusion systems on maximal class 3-groups of rank two.

math.GR2017

Weights in a Benson-Solomon block

Justin Lynd, Jason Semeraro

To each pair consisting of a saturated fusion system over a $p$ -group together with a compatible family of Külshammer-Puig cohomology classes, one can count weights in a hypothetic…

math.GR2017★ 8 cited

Reduced fusion systems over $p$ -groups with abelian subgroup of index $p$ : III

Bob Oliver, Albert Ruiz

We finish the classification, begun in two earlier papers, of all simple fusion systems over finite nonabelian $p$ -groups with an abelian subgroup of index $p$ . In particular, this…

math.CO2017

The cycle polynomial of a permutation group

Peter J. Cameron, Jason Semeraro

The cycle polynomial of a finite permutation group $G$ is the generating function for the number of elements of $G$ with a given number of cycles: \[F_G(x) = \sum_{g\in G}x^{c(g)},…

math.GR2016★ 1 cited

Fusion systems over a Sylow $p$ -subgroup of $G_{2} (p)$

Chris Parker, Jason Semeraro

For $S$ a Sylow $p$ -subgroup of the group $G_{2} (p)$ for $p$ odd, up to isomorphism of fusion systems, we determine all saturated fusion systems $F$ on $S$ with $O…

math.GR2016

Reduced fusion systems over $p$ -groups with abelian subgroup of index $p$ : II

David A. Craven, Bob Oliver, Jason Semeraro

Let $p$ be an odd prime, and let $S$ be a $p$ -group with a unique elementary abelian subgroup $A$ of index $p$ . We classify the simple fusion systems over all such groups $S$ in wh…

math.GR2016

Conway's groupoid and its relatives

Nick Gill, Neil I. Gillespie, Jason Semeraro +1

In 1997, John Conway constructed a $6$ -fold transitive subset $M_{13}$ of permutations on a set of size $13$ for which the subset fixing any given point was isomorphic to the Mathi…

math.GR2015★ 1 cited

Conway groupoids, regular two-graphs and supersimple designs

Nick Gill, Neil I. Gillespie, Cheryl E. Praeger +1

A $2 - (n, 4, λ)$ design $(Ω, B)$ is said to be supersimple if distinct lines intersect in at most two points. From such a design, one can construct a certain subset of Sym$(…

math.CO2015

Tournaments, 4-uniform hypergraphs, and an exact extremal result

Karen Gunderson, Jason Semeraro

We consider $4$ -uniform hypergraphs with the maximum number of hyperedges subject to the condition that every set of $5$ vertices spans either $0$ or exactly $2$ hyperedges and giv…

Modules with few Jordan blocks for rank 1 groups of Lie type and related groups

On character tables for fusion systems

Partial character tables for Zℓ​-spetses

Weight conjectures for fusion systems on an extraspecial group

Fusion systems related to polynomial representations of SL2​(q)

On e-local structures for Zℓ​-spetses

Weight conjectures for Parker--Semeraro fusion systems

Spectra of subrings of cohomology generated by characteristic classes for fusion systems

Weights for compact connected Lie groups

Weights for ℓ-local compact groups

The principal block of a Zℓ​-spets and Yokonuma type algebras

Weight conjectures for ℓ-compact groups and spetses

Algorithms for fusion systems with applications to p-groups of small order

A 2-compact group as a spets

Weight conjectures for fusion systems

Fusion systems on maximal class 3-groups of rank two revisited

Weights in a Benson-Solomon block

Reduced fusion systems over p-groups with abelian subgroup of index p: III

The cycle polynomial of a permutation group

Fusion systems over a Sylow p-subgroup of G2​(p)

Reduced fusion systems over p-groups with abelian subgroup of index p: II

Conway's groupoid and its relatives

Conway groupoids, regular two-graphs and supersimple designs

Tournaments, 4-uniform hypergraphs, and an exact extremal result

Modules with few Jordan blocks for rank $1$ groups of Lie type and related groups

Partial character tables for $Z_{ℓ}$ -spetses

Fusion systems related to polynomial representations of $SL_{2} (q)$

On $e$ -local structures for $Z_{ℓ}$ -spetses

Weights for $ℓ$ -local compact groups

The principal block of a $Z_{ℓ}$ -spets and Yokonuma type algebras

Weight conjectures for $ℓ$ -compact groups and spetses

Algorithms for fusion systems with applications to $p$ -groups of small order

A $2$ -compact group as a spets

Fusion systems on maximal class $3$ -groups of rank two revisited

Reduced fusion systems over $p$ -groups with abelian subgroup of index $p$ : III

Fusion systems over a Sylow $p$ -subgroup of $G_{2} (p)$

Reduced fusion systems over $p$ -groups with abelian subgroup of index $p$ : II