C. Ingalls

activity

20042026

most citedNoncrossing partitions and representations of quivers

132 citations · 204 across the 31 of their papers we have counts for

collaborators

38 papers

math.AG2026

Some terminal orders on 3-folds

Daniel Chan, Colin Ingalls

We produce the first known examples of non-trivial terminal local orders in the 3-dimensional case. We exhibit two different constructions. The first produces maximal orders with g…

math.OA2023

Remarks on computing the Grothendieck rings of C*-algebras

E. Ghamari, C. Ingalls, D. Kucerovsky

In this paper, we present a captivating construction by Grothendieck, originally formulated for algebraic varieties, and adapt it to the realm of C*-algebras. Our main objective is…

math.AC2023

Log Centres of Noncommutative Crepant Resolutions are Kawamata Log Terminal: Remarks on a paper of Stafford and van den Bergh

Colin Ingalls, Takehiko Yasuda

We show that if a finitely generated prime algebra $Δ$ is a finitely generated maximal Cohen-Macaulay module over its centre $Z$ , and has global dimension equal to $dim Z$ , then t…

math.RT2023

A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties

Yuly Billig, Colin Ingalls

We construct a quasi-coherent sheaf of associative algebras which controls a category of $A V$ -modules over a smooth quasi-projective variety. We establish a local structure theorem…

math.RA2022★ 2 cited

Terminal orders on arithmetic surfaces

Daniel Chan, Colin Ingalls

The local structure of terminal Brauer classes on arithmetic surfaces were classified in [CI21] generalising the classification on geometric surfaces carried out in [CI05]. Part of…

math.AG2022★ 1 cited

A differential analogue of the wild automorphism conjecture

Jason Bell, Colin Ingalls, Rahim Moosa +1

A differential analogue of the conjecture of Reichstein, Rogalski, and Zhang in algebraic dynamics is here established: if $X$ is a projective variety over an algebraically closed…

math.CO2022

Sets of mutually orthogoval projective and affine planes

Charles J. Colbourn, Colin Ingalls, Jonathan Jedwab +3

A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at…

math.AC2022

Matrix Factorizations of the discriminant of $S_{n}$

Eleonore Faber, Colin Ingalls, Simon May +1

Consider the symmetric group $S_{n}$ acting as a reflection group on the polynomial ring $k [x_{1}, \dots, x_{n}]$ , where $k$ is a field such that Char $(k)$ does not divide $n!$ . We use…

math.AG2022★ 1 cited

On stacky surfaces and noncommutative surfaces

Eleonore Faber, Colin Ingalls, Shinnosuke Okawa +1

Let $k$ be an algebraically closed field of characteristic $\geq 7$ or zero. Let $A$ be a tame order of global dimension $2$ over a normal surface $X$ over $\mat…

math.NT2022

Definite orthogonal modular forms: Computations, Excursions and Discoveries

Eran Assaf, Dan Fretwell, Colin Ingalls +3

We consider spaces of modular forms attached to definite orthogonal groups of low even rank and nontrivial level, equipped with Hecke operators defined by Kneser neighbours. After…

math.AG2021

The minimal model program for arithmetic surfaces enriched by a Brauer class

Daniel Chan, Colin Ingalls

We examine the noncommutative minimal model program for orders on arithmetic surfaces, or equivalently, arithmetic surfaces enriched by a Brauer class $β$ . When $β$ has prime index…

math.AG2020

Explicit coverings of families of elliptic surfaces by squares of curves

Colin Ingalls, Adam Logan, Owen Patashnick

We show that, for each $n > 0$ , there is a family of elliptic surfaces which are covered by the square of a curve of genus $2 n + 1$ , and whose Hodge structures have an action by ${\mat…

math.RT2020

McKay quivers and Lusztig algebras of some finite groups

Ragnar-Olaf Buchweitz, Eleonore Faber, Colin Ingalls +1

We are interested in the McKay quiver $Γ (G)$ and skew group rings $A * G$ , where $G$ is a finite subgroup of $GL (V)$ , where $V$ is a finite dimensional vector space over a f…

math.AG2020★ 1 cited

Crepant resolutions of double covers: On the Cynk-Hulek criterion for crepant resolutions of double cover

Colin Ingalls, Adam Logan

A collection $S = {D_{1}, \dots, D_{n}}$ of divisors in a smooth variety $X$ is an {\em arrangement} if intersections of all subsets of $S$ are smooth. We show that a double cover of…

math.RT2020★ 1 cited

$A V$ modules of finite type on affine space

Yuly Billig, Colin Ingalls, Amir Nasr

We study the category of modules admitting compatible actions of the Lie algebra $V$ of vector fields on an affine space and the algebra $A$ of polynomial funct…

math.NT2020

Quotient graphs and amalgam presentations for unitary groups over cyclotomic rings

Colin Ingalls, Bruce W. Jordan, Allan Keeton +2

Suppose $4∣ n$ , $n \geq 8$ , $F = F_{n} = Q (ζ_{n} + ζ ˉ_{n})$ , and there is one prime $p = p_{n}$ above $2$ in $F_{n}$ . We study amalgam presentations for $\operatornam…

math.NT2019

Sarnak's conjecture in quantum computing, cyclotomic unitary group coranks, and Shimura curves

Colin Ingalls, Bruce W. Jordan, Allan Keeton +2

Sarnak's conjecture in quantum computing concerns when the groups $PU_{2}$ and $PSU_{2}$ over cyclotomic rings $Z [ζ_{n}, 1/2]$ with $ζ_{n} = e^{2 π i / n}$ …

math.NT2019

The Clifford-cyclotomic group and Euler-Poincaré characteristics

Colin J. Ingalls, Bruce W. Jordan, Allan Keeton +2

For an integer $n \geq 8$ divisible by $4$ , let $R_{n} = Z [ζ_{n}, 1/2]$ and let $U_{2} (R_{n})$ be the group of $2 \times 2$ unitary matrices with entries in $R_{n}$ . Set $…

math.GR2018

The magic square of reflections and rotations

Ragnar-Olaf Buchweitz, Eleonore Faber, Colin Ingalls

We show how Coxeter's work implies a bijection between complex reflection groups of rank two and real reflection groups in $O (3)$ . We also consider this magic square of reflections…

math.RA2018

Low dimensional orders of finite representation type

Daniel Chan, Colin Ingalls

In this paper, we study noncommutative surface singularities arising from orders. The singularities we study are mild in the sense that they have finite representation type or, equ…

math.AG2017★ 6 cited

A McKay correspondence for reflection groups

Ragnar-Olaf Buchweitz, Eleonore Faber, Colin Ingalls

We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A = S * G$ . If $G$ is generated by order two…

math.AG2017

The minimal model program for b-log canonical divisors and applications

Daniel Chan, Kenneth Chan, Louis de Thanhoffer de Völcsey +8

We discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log va…

math.AG2017

Period-index bounds for arithmetic threefolds

Benjamin Antieau, Asher Auel, Colin Ingalls +2

The standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a $p$ -adic field predicts that the index divides the cube of the period. Using G…

math.RT2017

Homological behavior of idempotent subalgebras and Ext algebras

Colin Ingalls, Charles Paquette

Let $A$ be a (left and right) Noetherian ring that is semiperfect. Let $e$ be an idempotent of $A$ and consider the ring $Γ := (1 - e) A (1 - e)$ and the semi-simple right $A$ -module $S_e…

Some terminal orders on 3-folds

Remarks on computing the Grothendieck rings of C*-algebras

Log Centres of Noncommutative Crepant Resolutions are Kawamata Log Terminal: Remarks on a paper of Stafford and van den Bergh

A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties

Terminal orders on arithmetic surfaces

A differential analogue of the wild automorphism conjecture

Sets of mutually orthogoval projective and affine planes

Matrix Factorizations of the discriminant of Sn​

On stacky surfaces and noncommutative surfaces

Definite orthogonal modular forms: Computations, Excursions and Discoveries

The minimal model program for arithmetic surfaces enriched by a Brauer class

Explicit coverings of families of elliptic surfaces by squares of curves

McKay quivers and Lusztig algebras of some finite groups

Crepant resolutions of double covers: On the Cynk-Hulek criterion for crepant resolutions of double cover

AV modules of finite type on affine space

Quotient graphs and amalgam presentations for unitary groups over cyclotomic rings

Sarnak's conjecture in quantum computing, cyclotomic unitary group coranks, and Shimura curves

The Clifford-cyclotomic group and Euler-Poincaré characteristics

The magic square of reflections and rotations

Low dimensional orders of finite representation type

A McKay correspondence for reflection groups

The minimal model program for b-log canonical divisors and applications

Period-index bounds for arithmetic threefolds

Homological behavior of idempotent subalgebras and Ext algebras

Matrix Factorizations of the discriminant of $S_{n}$

$A V$ modules of finite type on affine space