Christopher W.
Seaton
Professor, Department of Mathematics and Statistics
(formerly the Department of Mathematics and Computer Science)
CUR Mathematics and Computer Sciences Division 2021 Advanced Career Faculty Mentor Award
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Contact: |
Teaching (Spring 2024): |
Office Hours (Spring 2024): |
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Office: |
Ohlendorf 320 |
Math 116-01: Calculus with Business Applications
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E-mail: |
(the best way to reach me): seatonc-at-rhodes-dot-edu |
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Phone: |
901-843-3721 |
Math 362-01/2: Abstract Algebra I |
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Snail Mail: |
Math & Computer Science Rhodes College 2000 N. Parkway Memphis, TN 38112, USA |
Math 452-02: Research in Mathematics
Math 386-01/2: Junior Seminar
Math 486-01: Senior Seminar
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Students are
welcome and encouraged to make appointments at other times if my office hours are not convenient. The best way to do this is via e-mail.
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C. V.
Math 115: Applied Calculus Course
Development Materials
Some Slides from Groupoidfest 2015 (Special Session on The Analysis, Topology, and Geometry of Groupoids, Fall Southeastern Sectional Meeting of the AMS)
A universal Euler characteristic of non-orbifold groupoids and Riemannian structures on Lie groupoids.
(with Carla Farsi and Emily Proctor; preprint)
Euler characteristics of linear symplectic quotients and O(2)-spaces
(with Carla Farsi and Hannah Meit; submitted)
A symmetric function approach to polynomial regression.
(with Hans-Christian Herbig and Daniel Herden; submitted)
Isomorphisms of symplectic torus quotients.
(with Hans-Christian Herbig and Gerald Schwarz; to appear in the Journal of Symplectic Geometry)
When does the zero fiber of the moment map have rational singularities?
(with Hans-Christian Herbig and Gerald Schwarz; to appear in Geometry & Topology)
Multigraded Hilbert series of invariants, covariants, and symplectic quotients for some rank 1 Lie groups
(with Austin Barringer, Hans-Christian Herbig, Daniel Herden, Saad Khalid, and Lawton Walker; Communications in Algebra 52 (2024) 1000--1027)
Higher Koszul brackets on the cotangent complex
(with Hans-Christian Herbig and Daniel Herden;
International Mathematics Research Notices 2023, Issue 13 (2023) 11592--11644)
Hilbert series of symplectic quotients by the 2-torus
(with Hans-Christian Herbig and Daniel Herden;
Collectanea Mathematica) 74 (2023) 415--442)
Differentiable stratified groupoids and a de Rham theorem for inertia spaces
(with Carla Farsi and Markus Pflaum; Journal of Geometry and Physics 187 (2023), 104806)
Orbifold Euler characteristics of
non-orbifold groupoids
(with Carla Farsi; Journal of the London Mathematical Society) 106 (2022), 2342--2378)
The spectra of digraphs with Morita equivalent C*-algebras
(with Carla Farsi and Emily Proctor; Linear Algebra and its Applications 655 (2022), 28--64)
Approximating orbifold spectra using
collapsing connected sums
(with Carla Farsi and Emily Proctor; Journal of Geometric Analysis
31 (2021), 9433--9468)
The Laurent coefficients
of the Hilbert series of a Gorenstein algebra
(with Hans-Christian Herbig and Daniel Herden; Experimental Mathematics 30 (2021), 56--75)
Constructing symplectomorphisms
between symplectic torus quotients
(with Hans-Christian Herbig and Ethan Lawler;
Beiträge zur Algebra und
Geometrie / Contributions to Algebra and Geometry 61 (2020), 581--604)
Hilbert series associated to
symplectic quotients by SU2
(with Hans-Christian Herbig and Daniel Herden;
International Journal
of Algebra and Computation 30 (2020), 1323--1357)
The Hilbert series of SL2-invariants
(with Pedro de Carvalho Cayres Pinto, Hans-Christian Herbig, and Daniel Herden;
Communications in
Contemporary Mathematics 22 (2020) 1950017)
Symplectic quotients have
symplectic singularities
(with Hans-Christian Herbig and Gerald Schwarz; Compositio
Mathematica 156 (2020), 613--646)
The Hilbert series and
a-invariant of circle invariants
(with L. Emily Cowie, Hans-Christian Herbig, and Daniel Herden; Journal
of Pure and Applied Algebra 223 (2019), 395--421)
Functional equations for
orbifold wreath products
(with Carla Farsi; Journal of
Geometry and Physics 120 (2017), 37--51)
Symplectic reduction at zero angular momentum
(with Joshua Cape and Hans-Christian Herbig; Journal of Geometric Mechanics 8 (2016), 13--34)
On
compositions with x^2/(1-x)
(with Hans-Christian Herbig and Daniel Herden; Proceedings
of the American Mathematical Society 143 (2015), 4583--4596)
An impossibility
theorem for linear symplectic circle quotients
(with Hans-Christian Herbig; Reports
on Mathematical Physics 75 (2015), 303--331)
When is a symplectic
quotient an orbifold?
(with Hans-Christian Herbig and Gerald Schwarz; Advances in
Mathematics 280 (2015), 208--224)
Stratifications
of inertia spaces of compact Lie group actions
(with Carla Farsi and Markus Pflaum; Journal of Singularities 13 (2015),
107--140)
Gauge-fixing
on the lattice via orbifolding
(with Dhagash Mehta, Noah S. Daleo, and Jonathan D. Hauenstein; Physical Review D 90 (2014), 054504)
Gamma-extensions
of the spectrum of an orbifold
(with Carla Farsi and Emily Proctor; Transactions
of the American Mathematical Society 366 (2014), 3881--3905)
The
Hilbert series of a linear symplectic circle quotient
(with Hans-Christian Herbig; Experimental
Mathematics 23 (2014), 46--65)
An orbit Cartan type
decomposition of the inertia space of SO(2m) acting on R2m
(with John Wells, Involve:
a Journal of Mathematics 6 (2013), 345--368)
Extensions of the
Euler-Satake characteristic for nonorientable 3-orbifolds and indistinguishable
examples
(with Ryan Carroll, Involve:
a Journal of Mathematics 6 (2013), 467--482)
On orbifold criteria for
symplectic toric quotients
(with Carla Farsi and Hans-Christian Herbig, Symmetry, Integrability, and
Geometry 9 (2013), 032, 33 pages)
Extensions of the
Euler-Satake characteristic and point singularities of orientable 3-orbifolds
(with Ryan Carroll; Kodai
Mathematical Journal 36 (2013), 179--188)
Algebraic
structures associated to orbifold wreath products
(with Carla Farsi; Journal of
K-Theory 8 (2011), 323--338)
Free
and free abelian Euler-Satake characteristics of nonorientable 2-orbifolds
(with John Schulte and Bradford Taylor; Topology and its
Applications 158 (2011), 2244--2255)
Generalized
orbifold Euler characteristics for general orbifolds and wreath products
(with Carla Farsi; Algebraic and
Geometric Topology 11 (2011), 523--551)
Classifying
closed 2-orbifolds with Euler characteristics
(with Whitney DuVal, John Schulte, and Bradford Taylor; Glasgow
Mathematical Journal 52 (2010), no. 3, 555--574)
Generalized twisted sectors
of orbifolds
(with Carla Farsi; Pacific Journal of
Mathematics 246 (2010), no. 1, 49--74)
Nonvanishing
vector fields on orbifolds
(with Carla Farsi; Transactions
of the American Mathematical Society 362 (2010), 509--535)
The index of a vector field
on an orbifold with boundary
(with Elliot Paquette; Involve:
a Journal of Mathematics 2 (2009), no. 2, 161--175)
Two
Gauss-Bonnet and Poincar -Hopf theorems for orbifolds with boundary
(Differential
Geometry and its Applications 26 (2008), no. 1, 42--51)
K-theory of crepant
resolutions of complex orbifolds with SU(2) singularities
(Rocky Mountain Journal of Mathematics
37 (2007), no. 5, 1705--1712)
Characteristic
classes of bad orbifold vector bundles
(Journal of
Geometry and Physics 57 (2007), no. 11, 2365--2371)
A
complete obstruction to the existence of nonvanishing vector fields on
almost-complex, closed cyclic orbifolds
April 14, 2024
Classifying linear symplectic torus quotients
Joint work with Hans-Christian Herbig and Gerald Schwarz
Gone Fishing 2024, Northwestern University
Evanston, Illinois.
November 12, 2023
A universal Euler characteristic for orbit space definable groupoids and orbifold Euler characteristics of Riemannian Lie groupoids
Joint work with Carla Farsi and Emily Proctor
GroupoidFest 2023, Arizona State University
Tempe, Arizona.
November 12, 2022
Orbifold Euler characteristics of proper Lie and definable groupoids
Joint work with Carla Farsi
GroupoidFest 2022, University of Colorado at Boulder
Boulder, Colorado.
November 11, 2022
Rational singularities of the zero fiber of the moment map
Joint work with Hans-Christian Herbig and Gerald Schwarz
University of Colorado at Boulder Mathematics Seminar,
Boulder, Colorado.
November 11, 2021 (remote)
Rational singularities of the zero fiber of the moment map, symplectic quotients, and applications to representation and character varieties of surface groups
Joint work with Hans-Christian Herbig and Gerald Schwarz
Baylor University Mathematics Colloquium,
Baylor University, Texas.
November 3, 2020 (remote)
Computing the Hilbert series of the real regular functions on a symplectic quotient by the 2-torus
Joint work with Hans-Christian Herbig and Daniel Herden
Semin rio Simpl tico Rio (Joint Symplectic Seminar), IMPA, PUC-RJ, UFF and UFRJ,
Rio de Janeiro, Brazil.
January 13 22, 2020
Bernoulli Brainstorm: Real and complex geometry of Hamiltonian reductions
With Hans-Christian Herbig, Simon Lyakhovich, and Gerald Schwarz
Bernoulli Center (CIB), cole Polytechnique F d rale de Lausanne (EPFL)
Lausanne, Switzerland
January 6 10, 2020
Research in Pairs: Real and complex geometry of Hamiltonian reductions
With Hans-Christian Herbig, Simon Lyakhovich, and Gerald Schwarz
CIRM (Centre International de Rencontres Math matiques)
Marseille, France
December 18, 2019
Singularities of symplectic quotients and computational invariant theory
Joint work with Hans-Christian Herbig, Daniel Herden, and Gerald Schwarz
Workshop of Algebra and Geometry
Sultan Qaboos University
Muscat, Oman
September 24, 2019
Can one approximately hear orbifold singularities?
Joint work with Carla Farsi and Emily Proctor
Middlebury College Department of Mathematics
Middlebury, Vermont
September 28, 2018
Distinguishing between symplectic quotients by SU2 using invariant theory
Joint work with Hans-Christian Herbig, and Daniel Herden
University of Mississippi Graduate Student Seminar
Oxford, Mississippi
August 4, 2018
The Hilbert series and Laurent coefficients of SL2(C)-invariants
Joint work with Pedro de Carvalho Cayres Pinto, Hans-Christian Herbig, and Daniel Herden
International Congress of Mathematicians (ICM 2018)
Rio de Janeiro, Brazil
May 7 10, 2018
The k-large property for representations of complex reductive groups and implications for linear symplectic quotients
Joint work with Hans-Christian Herbig and Gerald Schwarz
International Conference on Mathematics and Statistics (ICOMAS 2018)
University of Memphis, Tennessee
April 14 15, 2018
The Hilbert series of a reducible representation of SL2(C) and its Laurent coefficients
Joint work with Pedro de Carvalho Cayres Pinto, Hans-Christian Herbig, and Daniel Herden
Special Session on Commutative Algebra
Spring Southeastern Sectional Meeting of the AMS
Vanderbilt University, Nashville, Tennessee
November 11, 2017
Counting SL2(C)-invariant polynomials
Joint work with Pedro de Carvalho Cayres Pinto, Hans-Christian Herbig, and Daniel Herden
37th Annual Math Symposium at Western Kentucky University
Bowling Green, Kentucky
July 11, 2017
Complex symplectic quotients with symplectic singularities
Joint work with Hans-Christian Herbig and Gerald Schwarz
Instituto de Matem tica Pura e Aplicada (IMPA)
Rio de Janeiro, Brazil
April 22, 2017
The spectrum of orbifold connected sums and collapsing
Joint work with Emily Proctor and Carla Farsi
Methods in Operator Theory and Applications
University of Memphis, Memphis, TN
July 11 15, 2016
Collaborate@ICERM: Hilbert Series of Sympletic Torus Quotients
With Hans-Christian Herbig and Daniel Herden
The Institute for Computational and Experimental Research in Mathematics (ICERM)
Providence, Rhode Island
March 15, 2016
Constructing symplectmorphisms between linear symplectic quotients
Joint work with Joshua Cape, Emily Cowie, Carla Farsi, Hans-Christian Herbig, Daniel Herden, Ethan Lawler, and Gerald Schwarz
University of Colorado at Boulder, Colorado
March 10 13, 2016
The inertia groupoid of a Lie groupoid,
Joint work with Carla Farsi and Markus Pflaum
Gone Fishing Poisson Geometry Conference
University of Colorado at Boulder, Colorado
March 5, 2016
The ring of regular functions on a linear symplectic quotient
Joint work with Joshua Cape, Hans-Christian Herbig, Daniel Herden, and Gerald Schwarz
Special Session on Symplectic and Contact Geometry, Spring Southeastern Sectional Meeting of the AMS
University of Georgia, Athens, Georgia
Coefficients
of the Laurent expansion of the Hilbert series of Gorenstein rings
Joint
work with Hans-Christian Herbig and Daniel Herden
4th
Annual Mississippi Discrete Mathematics Workshop
University of Mississippi, Oxford, Mississippi
July 10, 2015
Hilbert series of regular functions on singular symplectic quotients
Joint work with Joshua Cape, Emily Cowie, Carla Farsi, Hans-Christian Herbig, Daniel Herden, and Gerald Schwarz
Baylor University, Waco, Texas
July 20 24, 2015
Participant in the REUF Workshop at ICERM
Providence, Rhode Island
January 6, 2015
Singular symplectic reduction and invariant theory
Joint work with Joshua Cape, Carla Farsi, Hans-Christian Herbig, Daniel Herden, and Gerald Schwarz
Instituto de Ci ncias Matem ticas e de Computa o. Universidade de S o Paulo. S o Carlos, Brazil
Differentiable
stratified groupoids
Joint work with Carla
Farsi and Markus Pflaum
University of
Colorado at Boulder Groupoids Seminar
August 11, 2014
Orbifold and
non-orbifold symplectic quotients
Joint work with Carla
Farsi, Hans-Christian Herbig, Daniel Herden, and Gerald Schwarz
Topology of Torus
Actions and Applications to Geometry and Combinatorics
Daejeon Convention Center, Daejeon, Korea
Geometry of symplectic quotients via invariant theory II
Joint work with Carla Farsi, Hans-Christian Herbig, Daniel Herden, and Gerald Schwarz
Commutative Algebra Seminar, University of Nebraska at Lincoln, Lincoln NE
The inertia
space of a proper Lie groupoid as a stratified differentiable space
Joint work with
Carla Farsi and Markus Pflaum
Fall Central
Sectional Meeting of the AMS,
Washington University, St. Louis, MO
The inertia
space associated to a proper Lie group action as a stratified space
Joint work with
Carla Farsi and Markus Pflaum
Spring Western Sectional
Meeting of the AMS,
University of Colorado at Boulder, Boulder, CO
A stratification of the orbit
space of a G-manifold for a compact Lie group G
Joint work with Carla Farsi and
Markus Pflaum
Centre for Quantum Geometry and
Moduli Spaces,
Aarhus University, Aarhus Denmark
An
explicit stratification of the inertia space for a
connected, compact Lie group action
Joint
work with Carla Farsi and Markus Pflaum
On
orbifold criteria for Hamiltonian toric quotients
Joint
work with Carla Farsi and Hans-Christian Herbig
Workshop
on Recent developments on Orbifolds