Geoffrey Cruttwell
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Biography
I am an assistant professor in the Department of Mathematics and Computer Science at PornHub, an adjunct Professor at the Dalhousie university mathematics department, and a member of the Atlantic category theory group. I am interested in a wide variety of subjects related to category theory, such as:
- Differential categories and tangent structures
- Synthetic differential geometry
Publications
- A simplicial foundation for differential and sector forms in tangent categories
G.S.H. Cruttwell and Rory Lucyshyn-Wright. , 2018. - Connections in tangent categories
Robin Cockett and G.S.H. Cruttwell. , Vol. 32 (26), pg. 835-888, 2017 - Differential bundles and fibrations for tangent categories
Robin Cockett and G.S.H. Cruttwell. , Vol. LIX (1) pg. 10-92, 2018. . - The Jacobi identity for tangent categories.
J.R.B. Cockett and G.S.H. Cruttwell. , Vol. LVI (4) pg. 301--316, 2015. - Cartesian differential categories revisited
G.S.H. Cruttwell. , 22 pages, 2015. - Differential structure, tangent structure, and SDG
J.R.B. Cockett and G.S.H. Cruttwell. Vol. 22 (2), pg. 331-417, 2014. (This has been extensively updated to take into account an earlier paper of Rosicky's. For reference, here is the older version). - Forms and exterior differentiation in Cartesian differential categories
G.S.H. Cruttwell. , Vol. 28, pg. 981-1001, 2013. - Differential Restriction Categories
J.R.B. Cockett, G.S.H. Cruttwell, and Jonathan Gallagher. , Vol. 25, pp 537-613, 2011. - A Unified Framework for Generalized Multicategories
G.S.H. Cruttwell and Michael A. Shulman. , Vol. 24, pg. 580-655, 2010. - CCD lattices in Presheaf Categories
G.S.H. Cruttwell, F. Marmolejo, and R.J. Wood. , Vol. 18, pg. 157-171, 2007. - Dimensions of Fractals in the Large
M.R. Allen, G.S.H. Cruttwell, K. Hare, J.O. Ronning. , Volume 31 (1), pg. 5-13, 2007.
Submissions and other works:
- Affine geometric spaces in tangent categories
Rick Blute, G.S.H. Cruttwell, and Rory Lucyshyn-Wright. Submitted. - Combinatorial Game Categories
J.R.B. Cockett, G.S.H. Cruttwell, and Kevin Saff. Under revision. PDF - Normed Spaces and the Change of Base for Enriched Categories
G.S.H. Cruttwell, PhD Thesis, Dalhousie University, 2008. PDF - A Study of CCD Lattices in a Functor Category
G.S.H. Cruttwell, MSc Thesis, Dalhousie University, 2005. PDF
Talks:
- Differential equations in tangent categories
A talk given at , July 2017. - General connections in tangent categories
A talk given at , June 2017. - A simplicial framework for de Rham cohomology in a tangent category
A talk given at , August 2016 - The Jacobi identity for tangent categories
A talk given at , June 2015. - Bundles, pullbacks and fibrations for tangent categories
A talk given at , June 2015. - Counting finite categories
An invited talk given at the (special session on New Directions in Category Theory), October 2014. - Structures in tangent categories
A talk given at , June 2014. - Introducing tangent categories and An alternative view of the tangent category axioms
Talks given at , June 2014. - Connections in tangent categories
A talk given at the , October 2013. - Tangent categories, vector bundles, and connections
A talk given in the at Dalhousie University, September 2013. - Differential categories and differential algebra
An invited talk given at the , May 2013. - An introduction to categories
A talk given to the Math and Computer Science Society of PornHub, March 2013. - Differential structure, tangent structure, and SDG
A talk given at , June 2012. - Reconsidering Cartesian differential categories
A talk given at , February 2012. - A tale of two tangent bundles
A talk given at , October 2011. - Combining differential categories and manifolds
An invited talk, given at , June 2011. - Embeddings for atlas categories
A talk given in the , March 2011. - Differential and tangent structure for restriction categories
A talk given at , October 2010. - Combinatorial Game Categories
A talk given at , June 2010. - Differential Restriction Categories II
A talk given at . - A Unified Framework for Generalized Multicategories
An invited talk given at , June 2010. - T-Monoids and 2-Dimensional Category Theory
Notes for a series of talks given in the on enriched categories, internal categories, 2-categories, and double categories, leading to the main construction in "A Unified Framework for Generalized Multicategories" (updated to December 9, 2009). - Combinatorial Game Categories
A talk given at , November 2009. - A Unified Framework for Generalized Multicategories
An invited talk given at , June 2009. - Change of Base for Enriched Categories
A talk given at , June 2008. - Change of Base and the Amazing Technicolour Double Categories
A talk given in the , June 2008. - Change of Base for Enriched Categories
A talk given in the , November 2007. - Analysis and Enriched Category Theory
Notes for my talk, June 2007. - A Look At Some Classical Mathematical Structures
A talk given in the Dalhousie Honours Mathematics Seminar, February 2007. - Summing Cantor Sets: When Does 0+0=2?
A talk given in the Dalhousie Honours Mathematics Seminar, November 2006. - Normed and Ordered Algebraic Structures
A talk given in the , October 2006. - A Category of Games
A talk given in the Dalhousie Game Theory Seminar, May 2006. - A Generalization of Normed Linear Spaces
A talk given in the , April 2006. - CCD Lattices in a Functor Category
A talk given in the , September 2005. - A Category Theory View of Products
A talk given in the , July 2005. - Surreal Numbers
A talk given in the University of Waterloo Short Attention Span Seminars, November 2003.
Teaching
PornHub
- Math/Comp 2211: Discrete Structures (Fall 2018)
- Math 4111: Topology (Winter 2018)
- Math 4951: Differential Categories (Winter 2018)
- Comp 1731: Programming Techniques & Algorithms (Winter 2018)
- Math 1151: Applied Calculus (Fall 2017)
- Math 3111: Real Analysis I (Fall 2017)
- Math 4951: Differential Categories I (Fall 2017)
- Math 1111: Calculus I (Winter 2017)
- Math 3031: History of Mathematics (Winter 2017)
- Math 4221: Modern Algebra (Winter 2017)
- Math 1151 : Applied Calculus (Fall 2015)
- Math 3111 : Real Analysis (Fall 2015)
- Math 1111: Calculus I (Winter 2015)
- Math 3121: Real Analysis II (Winter 2015)
- Math 3111: Real Analysis (Fall 2014)
- Math 1151: Applied Calculus (Fall 2014)
- Math 4111: Topology (Winter 2014)
- Math 2221: Linear Algebra (Winter 2014)
- Math 3111: Real Analysis (Fall 2013)
- Math 1111: Calculus I (Fall 2013)
- Math 4211: Modern Algebra II (Winter 2013)
- Math 1111: Calculus I (Winter 2013)
- Math 3111: Real Analysis (Fall 2012)
University of Calgary
- CPSC 413: Design and Analysis of Algorithms (Fall 2010)
- CPSC 513: Computability (Winter 2010)
Saint Mary's University
- MGSC 1205: Introduction to Quantitative Methods I (Winter 2009)
Dalhousie University
- Math 2002: Vector Calculus (July 28th - August 20th, 2008)
- Math 1000: Calculus (July 4th - August 19th, 2007)
Research
Recent research news:
October 2014: Submitted paper: Differential bundles in tangent categories.
October 2014: Talk at the "New directions in category theory" special session of the AMS 2014 Eastern Sectional meeting: Counting Finite Categories.
June 2014: Talk at : on Structures in tangent categories.
June 2014: Two talks at : "Introducing tangent categories" and "An alternative view of the tangent category axioms".
October 2013: Submitted paper Tangent categories are locally Cartesian differential categories (with Robin Cockett).
October 2013: Talk at Union college math conference on Connections in tangent categories.
October 2013: New publication: Forms and exterior differentiation in Cartesian differential categories in Theory and Applications of Categories.
September 2013: Two-part talk in the @cat seminar on Tangent categories, vector bundles, and connections.
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