S. Krishnan [academic]

me research teaching

	sanjeevi@math.osu.edu
	Math Tower 754
	231 West 18th Avenue
	Columbus OH, 43210-1174
	(614) 292-8434

I do math at OSU.

I'm primarily interested in directed algebraic topology, a refinement of clasical algebraic topology for spaces with some structure of time on them.

	dat.py python/sage libraries for directed algebraic topology S. Krishnan, created 2019.
	cubcat.app repl+spreadsheet S. Krishnan, created 2019.
	demo: model-checking with directed algebraic topology S. Krishnan, created 2019.
	demo: second homotopy groups as derived group completions S. Krishnan, created 2019.
	demo: directed (co)homology semigroups of simplicial sets S. Krishnan, created 2019.
	demo: gaps in dynamic sensor networks as cohomology cones S. Krishnan, created 2019.
	demo: detecting inverse structures in category representations S. Krishnan, created 2019.
	Dihomotopy type theory S. Krishnan , P. North, submitted 2016
	Directed Poincare Duality S. Krishnan, submitted 2016
	Directed (Co)homology S. Krishnan, submitted 2020
	Dihomotopy (co)limits S. Krishnan, P. North, submitted 2016
	The directed homotopy of directed spheres S. Krishnan, submitted 2016
	A convenient category of cubes S. Krishnan, E. Rudman, submitted 2025
	Cubical approximation for directed topology II S. Krishnan, to appear in Algebraic Geometry and Topology, 2025
	The Uniform Homotopy Category S. Krishnan, C. Ogle, Journal of Pure and Applied Algebra, 2024
	Invertibility in category representations S. Krishnan, C. Ogle, unpublished 2020. under further development.
	A Hurewicz model structure for directed topology S. Krishnan, P. North, Theory and Application of Categories, 2021
	Triangulations of conal manifolds S. Krishnan, unpublished 2019. under further development.
	Positive Alexander Duality for Pursuit and Evasion R. Ghrist, S. Krishnan, SIAM 2017
	Flow-cut dualities for sheaves on graphs S. Krishnan, unpublished 2015. under further development.
	A Topological Max-Flow Min-Cut Theorem R. Ghrist, S. Krishnan, Proceedings of Global Signal Inference, 2013.
	Cubical approximation for directed topology I S. Krishnan, Applied Categorical Structures, 2013, vol. 23, no 2, p. 177-214.
	A free object in quantum information theory J. Feng, K. Martin, S. Krishnan, Electronic Notes in Theoretical Computer Science, 2010.
	Future path-components in directed topology E. Goubault, E. Haucourt, S. Krishnan, Electronic Notes in Theoretical Computer Science, 2010, vol. 265, p. 325-335.
	Covering space theory for directed topology E. Goubault, E. Haucourt, S. Krishnan, Theory and Application of Categories, 2009, vol. 22, no 9, p. 252-268.
	Criteria for homotopic maps to be so along monotone homotopies S. Krishnan, GETCO 2004-2006 Proc., Electr. Notes Theor. Comput. Sci., (2009), vol. 230, pp. 141-148.
	A convenient category of locally preordered spaces S. Krishnan, Applied Categorical Structures, 2009, vol. 17, no 5, p. 445-466.

intro article app code

I am currently teaching undergraduate finite-dimensional Linear Algebra (OSU Math 2568/4568). For students, the course page can be found on Carmen.

	practice: computing homotopy groups S. Krishnan, created 2019.
	practice: filling in bigraded spectral sequences S. Krishnan, created 2019.
	demo: spin foam networks S. Krishnan, created 2019.
	demo: Regge calculus S. Krishnan, created 2019.
	demo: monoid homology from complete rewriting systems S. Krishnan, created 2019.
	demo: (co)homology groups of simplicial sets S. Krishnan, created 2019.
	demo: cellular sheaf (co)homology S. Krishnan, created 2019.
	demo: synthetic homotopy theory S. Krishnan, created 2019.
	demo: bigraded spectral sequences S. Krishnan, created 2019.
	Homotopy Theory (OSU MATH 7811) syllabus S. Krishnan, created 2019.
	homework 1 S. Krishnan, created 2019.

intro hw docs app