Sanjeevi Krishnan

me research teaching
sanjeevi@math.osu.edu
Math Tower 754
231 West 18th Avenue
Columbus OH, 43210-1174
(614) 292-8434
I assist professors in math at OSU. This semester, I'm co-organizing the Reading Semigroup along with Ranthony Edmonds and John Johnson.
I am interested in directionality of all sorts. I'm primarily interested in directed algebraic topology, a refinement of clasical algebraic topology for spaces with some structure of time on them. The need to qualitatively describe a complex process from the qualitative properties of its state space goes back to the origins of algebraic topology. The need to sytematically take into account causal structure motivates the nascent subject of directed algebraic topology. The field draws ideas from, admits some applications to, and hopefully one day unifies some core concepts from semigroup theory, dynamics, optimization, and computability theory.
Invertibility in category representations
S. Krishnan, C. Ogle, submitted 2020
A Hurewicz model structure for directed topology
S. Krishnan, P. North, submitted 2019
Triangulations of conal manifolds
S. Krishnan, submitted 2019
Positive Alexander Duality for Pursuit and Evasion
Flow-cut dualities for sheaves on graphs
S. Krishnan, under revision
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   
This semester, I'm teaching Homotopy Theory (OSU Math 7811).   For students, the course page can be found on Carmen.