John R. Klein

senior fellow
EURIAS cohort 2017/2018
discipline Mathematics
Tenured Full Professor of Mathematics, Mathematics Department at the College of Liberal Arts and Sciences, Wayne State University, Detroit

Research project

Topological Stochastics

 

From the beginning, the field of algebraic topology  developed in part as a toolbox to solve problems arising in the theory of manifolds. A unifying theme relates analytical properties to topological ones. For example, invariants constructed from gradient dynamics (Morse theory), such as the Euler number and Whitehead torsion,  have a topological interpretation. Similarly, the roots of symplectic topology  lie in the study of periodic orbits of Hamiltonian systems.
   
 The proposed project will make the case that  another kind of dynamics, stochastic dynamics, creates scaffolding for yet another bridge between the fields. I will also suggest how these considerations might lead to new invariants of manifolds, or at least to novel and interesting interpretations of the existing ones.

 

The project is multidisciplinary: it will bridge algebraic topology, statistical mechanics, and higher dimensional combinatorics.

 

 

 

Biography

 

John R. Klein is Tenured Full Professor of Mathematics at the Department of Mathematics at the College of Liberal Arts and Sciences, Wayne State University in Detroit. He holds a Ph.D in Mathematics from Brandeis University. His main research areas are algebraic topology, manifold theory, homotopical methods, spaces of embeddings, embeddings, intersections and symmetries.

 

 

 

Selected publications

 

'Charged Spaces', with J.W. Peter, Forum Mathematicum, vol. 27, no. 5, 2015, pp. 2661-2689.

 

'Kirchho's Theorems in Higher Dimensions and Reidemeister Torsion', with M. J. Catanzaro & V. Y. Chernyak, Homology, Homotopy and Applications, vol. 17, no. 1, 2015, pp. 165-189.

 

'Multiple Disjunction for Space of Smooth Embeddings’, with T. G. Goodwillie, Journal of Topology, vol. 8, no. 3, 2015, pp. 651-674.

 

'Fake Wedges', with J.W. Peter, Transactions of the American Mathematical Society, vol. 366, 2014, pp. 3771-3786.

 

'On Kirchho's Theorems with Coefficients in a Line Bundle', with M. J. Catanzaro & V. Y. Chernyak, Homology, Homotopy and Applications, vol. 15, no. 2, 2013, pp. 267-280.

 

 

 

institut

senior fellow
EURIAS promotion 2018/2019
Israel Institute for Advanced Studies (IIAS)
discipline Southeast Asian Studies
2018
junior fellow
EURIAS promotion 2016/2017
Israel Institute for Advanced Studies (IIAS)
discipline History
2016
senior fellow
EURIAS promotion 2013/2014
Israel Institute for Advanced Studies (IIAS)
discipline Religious Studies
2013
senior fellow
EURIAS promotion 2013/2014
Israel Institute for Advanced Studies (IIAS)
discipline History
2013