John R. Klein
Research project
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.
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