Welcome

Contact Info

Courses (Fall 2022)

Elem. Real Analysis (Math 310)
Structures on Manifolds (86600-01)

Seminars

Differential Geometry and Topology

PhD Advising

Matthew Cushman (2021)
Qian Chen (2020)
Arthur Parzygnat (2016)

Editorial

Journal of Homotopy and Related Structures

Publications and Preprints

A ddc-type condition beyond the Kahler realm, with J. Stelzig.

Hodge-de Rham numbers of almost complex 4-manifolds, preprint with J. Cirici.

Dolbeault cohomology for almost complex manifolds, with J. Cirici, Advances in Mathematics, Volume 391, 2021. Preprint arxiv:1809.01416.

Almost complex manifolds with small Nijenhuis tensor, with L. Fernandez, and T. Shin, Complex Manifolds 8:329-335, 2021. Preprint arxiv:2103.06090.

Almost Hermitian Identities, with J. Cirici, Mathematics 2020, 8, 1357. Preprint arxiv:2008.04390.

Harmonic symmetries for Hermitian manifolds, Proc. of AMS, Vol 148, No.7 , July 2020, Pages 3039-3045. Preprint arxiv:1906.02952. A useful related reference: Structure table and identities.

Topological and geometric aspects of almost Kahler manifolds via harmonic theory, with J. Cirici, Selecta Mathematica New Series, 26, 35 (2020). Preprint arxiv:1809.01414.

Center of mass and Kahler structures with Mahmoud Zeinalian, J. Geom. 110 (2019), no. 2, 110:33. Preprint arxiv:1802.06315

Results concerning almost complex structures on the six-sphere, Symmetry, Integrability and Geometry: Methods and Applications, 14 (2018), 034, 21 pages.

Differential K-theory as equivalence classes of maps to Grassmannians and unitary groups, with Thomas Tradler and Mahmoud Zeinalian, New York Journal of Mathematics, Vol. 22 (2016), p. 527-581.

One more proof of the index formula for block Toeplitz operators, with Thomas Tradler and Mahmoud Zeinalian, Journal of Operator Theory, 76(1):2016, p. 101-104.

A loop group extension of the odd Chern character, Journal of Geometry and Physics, Vol 102, 2016, p. 32-43.

Loop differential K-theory, with T. Tradler and M. Zeinalian. Annales Mathematiques Blaise Pascal, Vol 22, No. 1, p. 121-163, 2015.

Pseudodeterminants and perfect square spanning tree counts, with J. L. Martin, M. Maxwell, V. Reiner, Journal of Combinatorics, Vol. 6, Num. 3, 295-325, 2015. arxiv:1311.6686

An elementary differential extension of odd K-theory, with T. Tradler and M. Zeinalian, J. of K-theory, volume 12, issue 02, Oct. 2013, pp. 331-361. arxiv:1211.4477

Equivariant holonomy for bundles and abelian gerbes, with T. Tradler and M. Zeinalian, Comm. Math. Phys., Vol. 315, Issue 1, 2012, pg 38-108.

Homotopy DG algebras induce homotopy BV algebras, with John Terilla and Thomas Tradler, J. of Homotopy Related Structures, vol 6 (1), 2011, pp. 177-182.

Differential forms, fluids, and finite models, Proc. of Amer. Math. Soc. 139 (2011), 2597-2604.

Rectifying partial algebras over operads of complexes, Topology and Its Appl., Vol 157, Issue 18, Dec. 1, 2010, 2880-2888.

Some algebra and applications related to mapping spaces, joint with T. Tradler and M. Zeinalian, Mathematisches Forschungsinstitut Oberwolfach, Report No. 28 2009, Strings, Fields and Topology. June 7-13 2009.

Conformal cochains, Trans. Amer. Math. Soc. 360 (2008), 5247-5264. Addendum.

Cochain algebra on manifolds and convergence under refinement, Topology and its Appl, 154 no. 9 (2007) 1898-1920.

On the Algebra and Geometry of a Manifold's Chains and Cochains. PhD dissertation, Stony Brook University. August 2005.

Videos

Topological implications of Kahler-type symmetries for Hermitian and Almost Kahler manifolds

Chern Simons forms, free loopspaces, and K-theory

Loop Differential K-theory