Hisham Sati (faculty page) is working on non-perturbative phenomena in string theory/M-theory using tools of cohomology, homotopy theory, algebraic topology and higher category theory. His thesis advisor was Michael Duff.
Hisham Sati is an associate professor of mathematics at NYU Abu Dhabi and lead-PI of the Center for Quantum and Topological Systems.
From his cached Pitt faculty page:
My research is interdisciplinary and lies in the intersection of differential geometry, algebraic topology, and mathematical/theoretical physics. I am mainly interested in geometric and topological structures arising from quantum (topological) field theory, string theory, and M-theory. This includes orientations with respect to generalized cohomology theories, and corresponding description via higher geometric, topological, and categorical notions of bundles.
Geometric perspectives on topological action functionals, talk at The CUNY Workshop on differential cohomology, New York, August 2014 (video recording)
M-theory and cohomotopy, talk at M-Theory and Mathematics, NYU AD 2020 (pdf slides)
(on Hypothesis H)
Hisham Sati, Geometric and topological structures related to M-branes,
part I, Proc. Symp. Pure Math. 81 (2010), 181-236 (arXiv:1001.5020),
part II: Twisted $String$ and $String^c$ structures, J. Australian Math. Soc. 90 (2011), 93-108 (arXiv:1007.5419);
part III: Twisted higher structures, Int. J. Geom. Meth. Mod. Phys. 8 (2011), 1097-1116 (arXiv:1008.1755)
on cohomology and twisted cohomology structures in string theory/M-theory. See also twisted smooth cohomology in string theory.
On modular equivariant elliptic cohomology in type II string theory/F-theory:
Igor Kriz, Hisham Sati, M-theory, type IIA superstrings, and elliptic cohomology, Adv. Theor. Math. Phys. 8 (2004), no. 2, 345–394 (euclid:atmp/1091543172, arXiv:hep-th/0404013)
Igor Kriz, Hisham Sati, Type IIB String Theory, S-Duality, and Generalized Cohomology, Nucl.Phys. B715 (2005) 639-664 (arXiv:hep-th/0410293)
Igor Kriz, Hisham Sati, Type II string theory and modularity, JHEP 0508 (2005) 038 (arXiv:hep-th/0501060)
On the Diaconescu-Moore-Witten anomaly interpreted in integral Morava K-theory:
Hisham Sati, Craig Westerland, Twisted Morava K-theory and E-theory (arXiv:1109.3867)
(this is followed up on in remark 5.4.12 in Hopkins, Lurie, Ambidexterity in K(n)-Local Stable Homotopy Theory )
On F4 and Cayley plane-fiber bundles in M-theory, relating to bosonic M-theory:
Hisham Sati, $\mathbb{O}P^2$-bundles in M-theory, Commun. Num. Theor. Phys 3:495-530,2009 (arXiv:0807.4899)
Hisham Sati, On the geometry of the supermultiplet in M-theory, Int. J. Geom. Meth. Mod. Phys. 8 (2011) 1-33 (arXiv:0909.4737)
On mathematical foundations of quantum field theory and perturbative string theory:
Hisham Sati, Urs Schreiber, Mathematical Foundations of Quantum Field and Perturbative String Theory, Proceedings of Symposia in Pure Mathematics, volume 83 AMS (2011)
Hisham Sati, Urs Schreiber, Jim Stasheff, L-∞ algebra connections in Quantum Field Theory, Birkhäuser (2009), 303-424, DOI: 10.1007/978-3-7643-8736-5_17 (publisher link, arXiv:0801.3480)
Hisham Sati, Urs Schreiber, Jim Stasheff, Twisted Differential String and Fivebrane Structures Communications in Mathematical Physics October 2012, Volume 315, Issue 1, pp 169-213
H. S. , Urs Schreiber, Jim Stasheff Fivebrane structures Rev. Math. Phys.21:1197-1240 (2009) (arXiv:0805.0564)
Domenico Fiorenza, H. S., Urs Schreiber, 7d Chern-Simons theory and the 5-brane (arXiv:1201.5277)
Domenico Fiorenza, Hisham Sati , Urs Schreiber, The moduli 3-stack of the C-field (arXiv:1202.2455)
Domenico Fiorenza, Hisham Sati , Urs Schreiber, Extended higher cup-product Chern-Simons theories Journal of Geometry and Physics, Volume 74, 2013, Pages 130–163 (arXiv:1207.5449)
Domenico Fiorenza, Hisham Sati, Urs Schreiber, A higher stacky perspective on Chern-Simons theory (arXiv:1301.2580) in Damien Calaque et al. (eds.) Mathematical Aspects of Quantum Field Theories Springer 2014
Hisham Sati, Framed M-branes, corners, and topological invariants, J. Math. Phys. 59 (2018), 062304 (arXiv:1310.1060)
(on the Hopf-Wess-Zumino term of the M5-brane, rational Cohomotopy in the 11d supergravity equations of motion and …)
Domenico Fiorenza, H. S., Urs Schreiber, Super Lie n-algebra extensions, higher WZW models and super p-branes with tensor multiplet fields (arXiv:1308.5264)
Varghese Mathai, Hisham Sati, Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality, J. Geom. Phys. 92:240-251, 2015 (arXiv:1404.2257)
(on a non-commutative geometry-deformation of the self-dual higher gauge theory as it appears on the M5-brane worldvolume, and its S-duality)
On spherical T-duality in iterated algebraic K-theory:
John Lind, Hisham Sati, Craig Westerland, A higher categorical analogue of topological T-duality for sphere bundles, Annals of K-Theory, Vol. 5 (2020), No. 1, 1–42 (arXiv:1601.06285, doi:doi:10.2140/akt.2020.5.1)
Domenico Fiorenza, Hisham Sati, Urs Schreiber, T-Duality from super Lie n-algebra cocycles for super p-branes, ATMP Volume 22 (2018) Number 5 (arXiv:1611.06536)
Discussion of twisted differential K-theory and its relation to D-brane charge in type II string theory (see also there):
Discussion of twisted differential orthogonal K-theory and its relation to D-brane charge in type I string theory (on orientifolds):
On (co-)homotopical foundations of M-theory (Hypothesis H):
Domenico Fiorenza, Hisham Sati, Urs Schreiber The rational higher structure of M-theory, Proceedings of the LMS-EPSRC Durham Symposium: Higher Structures in M-Theory, August 2018. Fortschritte der Physik, 2019 (doi:10.1002/prop.201910017, arXiv:1903.02834)
Domenico Fiorenza, Hisham Sati, Urs Schreiber, Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds (arXiv:1904.10207)
In relation to the Hopf WZ term and Page charge:
On Cohomotopy and Hypothesis H:
On U-duality (and possibly mysterious duality) via Hypothesis H as automorphisms of iterated (rational) cyclic loop spaces of the (rational) 4-sphere:
Last revised on September 10, 2022 at 08:04:46. See the history of this page for a list of all contributions to it.