# Research

## Papers

*Deformation classes of invertible field theories and the Freed--Hopkins conjecture,*in preparation.*The geometric cobordism hypothesis,*with D. Pavlov, preprint, https://arxiv.org/abs/2111.01095*Extended field theories are local and have classifying spaces,*with D. Pavlov, preprint https://arxiv.org/abs/2011.01208*Ramond-Ramond fields and twisted differential K-theory,*with H. Sati, preprint https://arxiv.org/abs/1903.08843*Twisted differential KO theory,*with H. Sati, preprint https://arxiv.org/abs/1905.09085*Cobordisms of global quotient orbifolds and an equivariant Pontrjagin-Thom construction,*preprint, https://arxiv.org/abs/1811.08794.*Parametrized geometric cobordism and smooth Thom stacks*, with H. Sati, preprint, https://arxiv.org/pdf/1709.00686.*Differential KO theory: Constructions, computations and applications,*with H. Sati, Advances in Math,**384**(2021) 107671*Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers,*with H. Sati, Journal of Geometry and Physics,**165**(2021) 104203*Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence,*with H. Sati, Algebraic and Geometric Topology,**19**-6 (2019), 2899-2960.*Higher twisted Deligne cohomology,*Homology, Homotopy and Applications,**21**-1 (2019), 129-159.*Primary operations in differential cohomology,*with H. Sati, Advances in Math,**335**(2018), 519-562.*Twisted smooth Deligne cohomology,*with H. Sati,**53**-3 (2018), 445-466.*Spectral sequences in smooth generalized cohomology,*with H. Sati,**17**-4 (2017), 2357-2412.*Massey products in differential cohomology via stacks,*with H. Sati, Journal of Homotopy and Related Structures,**13**-1 (2017), 1-55.

## Some notes

Brief note on anomalies in gauge theory and the AS index theorem

Lectures on cohomology, notes (incomplete) from a 2013 course taught by Hisham Sati at Pitt

Notes on Dan Freed's Lectures on invertible QFT's, at CBMS conference 2017 (with contributions by Matt Wheeler)

An introductory text that I am writing on differential cohomology .

## Lectures, talks and slides

**2022**

*Deformation classes of invertible field theories and the Freed Hopkins conjecture,*University of Lisbon slides

**2021**

*The geometric cobordism hypothesis,*Topology seminar, University of Minnesota*The geometric cobordism hypothesis,*Geometry and Topology seminar, NYU Abu Dhabi*The geometric cobordism hypothesis,*Algebra, combinatorics and geometry seminar, University of Pittsburgh*The geometric cobordism hypothesis,*Topology seminar*,*University of Oregon*Extended field theories are local and have classifying spaces,*AG seminar, University of Regensburg

**2020**

*The homotopy type of the cobordism category (3 talks),*Topology and Geometry seminar, TTU*Introduction to equivariant homotopy theory,*Quantum homotopy seminar, TTU*Smooth stacks and Cech cocycles (2 talks),*Quantum homotopy seminar, TTU*Bundle gerbes with connection,*Quantum homotopy seminar, TTU*Lifting M-theory to cohomotopy via obstruction theory,*Topology and Geometry seminar, TTU

**2019**

*RR-fields and twisted differential K-theory,*UAE Math day, American University of Sharjah. Slides*An introduction to differential cohomology,*Topology and Geometry seminar, TTU*The Atiyah–Hirzebruch spectral sequences for differential cohomology theories (2 talks),*Topology and Geometry seminar, TTU*Twisted differential cohomology and the twisted Atiyah–Hirzebruch spectral sequence (5-talks),*Topology and Geometry seminar, TTU

**2018 **

*A differential Riemann-Roch theorem for KO-theory,*The Regional Collaborative Seminar on Geometry, Topology, and Physics, NYUAD. Slides*Geometric invariants of vector bundles and the index of elliptic operators,*Math colloquium, NYUAD. Slides

**2017 **

*Twisted Differential K-theory and a refinement of the Atiyah-Hirzebruch spectral sequence,*Topology seminar, KIAS. 4 talks. Slides 1, Slides 2*An Atiyah-Hirzebruch spectral sequence for twisted differential K-theory,*Geometry-Topology seminar, University of Pennsylvania. Slides*An Atiyah-Hirzebruch spectral sequence for twisted differential K-theory,*GAP seminar, Penn State.*Lectures on the Atiyah-Singer index theorem,*Postdoc seminar, NYUAD.*Cobordism via higher geometry,*Higher structures in geometry, topology and physics workshop, NYUAD. Slides*Parametrized geometric cobordism and smooth Thom stacks,*Cohomology theories, categories and applications, University of Pittsburgh.

**2016*** *

*Moduli stacks and higher gerbes,*UAE math day, NYUAD.*What is differential cohomology and why should you care?*American University of Sharjah.

**2015 **

*Massey products in differential cohomology,*Higher structures and cohomology workshop, University of Pittsburgh.

**2014**** **

*Minimal models*, geometry proseminar, University of Pittsburgh.*Sheaf, deRham, and Čech cohomology,*GTP seminar, University of Pittsburgh.

**2013 **

*Topological index theorem for differential K theory,*topics course on AS index theoremUniversity of Pittsburgh.**,***An example of a rarely seen characteristic class in ‘nature’,*geometry proseminar, University of Pittsburgh.

**2012**** **

*What is a gerbe?*GTP Seminar, University of Pittsburgh .