# 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 periodic smooth Deligne cohomology, with H. Sati, 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, Annals of Global Analysis and Geometry, 53-3 (2018), 445-466.

Spectral sequences in smooth generalized cohomology, with H. Sati, Algebraic and Geometric Topology, 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).

## 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 theorem, University 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 .