Algebra is concerned with manipulation in time, and geometry is concerned with space… “Should you just be an algebraist or a geometer?” is like saying “Would you rather be deaf or blind?”
Sir Michael Atiyah, Mathematics in the 20th Century
Research Interests:
Group Representations, Operator Algebras, and Geometric Quantization
My current research is focused on the geometric quantization, the orbit method and in particular Kirillov’s character formula.
… “Is it unitary?”… “I’ll explain it to you,” Feynman said, “and then you can tell me if it is unitary.” He went on and from time to time he thought he could still hear Dirac muttering, “Is it unitary?”
Research Publications and Preprints:
- Quantization of Coadjoint Orbits via Kirillov’s Character Formula (in progress)
- On the Existence of Nowhere-zero Vectors for Linear Transformations (with S. Akbari, K. Hassani Monfared, M. Jamaali, and D. Kiani) Bull. Austral. Math. Soc, 82 (2010), 480–487.
My undergraduate project, inspired by a conjecture of Noga Alon and his combinatorial Nullstellensatz, studies the existence of vectors with no zero entries in the kernel and image of linear transformations.
Other Publications, Preprints, and Notes:
- Topics in Advanced Linear Algebra, +100-page draft of my notes on Linear Algebra.
In these notes, in addition to exploring some advanced topics in linear and multilinear algebra, I discuss linear algebraic techniques applied in a variety of areas including analysis, symplectic geometry, representation theory, K-theory, and combinatorics. I intend to make these notes available online when they are in a reasonably good shape.
- Slides for my colloquium talk for undergraduate students at Amherst College on The Spectacular Spectral Theory (2015)
- Slides for the first part of my introductory talk on The Probabilistic Method in Graph Theory (2010)
- Errata for An Introduction to Manifolds, by Loring W. Tu, Second Edition
Several years ago I used the first edition of Loring W. Tu’s An Introduction to Manifolds as a warm-up to self-study the classic Differential Forms in Algebraic Topology by Bott and Tu. Soon after the second edition of the former book was published, I prepared a list of minor corrections and suggestions for the new edition and sent them to Professor Tu. However, since the list of errata has not appeared anywhere on the internet yet, I have decided to upload the file here for the convenience of the other readers of this wonderful introductory book on smooth manifolds.
- Teaching Mathematics, Journal of Science and Society, 88 (2009), 19–21. (In Persian)