Ali is a PhD student with research interests in C* - algebras. This is a branch of Functional Analysis that arises as a natural generalization of the structure observed when studying bounded linear operators between Hilbert spaces.
Specifically, Ali works on Cartan subalgebras of C*-algebras. These are maximal Abelian C*-subalgebras which are regular, contain an approximate identity of the algebra in which they sit, and admit a faithful conditional expectation. Cartan subalgebras are essential in building a bridge between C*-algebras on the one hand, and topological dynamics and geometric group theory on the other. Ali is supervised by Dr. Xin Li.
Ali graduated from Part III of the Mathematical Tripos at the University of Cambridge in 2016. He received his BSc. in Pure Mathematics in 2015, from the University of Edinburgh.
Ali's hobbies include card magic, chess and writing poetry.
Jan. 2019 - Jun. 2019
- TA and Marker for MTH 4115/4215 - Vectors and Matrices
- Marker for SEF 015 - Discrete Mathematics
Sep. 2018 - Dec. 2018
- TA for MTH 5104 - Convergence and Continuity
- Demonstrator and Marker for MTH 5112 - Linear Algebra 1
- Marker for MTH5123 - Differential Equations
Jan. 2018 - Jun. 2018
- TA and Marker for MTH 4104 - Introduction to Algebra
C* - algebras, specifically Cartan subalgebras.