Biography
I am currently a Senior Lecturer in Mathematics at the Deakin Mathematics Research and Teaching Lab at Deakin University (Burwood campus).
Priot to that, I was a Lecturer in Mathematics at the Department of Mathematics at Brunel University London.
Before that, I was a postdoc in the Geometry group at the University of Potsdam lead by Christian Bär, funded via the SPP2026 - Geometry at Infinity
which is a Special Priority Program of the
DFG (Deutsche Forschungsgemeinschaft/German Reserach Foundation).
Previously, I did a postdoc with Andreas Rosén at Mathematical Sciences at University of Gothenburg in Sweden funded via a Knut and Alice Wallenberg Fellowship.
My PhD supervisor was the late Alan McIntosh.
A link to my thesis is here.
Read more on Lashi's profileResearch interests
- Global analysis - Use of operator methods in geometry, index theory.
- Harmonic analysis - in the flavour of Calderon, Zygmund, Stein, etc.
- Geometric analysis - analysis on non-compact manifolds, non-smooth metrics, analysis on measure metric spaces, Spin geometry.
- Boundary value problems - first-order boundary value problems on bundles, non-smooth coefficients, non-compact boundary.
- Spectral and operator theory - essential self-adjointness, asymptotics of eigenvalues, etc.
Affiliations
Australian Mathematics Society, London Mathematics Society, Geometry at Infinity (Germany)
Teaching interests
- Mathematical analysis
- Mathematical logic
- Partial Differential Equations
- Programming in C/C++
- Stochastic optimisation
Units taught
- 2021-2023: Fundamentals of Mathematics (Brunel University London, course code: MA1612; National Chinese University of Technology via Brunel TNE, course code: MA1604)
- 2021-2023: Final Year Project (Brunel University London, course code: MA3990)
- 2022: Programming and Mathematical Projects (Brunel University London, course code: MA1691)
- 2021: Boundary Value Problems and Index Theory (University of Potsdam, MSc course)
- 2019: Lorenztian Geometry (University of Potsdam, MSc course)
Knowledge areas
Global Analysis, Geometry, Operator Theory, Functional Analysis
Conferences
- 13th International Conference on Clifford Algebras and Their Applications in Mathematical Physics, Holon Institute of Technology, Israel, June 2023.
- Geometry and Analysis Meet at Brunel, (Organiser), Brunel University London, March 2023.
- Analysis of Dirac Type and Higher Spin Operators Conference: Honoring John Ryan, Chapman University, USA, Nov 2022.
- Global Analysis on Manifolds, (Organiser) Freiburg University, Germany, ·Sep 2022.
- Microlocal and global analysis in geometry and mathematical physics, University of Potsdam, Germany, Feb 2021.
- Bivariant K-theory in Geometry and Physics Program, Erwin Schrödinger International Institute for Mathematics and Physics, Austria, Nov 2018.
- Harmonic Analysis Conference Celebrating the Mathematical Legacy of Alan McIntosh, Australian National University, Australia, Feb 2018.
- HIM Junior trimester program follow-up meeting, (Member of main organising committee), Hausdorff Research Institute for Mathematics, Germany, Sep 2015.
- Australian Mathematical Sciences Student Conference, (Member of main organising committee), Australian National University, Australia, Jul 2013.
Publications
The Relative Index Theorem for General First-Order Elliptic Operators
L Bandara
(2023), Vol. 33, pp. 1-20, Journal of Geometric Analysis, Berlin, Germany, C1-1
Realisations of elliptic operators on compact manifolds with boundary
Lashi Bandara, Magnus Goffeng, Hemanth Saratchandran
(2023), Vol. 420, pp. 1-123, Advances in Mathematics, Amsterdam, The Netherlands, C1-1
Boundary value problems for general first-order elliptic differential operators
Christian Baer, Lashi Bandara
(2022), Vol. 282, pp. 1-69, Journal of Functional Analysis, Amsterdam, The Netherlands, C1-1
Functional calculus and harmonic analysis in geometry
L Bandara
(2021), Vol. 15, pp. 20-53, Sao Paulo Journal of Mathematical Sciences, Berlin, Germany, C1-1
Heat kernels and regularity for rough metrics on smooth manifolds
L Bandara, P Bryan
(2020), Vol. 293, pp. 2255-2270, Mathematische Nachrichten, London, Eng., C1-1
L Bandara, A Rosén
(2019), Vol. 44, pp. 1253-1284, Communications in Partial Differential Equations, London, Eng., C1-1
Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric
L Bandara, A McIntosh, A Rosén
(2018), Vol. 370, pp. 863-915, Mathematische Annalen, Berlin, Germany, C1-1
Marta Vidal‐García, Lashi Bandara, J Keogh
(2018), Vol. 8, pp. 4669-4675, Ecology and Evolution, London, Eng., C1-1
L Bandara, H Saratchandran
(2017), Vol. 273, pp. 3719-3758, Journal of Functional Analysis, Amsterdam, The Netherlands, C1-1
Continuity of solutions to space-varying pointwise linear elliptic equations
Lashi Bandara
(2017), Vol. 61, pp. 239-258, Publicacions Matematiques, Barcelona, Spain, C1-1
Geometric singularities and a flow tangent to the Ricci flow
Lashi Bandara, Sajjad Lakzian, Michael Munn
(2017), Vol. 17, pp. 763-804, Annali della Scuola normale superiore di Pisa - Classe di scienze, Pisa, Italy, C1-1
The Kato Square Root Problem on Vector Bundles with Generalised Bounded Geometry
Lashi Bandara, Alan McIntosh
(2016), Vol. 26, pp. 428-462, Journal of Geometric Analysis, Berlin, Germany, C1-1
Rough metrics on manifolds and quadratic estimates
Lashi Bandara
(2016), Vol. 283, pp. 1245-1281, Mathematische Zeitschrift, Berlin, Germany, C1-1
Self-adjointness of the Gaffney Laplacian on Vector Bundles
Lashi Bandara, Ognjen Milatovic
(2015), Vol. 18, MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, C1-1
DENSITY PROBLEMS ON VECTOR BUNDLES AND MANIFOLDS
Lashi Bandara
(2014), Vol. 142, pp. 2683-2695, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, C1-1
Square roots of perturbed subelliptic operators on Lie groups
Lashi Bandara, A ter Elst, Alan McIntosh
(2013), Vol. 216, pp. 193-217, STUDIA MATHEMATICA, C1-1
Real Harmonic Analysis Lectures by Pascal Auscher with the Assistance of Lashi Bandara
Pascal Auscher, Lashi Bandara
(2012), Acton, A.C.T., A1-1
Funded Projects at Deakin
No Funded Projects at Deakin found
Supervisions
No completed student supervisions to report