Profile image of Lashi Bandara

Dr Lashi Bandara

STAFF PROFILE

Position

Senior Lecturer, Mathematics

Faculty

Faculty of Sci Eng & Built Env

Department

School of Info Technology

Campus

Melbourne Burwood Campus

Qualifications

Fellow (FHEA) of AdvanceHE, Advance HE, 2022
Doctor of Philosophy, Australian National University, 2013
Bachelor of Science (Honours), Monash University, 2007
Bachelor of Computer Science, Monash University, 2007

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 profile

Research 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

Filter by

2023

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

journal article

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

journal article
2022

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

journal article
2021

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

journal article
2020

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

journal article
2019

Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions

L Bandara, A Rosén

(2019), Vol. 44, pp. 1253-1284, Communications in Partial Differential Equations, London, Eng., C1-1

journal article
2018

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

journal article

ShapeRotator: An R tool for standardized rigid rotations of articulated three‐dimensional structures with application for geometric morphometrics

Marta Vidal‐García, Lashi Bandara, J Keogh

(2018), Vol. 8, pp. 4669-4675, Ecology and Evolution, London, Eng., C1-1

journal article
2017

Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics

L Bandara, H Saratchandran

(2017), Vol. 273, pp. 3719-3758, Journal of Functional Analysis, Amsterdam, The Netherlands, C1-1

journal article

Continuity of solutions to space-varying pointwise linear elliptic equations

Lashi Bandara

(2017), Vol. 61, pp. 239-258, Publicacions Matematiques, Barcelona, Spain, C1-1

journal article

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

journal article
2016

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

journal article

Rough metrics on manifolds and quadratic estimates

Lashi Bandara

(2016), Vol. 283, pp. 1245-1281, Mathematische Zeitschrift, Berlin, Germany, C1-1

journal article
2015

Self-adjointness of the Gaffney Laplacian on Vector Bundles

Lashi Bandara, Ognjen Milatovic

(2015), Vol. 18, MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, C1-1

journal article
2014

DENSITY PROBLEMS ON VECTOR BUNDLES AND MANIFOLDS

Lashi Bandara

(2014), Vol. 142, pp. 2683-2695, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, C1-1

journal article
2013

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

journal article
2012

Real Harmonic Analysis Lectures by Pascal Auscher with the Assistance of Lashi Bandara

Pascal Auscher, Lashi Bandara

(2012), Acton, A.C.T., A1-1

book
2011

Quadratic estimates for perturbed dirac type operators on doubling measure metric spaces

Lashi Bandara

(2011), AMSI International Conference on Harmonic Analysis and Applications., C1-1

journal article

Funded Projects at Deakin

No Funded Projects at Deakin found

Supervisions

No completed student supervisions to report