Lashi Bandara


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Position
I'm on a postdoc in the Geometry group at the University of Potsdam lead by Prof. Dr. Christian Bär.

My position is funded via 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 Alan McIntosh. A link to my thesis is here.
 
Google Scholar Page

Research interests
I'm primarily interested in the interactions between harmonic analysis and geometry, and in particular using harmonic analysis to analyse low-regularity situations on manifolds and also vector bundles. Currently, I'm hot and bothered by boundary value problems for first-order operators on bundles, using the language of sectorial operators. Also:
 
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.
 
 
Maths Publications
[13] Functional calculus and harmonic analysis in geometry, SPJM, Special Section: An Homage to Manfredo P. do Carmo. (Online first). [Arxiv version] [Journal version].
 
[12] Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions, (with A. Rosén), Comms. PDE. Volume 44, Issue 12, 2019, Pages 1253-1284. [Arxiv version] [Journal Version].
 
[11] Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric, (with A. McIntosh and A. Rosén), Math. Ann. Volume 370, Issue 1–2, 2018, Pages 863–915. [Arxiv version] [Journal version].
 
[10] Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics , (with H. Saratchandran), J. Funct. Anal., Volume 273, Issue 12, 2017, Pages 3719-3758. [Arxiv version] [Journal version].
 
[09] Continuity of solutions to space-varying pointwise linear elliptic equations, Publ. Mat. 61 (2017), no. 1, 239-258. [Arxiv version] [Journal version].
 
[08] Geometric singularities and a flow tangent to the Ricci flow, (with S. Lakzian and M. Munn), Ann. Sc. Norm. Super. Pisa Cl. Sci. Vol. 17, No 2, 2017, pages. 763-804. [Arxiv version] [Journal version]
 
[07] Rough metrics on manifolds and quadratic estimates, Math. Z. 283 (2016), no. 3-4, 1245-1281. [Arxiv version] [Journal version].
 
[06] Self-adjointness of the Gaffney Laplacian on vector bundles, (with O. Milatovic), Math. Phys. Anal. Geom. 18 (2015), no. 1, Art. 17, 14 pp. [Arxiv version] [Journal version].
 
[05] The Kato square root problem on vector bundles with generalised bounded geometry, (with A. McIntosh), J. Geom. Anal. 26 (2016), no. 1, 428-462. [Arxiv version] [Journal version].
 
[04] Density problems on vector bundles and manifolds, Proc. Amer. Math. Soc. 142 (2014), no. 8, 2683-2695. [Arxiv version] [Journal version].
 
[03] Square roots of perturbed subelliptic operators on Lie groups, (with A.F.M ter Elst and A. McIntosh), Studia Math. 216 (2013), no. 3, 193-217. [Arxiv version] [Journal version].
 
[02] Quadratic Estimates and perturbations of Dirac type operators on doubling measure metric spaces, AMSI International Conference on Harmonic Analysis and Applications, Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 45, Austral. Nat. Univ., Canberra, 2011, pp. 1-21. [Arxiv version] [Journal version].
 
[01] Real Harmonic Analysis, Lectures by Pascal Auscher with the assistance of Lashi Bandara, ANU Eview, 2012, [Online version].
 

Other Publications
[01] ShapeRotator: An R tool for standardized rigid rotations of articulated three-dimensional structures with application for geometric morphometrics, Marta Vidal-García, Lashi Bandara, J. Scott Keogh, Ecology and Evolution. [Journal version].
 

Preprints
[03] Boundary value problems for general first-order elliptic differential operators, (with C. Bär), [Arxiv version].
 
[02] Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary, (with M. Nursultanov and J. Rowlett), [Arxiv version].
 
[01] Heat kernels and regularity for rough metrics on smooth manifolds, (with P. Bryan), [Arxiv version].
 

Thesis
Geometry and the Kato Square root problem
 

Posters
Boundary value problems for general first-order elliptic operators
(International Congress of Mathemmaticians 2018)
 

Talks
When Functional Calculus, Harmonic Analysis and Geometry party together... (slides)
(Colloquium talk, Linköping University, 21 September 2018)
 
First-order elliptic boundary value problems beyond self-adjoint adapted boundary operators (slides)
(Instituto de Matemática Pura e Aplicada, 31 July 2018)
 
Spectral flow and the Riesz stability of the Atiyah-Singer Dirac operator under bounded perturbations of local boundary conditions (slides)
(University of Oxford, 16 March 2017)
 
Rough metrics, the Kato Square root problem, and the continuity of a flow tangential to the Ricci flow (slides)
(Université Paris-Sud, 21 September 2015)
 
Geometry and the Kato square root problem (slides)
(Beijing International Centre for Mathematical Research, 29 July 2014)
 
Geometry and the Kato square root problem (slides)
(University of Wollongong, 7 June 2013)
 
L^\infty coefficient operators and non-smooth Riemannian metrics (slides)
(Stanford University, 17 October 2012)
 
Square roots of perturbed sub-elliptic operators on Lie groups (slides)
(University of Calgary, 13 August 2012)
 
The Kato square root problem on vector bundles with generalised bounded geometry (slides) (Video of the talk)
(Recent trends in geometric and nonlinear analysis, BIRS, Canada, 7 August 2012)
 
Quadratic Estimates and perturbations of Dirac type operators on doubling measure metric spaces
(Macquarie University, 10 Feb 2011)
 

Videos
YouTube Channel
 

Brownian motion on a Riemannian Manifold (2016)
 
Theorema Egregium and the birth of Riemannian Geometry (ANU, 2014)
 
The Kato square root problem on vector bundles with generalised bounded geometry
(Recent trends in geometric and nonlinear analysis, BIRS, Canada, 7 August 2012)
 

Unpublished documents
Logic and Mathematics: Mathematicians in Schools program (ANU/Hawker College, Jul 2011)
 
An Overview of Functional Calculi for Noncommuting Operators (ANU, Dec 2009)
Motivation towards Clifford Analysis: The classical Cauchy's Integral Theorem from a Clifford perspective (ANU, Nov 2009)
 
White's Compactness Theorem for Integral Currents (Honours Thesis, Monash University, Oct 2006)
Zermelo-Frankel Set Theory and Well Orderings (Honours Essay, Monash University, May 2006)
 
Graph Colouring with Small Monochromatic Components (Final year Computer Science project, Monash University, June 2004)
 

Lecture notes
I have decided to make lecture notes I take at seminars, summer schools, and workshops available to the public, in the hope that it will be useful. Caveat: I pick and choose which notes I take and I can't guarantee that I have copied everything down exactly!
 
Go to the lecture notes
 

Awards
I was the recipient of a 2011 Australian-American Postgraduate Fulbright Scholarship which I took as a part of my PhD. During 2012, I used this scholarship to visit Steve Hofmann at the University of Missouri, Columbia, Missouri and Richard M. Schoen at Stanford University, Stanford, California.
 
Pure Mathematics Prize, Monash University, 2006.
 
Media and public outreach
Lashi Bandara: “Um problema de Matemática é como uma amante" (Portuguese) (Nov 2016)
 
Window of Sciences - Science Slam, Gothenburg University (Oct 2016)
 
Global Week - Science Slam, Gothenburg University (10 Dec 2014)
 
Radio appearance on Fuzzy Logic - Fuzzy with numbers on Canberra Community Radio 2XX (20 Oct 2013)
 
The point of pure mathematics (2 August 2011)
 
Appearance on ABC Catalyst: Mad for Maths (19 May 2011)
 
Radio Interview on Alex Sloan's show, ABC 666, Canberra (15 March 2011)
 
Mathematicians in Schools program (now called STEM Professionals in Schools) (Hawker College, Oct 2010)
For the subject notes I'm writing, please see above in Unpublished documents.
 
Interview for Plus Magazine (ICM, Hyderabad, August 2010)

 
Curriculum Vitae, ORCID, etc.
Curriculum Vitae (Sep, 2017)
ORCID Profile (Oct, 2017)

Academic Links
Notes on typesetting a thesis at ANU
Measure Theory Lectures by Marty Ross from 2006 AMSI Summer School
Australian-American Fulbright Institute
 

Personal Links
Personal web page
Slashdot - News for Nerds
 

Email Address
lashi.bandaraatuni-potsdam.de
Postal Address
Institut für Mathematik
Universität Potsdam
Campus Golm, Haus 9
Karl-Liebknecht-Str. 24-25
D-14476 Potsdam OT Golm
Germany
Phone
+49-331-977-1248