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.
 
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. More recently, I've been working on 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 Riemannian manifolds, in situations where the metric may fail to be smooth, analysis on measure metric spaces, Spin geometry.
 
 
Publications
[11] Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric, (with A. McIntosh and A. Rosén), Math. Ann. (online so far). [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].
 

Preprints
[02] Heat kernels and regularity for rough metrics on smooth manifolds, (with P. Bryan), [Arxiv version].
 

[01] Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions, (with A. Rosén), [Arxiv version].
 

Thesis
Geometry and the Kato Square root problem
 

Talks
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)
 

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
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)
 
Profile on choose your own adventure at ANU (1 Jun 2012)
 
Article in the ANU Reporter: Taking maths to the masses (22 Nov 2011)
 
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)
 
Article in the Canberra Times (15 March 2011)
 
Fulbright Media Release (March 2011)
 
Mathematicians in Schools program (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)

Interesting maths people (in alphabetical order)
Christian Bär
Steve Hofmann
Sajjad Lakzian
Alan McIntosh
Ognjen Milatovic
Mike Munn
Pierre Portal
Andreas Rosén
Julie Rowlett
Rick Schoen
 

Academic Links
Harmonic Analysis and PDE at Chalmers/GU
Notes on typesetting a thesis at ANU
Measure Theory Lectures by Marty Ross from 2006 AMSI Summer School
Analysis and Geometry Program at ANU
Applied and Nonlinear Analysis Program at ANU
Alan McIntosh's Page
Various academic stuff I've done
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