# Nageswari Shanmugalingam

## Professor

## Professor

### French Hall

5428F

A&S Mathematical Sciences - 0025

## Professional Summary

I received my Bachelors degree from the University of Rochester in 1994 and my doctoral degree from the University of Michigan in 1999, under the supervision of Professor Juha Heinonen. More up-to-date information can be found on my

google website or the website https://homepages.uc.edu/~shanmun/

## Education

Ph.D: University of Michigan at Ann Arbor 1999

BSc: University of Rochester Rochester, NY, 1994 (Physics, minor in Astronomy)

## Research and Practice Interests

My research area is geometric analysis. I am interested in the connection between inequalities in analysis and their geometric implications, and also in quasiconformal maps and the geometric properties of metric measure spaces conserved by them. I am also currently interested in the geometry behind the theory of functions of bounded variation (BV) and Besov spaces, and I am also interested in various notions of boundary in potential theory, and in the study of transformations of metric measure spaces that preserve bounded geometry.

## Research Support

Grant: #DMS-1500440 Investigators:Shanmugalingam, Nageswari 07-01-2015 -06-30-2018 National Science Foundation Potential theory of functions of bounded variation and quasiconformal maps Role:PI $297,800 Active Type:Grant

Grant: #DMS-1200915 Investigators:Shanmugalingam, Nageswari 06-01-2012 -05-31-2015 National Science Foundation Metric Geometry and Functions of Bounded Variation Role:PI $137,659.00 Active Level:Federal

Grant: #DMS-1200915 06-2012 -05-2015 NSF Metric geometry and functions of bounded variation Role:PI 237,809 Active Type:Grant

Grant: #200474 Investigators:Shanmugalingam, Nageswari 07-01-2011 -08-31-2016 Simons Foundation Geometry and Potential Theory in Metric Measure Spaces Role:PI $35,000.00 Closed Level:Private Non-Profit

Grant: #200474 Investigators:Nageswari Shanmugalingam 07-2011 -06-2016 Simons Foundation Geometry and potential theory in metric measure spaces 35000 Completed Type:Grant Level:National

Grant: #OISE-1019689 Investigators:Shanmugalingam, Nageswari 06-01-2010 -05-31-2012 National Science Foundation p-Harmonic Mappings and Quasiconformal Maps Role:PI $45,540.00 Closed Level:Federal

Grant: #OISE-1019689 Investigators:Nageswari Shanmugalingam 06-2010 -06-2012 NSF U.S.-India Workshop and ICM Satelite Conference on p-Harmonic and Quasiconformal Mappings, Chennai, India, August 2010 Role:PI 45540 Completed Type:Grant Level:International

08-2005 -05-2006 Taft Research Seminar fund Type:Grant

Grant: #DMS-0355027 Investigators:Shanmugalingam, Nageswari 09-01-2004 -08-31-2008 National Science Foundation Potential Theory on Metric Measure Spaces Role:PI $98,481.00 Closed Level:Federal

Grant: #DMS–0355027 08-2004 -08-2008 NSF grant 98481 Type:Grant

Grant: #DMS--0355027 08-2004 -08-2008 NSF Role:PI 98481 Completed Type:Grant Level:National

Grant: #DMS-0243355 Investigators:Shanmugalingam, Nageswari 08-20-2002 -08-31-2004 National Science Foundation Harmonic Analysis and Green Functions on Metric Spaces Role:PI $38,063.00 Closed Level:Federal

Grant: #DMS-0243355 08-2001 -08-2004 NSF Role:PI 65061 Completed Type:Grant Level:National

Grant: #DMS–0100132/0243355 08-2001 -08-2004 NSF grant 65061 Type:Grant

01-2001 -05-2001 University of Jyv¨askyl¨a European Union CMU grant Type:Grant

09-1999 -12-1999 Mittag-Leffler Institute Post-doctoral visiting fellowship Type:Fellowship

01-1993 -05-1994 University of Rochester Wilson Scholarship Type:Grant

Grant: #DMS-1800161 Investigators:Shanmugalingam, Nageswari 09-01-2018 -08-31-2021 National Science Foundation Notions of curvature and their role in analysis on metric measure spaces Role:PI $240,000.00 Awarded Level:Federal

Grant: #DMS-2054960 Investigators:Shanmugalingam, Nageswari 09-01-2021 -08-31-2024 National Science Foundation Role of Gromov hyperbolicity and Besov spaces in quasiconformal analysis Role:PI 300000.00 Awarded Level:Federal

## Abbreviated Publications

### Peer Reviewed Publications

The Mazurkiewicz distance and sets that are finitely connected at the boundary (with Anders Bjorn and Jana Bjorn) appeared in J. Geom. Anal. **26** No. 2 (2016) 873--897.

Characterizations of sets of finite perimeter using heat kernels in metric spaces,

(with Niko Marola and Michele Miranda Jr.), Potential Analysis, **45** (2016), Issue 4, pp 609--633.

Fine properties and a notion of quasicontinuity for BV functions on metric spaces (with Panu Lahti), Journal de Mathématiques Pures et Appliquées, *J. Math. Pures Appl. (9)* 107 (2017), no. 2, 150–182.

The Dirichlet problem for $p$-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities

(with Anders Bjorn and Jana Bjorn ) appeared in Journal of Differential Equations

**259** (2015) no. 7, 3078--3114.

Stability and continuity of functions of least gradient,

(with Heikki Hakkarainen, Riikka Korte, Panu Lahti), appeared in

Analysis and Geometry in Metric Spaces **3 **(2015) no. 1, 123--139.

Newton-Besov Spaces and Newton-Triebel-Lizorkin Spaces on Metric Measure Spaces, (with Dachun Yang and Wen Yuan) appeared in Positivity. **19 **no. 2 (2015), 177--220.

Hajłasz Gradients Are Upper Gradients (with Renjin Jiang, Dachun Yang, and Wen Yuan), appeared in JMAA, **422 **(2015) 397--407.

Geometry of prime end boundary and the Dirichlet problem for bounded domains in metric measure spaces (with Dewey Estep), appeared in Potential Analysis, ** 42 **(2015) 335--363.

Geometric characterizations of p-Poincare inequalities (with Estibalitz Durand-Cartagena and Jesus Jaramillo), appeared in Pub. Mat.. **60** (2016), 81--111

Semmes family of curves and a characterization of functions of bounded variation in terms of curves,

(with Riikka Korte and Panu Lahti)

appeared in Calc. Var. PDE October 2015, Volume **54**, Issue 2, pp 1393--1424

Boundary measures, generalized Gauss-Green formulas and the mean value property in metric measure spaces

(with Niko Marola and Michele Miranda Jr.), appeared in Revista Mat. Iberoamericana **31** (2015) no. 2, 497--530.

A characterization of BMO self-maps of a metric measure space,(with Juha Kinnunen,Riikka Korte and Niko Marola), appeared in Collectanea Math. September 2015, Volume **66**, Issue 3, pp 405--421

Geometry and Analysis of Dirichlet forms (II),

(with Pekka Koskela and Yuan Zhou)

appeared in J. Funct. Anal., **267** No. 7 (2014), 2437--2477.

Pointwise properties of functions of bounded variation in metric spaces (with Juha Kinnunen, Riikka Korte, and Heli Tuominen), appeared in Revista Mat. Complutense, ** 27 ** (2014), 41--67.

**Preservation of bounded geometry under sphericalization and flattening** (with Xining Li) appeared in Indiana Univ. Math. J. **64** No. 5 (2015), 1303--1341.

Quasiadditivity of variational capacity (with Juha Lehrback) Potential Anal. **40** (2014) 247--265

Geometric analysis on Cantor sets and trees(with Anders Bjorn, Jana Bjorn, and Jim Gill) appeared in Journal für die reine und angewandte Mathematik (Crelle's journal) *J. Reine Angew. Math.* 725 (2017), 63–114.

Intrinsic Geometry and Analysis of Diffusion Processes and $L^\infty$-Variational Problems, (with Pekka Koskela and Yuan Zhou), appeared in

Arch. Rat. Mech. Anal. (ARMA), ** 214 **No. 1 (2014) 99--142

Prime ends for domains in metric spaces

(with T. Adamowicz, A. Bjorn, J. Bjorn),

Appeared in Adv. Math. ** 238 **(2013) 459--505.

Regularity of sets with quasiminimal boundary surfaces in metric spaces,

(with Juha Kinnunen, Riikka Korte , and Andrew Lorent),

J. Geom. Anal., **23** (2013) 1607--1640.

First order Poincar\'e inequalities in metric measure spaces

(with Jesus Jaramillo and Estibalitz Durand-Cartagena)

Appeared in Ann. Acad. Scie. Fenn. Math. **38 **(2013), 287--308.

$L^\infty$-variational problem associated to Dirichlet forms

(with Pekka Koskela and Yuan Zhou)

Appeared in Mathematical Research Letters **19 **(2012) No. 6 (published: 2013)

Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property

(with Niko Marola and Riikka Korte)

Ark. Mat. 50 (2012) 111--134.

The $\infty$-Poincare inequality in metric measure spaces

(with Estibalitz Durand-Cartagena and Jesus A. Jaramillo),

Michigan Math. J **61** No.1 (2012) 63--85.

$p$-Poincaré inequality vs. $\infty$-Poincaré inequality; some counter-examples,

(with Estibalitz Durand-Cartagena and Alex Williams)

Math. Z., **271 **No. 1--2 (2012) 447--467.

A rigidity property of some negatively curved solvable Lie groups

(with Xiangdong Xie),

appeared in Comment. Math. Helv. **87 **No. 4 (2012) 805--823**.**

A characterization of Newtonian functions with zero boundary values,

(with Juha Kinnunen, Riikka Korte, and Heli Tuominen),

Calc. Var. PDE, **43** (2012) 507--528

Comparisons of relative BV-capacities and Sobolev capacity in metric spaces,

(with Heikki Hakkarainen),

Nonlinear Anal., **74** (2011) 5525--5543

Equivalence and self-improvement of $p$-fatness and Hardy's inequality, and association with uniform perfectness

(with Riikka Korte)

Math. Z. **264** (No. 1) (2010) 99--110

Interpolation properties of Besov spaces defined on metric spaces

(with Pekka Koskela and Amiran Gogatishvili)

appeared in Math. Nachr., **283** no.2 (2010) 215--231

The DeGiorgi measure and an obstacle problem related to minimal surfaces in metric spaces,

(with Juha Kinnunen, Riikka Korte, and Heli Tuominen),

appeared in J. Math. Pures Appl., **93** (2010) 599--622

Non-conformal Loewner type estimates for modulus of curve families

(with Tomasz Adamowicz),

appeared in Ann. Acad. Sci. Fenn. Math., **35** (2010) 609--626

Uniformity from Gromov hyperbolicity

(with David Herron and Xiangdong Xie),

appeared in Illinois J. Math. **52** No. 4 (2008) 1065--1109 (published in November 2009)

Quasicontinuity of Newton--Sobolev functions and density of Lipschitz functions in metric measure spaces

(with Anders Björn and Jana Björn)

appeared in Houston J. Math., **34** No. 4 (2008) 1197--1211

Lebesgue points and capacities via boxing inequalities in metric spaces

(with Juha Kinnunen, Riikka Korte, and Heli Tuominen)

appeared in Indiana Univ. Math. J., **57** no. 1 (2008) 401-430

Maximal regularity via reverse Holder inequalities for elliptic systems of $n$-Laplace type involving measures, (with Xiao Zhong and Tero Kilpeläinen)

appeared in Ark. Mat. **46** (No. 1) (2008) 77--93

Boundary Harnack principle for $p$-harmonic functions in smooth Euclidean domains

(with Hiroaki Aikawa, Tero Kilpeläinen, and Xiao Zhong),

appeared in Potential Analysis **26** No.3 (2007) 281--301

Measurability of equivalence classes and $MEC_p$-property in metric spaces

(with Esa Järvenpää, Maarit Järvenpää, Kevin Rogovin, and Sari Rogovin.)

appeared in Rev. Mat. Iberoamericana, **23** no. 3 (2007) 811--830

Sobolev extensions of Hölder continuous and characteristic functions on metric spaces

(with Anders Björn and Jana Björn)

appeared in Canadian Journal of Mathematics, **59** (No. 6) (2007), 1135--1153

Poincare inequalities, uniform domains, and extension properties for Newton-Sobolev spaces in metric spaces

(with Jana Björn)

appeared in J. Math. Anal. Appl., **332**, No. 1 (2007) 190--208

A problem of Baernstein on the equality of the $p$-harmonic measure of a set and its closure

(with Anders Björn and Jana Björn)

appeared in Proc. Amer. Math. Soc. **134** (2006) 509-519

Hölder estimates of $p$-harmonic extension operators

(PDF file) (with Hiroaki Aikawa)

appeared in J. Differential Equations **220** (2006) No. 1, 18--45

Polar sets on metric spaces

(with Juha Kinnunen)

appeared in Transactions Amer. Math. Soc. **358** (2006) 11--37

Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces (pdf file)

(with Petri Juutinen)

appeared in Math. Nachr. **279** (2006) 1083--1098

Carleson type estimates for $p$-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces.

(with Hiroaki Aikawa)

appeared in Michigan Math. J. **53** (2005) 165--188

Singular behavior of conformal Martin kernels, and non-tangential limits of conformal mappings

appeared in Ann. Acad. Sci. Fenn. Math. **29** (2004) 195--210

Dirichlet forms, Poincare inequalities, and the Sobolev spaces of Korevaar-Schoen

(with Pekka Koskela and Jeremy Tyson)

appeared in Potential Analysis. **21** No.3 (2004) 241--262

Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces

(with Pekka Koskela and Kai Rajala)

appeared in J. Funct. Anal. **202** (2003) 147--173

The Dirichlet problem for $p$-harmonic functions on metric measure spaces

(with Anders Björn and Jana Björn)

appeared in J. Reine Angew. Math. (Crelle) **556** (2003) 173--203

Some convergence results for $p$-harmonic functions on metric measure spaces

appeared in the Proceedings of the London Math. Soc. **87** (2003) 226--246

The Perron method for $p$-harmonic functions in metric spaces

(with Anders Björn and Jana Björn)

appeared in J. Differential Equations **195** (2003) 398--429

Singular functions on metric measure spaces

(with Ilkka Holopainen)

appeared in Collect. Math., **53** (2002) 313--332

Harmonic functions on metric spaces

appeared in Illinois J. Math., **45** no. 3 (2001) 1021--1050

Regularity of quasi-minimizers on metric spaces

(with Juha Kinnunen)

appeared in Manuscripta Math., **105** (2001) 401--423

Fat sets and pointwise boundary estimates for $p$-harmonic functions in metric spaces

(with Jana Björn and Paul MacManus)

appeared in J. Anal. Math., **85** (2001) 339--369

Modulus and continuous capacity

(with Sari kallunki)

appeared in Ann. Acad. Sci. Fenn. Math., **26** (2001) 455--464

Sobolev classes of Banach space-valued functions and quasiconformal mappings

(with Juha Heinonen, Pekka Koskela, and Jeremy Tyson)

appeared in J. Anal. Math., **85** (2001) 87--139

Newtonian spaces: An extension of Sobolev spaces to metric measure spaces

appeared in Rev. Mat. Iberoamericana, **16** (2000) 243--279.

Removable sets for the Poincare inequality on metric spaces

(with Pekka Koskela and Heli Tuominen)

appeared in Indiana Univ. Math. J., **49** (2000) 333--352

### Book

Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients (with Juha Heinonen, Pekka Koskela, Jeremy Tyson), published by

Cambridge University Press (2015 February)

### Peer Reviewed Conference/Workshop Proceedings

An elementary proof of Cheeger's theorem on reflexivity of Newton-Sobolev spaces of functions in metric measure spaces, (with Estibalitz Durand-Cartagena), appeared in J. Analysis , **21 **(volume year 2013, published 2015) 73--83

On the conformal Martin boundary of domains in metric spaces

(with Ilkka Holopainen and Jeremy Tyson)

appeared in Papers on Analysis: A volume dedicated to Olli Martio on the occasion of his 60th birthday Report. Univ. Jyväskylä 83 (2001) 147--168

### Under Review

Trace theorems for functions of bounded variation in metric spaces,

(with Panu Lahti), on CVGMT preprint server.

### Conference/Workshop Proceedings

Introduction to $p$-modulus of path-families and Newtonian spaces,

appeared in J. Anal., ** 18 ** (2010), 349--360

Sobolev type spaces on metric measure spaces.

*Potential theory in Matsue, *77–90, Adv. Stud. Pure Math., 44, *Math. Soc. Japan, Tokyo,* 2006

### Invited Publication

Geometric properties of planar BV extension domains

(with Pekka Koskela and Michele Miranda)

appeared in Function Spaces; Topics Around the Research of Prof. Maz'ya I,

International Mathematical Series (2010) (Springer collection)

A universality property of Sobolev spaces in metric measure spaces

appeared in the Springer collection Sobolev Spaces in Mathematics I, II, III (2009)

of the International Mathematical Series

### In Press

Trace and extension theorems for functions of bounded variation,

(with Lukáš Malý and Marie Snipes), to appear in Annali SNS.

**Brief survey on infinity-Poincar\'e inequality and existence of infinity-harmonic functions**, to appear in the book collection: *Measure Theory in Non-Smooth Spaces*, edited by Nicola Gigli (De Gruyter Open), 248--266

Dichotomy of global capacity density in metric measure space,

(with Hiroaki Aikawa, Anders Björn, Jana Björn),

to appear in Advances in Calculus of Variation

## Presentations

### Invited Presentations

Nageswari Shanmugalingam
(01-07-2016. )
*Fine properties of BV functions - analogs of quasicontinuity. *2016 Joint Mathematics Meetings, Washington State Convention Center and the Sheraton Seattle Hotel, Seattle, WA January 6--9, 2016, Seattle, WA.. Professional Meeting. .
Level:National

Nageswari Shanmugalingam
(12-2015. )
*Geometry behind the Poincare inequalities in the metric setting *.University of Helsinki, Helsinki, Finland. Conference. .
Level:International

Nageswari Shanmugalingam
(10-2015. )
*Trees and Cantor sets; Sobolev spaces and Besov spaces; rough quasiisometries and quasisymmetries *.Loyola University, Chicago, Chicago, IL. Professional Meeting. .
Level:National

Nageswari Shanmugalingam
(10-2015. )
*Traces of BV functions in metric setting *.California State University, Fullerton, Fullerton, CA. Professional Meeting. .
Level:National

Nageswari Shanmugalingam
(10-2015. )
*Geometry behind the Poincare inequalities *.University of Connecticut, colloquium, mathematics department, UConn, Storrs, CT.. Other Institution. .

UConn Department colloquium website

Nageswari Shanmugalingam
(06-2015. )
*Functions of bounded variation in metric setting: three definitions. *ICMAT (Universidad Autonoma de Madrid), Madrid, Spain. Conference. .
Level:International

Workshop on analysis and geometry in metric setting

Nageswari Shanmugalingam
(06-2015. )
*Trees and ultrametrics, Sobolev spaces and Besov spaces, rough quasiisometries and quasi symmetries. *Aalto University, Helsinki, Finland. Conference. .
Level:International

Workshop on harmonic analysis and partial differential equations

Nageswari Shanmugalingam
(06-2015. )
*Sphericalization and flattening transformations of metric measure spaces *.Linkoping University, Linkoping, Sweden. Conference. .
Level:International

PDEs, Potential theory, and Function spaces

Nageswari Shanmugalingam
(05-2015. )
*Introduction to Sobolev spaces in metric setting; a short course *.ICMAT (Universidad Autonoma de Madrid), Madrid, Spain. Workshop. .
Level:International

Research term on analysis and geometry in metric spaces

Nageswari Shanmugalingam
(12-2014. )
*Functions of least gradient in the metric setting *.Institute of Pure and Applied Mathematics conference, Lake Arrowhead (UCLA conference center). Professional Meeting. .
Level:Prof. Org.

Nageswari Shanmugalingam
(11-2014. )
*p-Poincare inequalities :finite versus infinite p. *The Red Raider Mini-Symposium, in honor of Professor Roger Barnard, Texas Tech University, Lubbock, TX. Conference. .
Level:National

Nageswari Shanmugalingam
(06-2014. )
*Geometry of quasiminimal surfaces in metric spaces *.Conference: 5th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals, Cornell University, Ithaca, NY. Conference. .
Level:International

Nageswari Shanmugalingam
(03-2014. )
*Sphericalization and Flattening *.American Math. Soc. Southern Sectional Meeting, University of Tennessee, Knoxville, TN.. Professional Meeting. .
Level:Regional

Nageswari Shanmugalingam
(02-2014. )
*Geometric implications of Poincare inequalities *.Conference: Function Theory on Infinite Dimensional Spaces XIII, ICMAT, Madrid, Spain. Conference. .
Level:International

Nageswari Shanmugalingam, Xining Li
(11-2013. )
*Sphericalization and Flattening *.University of Linkoping. Other Institution. .
Level:International

(10-2013. )
*Prime end boundary and Dirichlet problem *."Evolutionary problems" program, Institut Mittag-Leffler, Djursholm, Sweden. Workshop. .
Level:International

Nageswari Shanmugalingam, Dewey Estep
(08-2013. )
*Dirichlet problem for prime end boundary in metric setting *.A quasiconformal life: Celebration of the legacy and work of F.W.Gehring, University of Helsinki, Helsinki, Finland. Conference. .
Level:International

Nageswari Shanmugalingam
(03-2013. )
*Week-long graduate course: Analysis on metric measure spaces *.Institute of Pure and Applied Mathematics (UCLA), UCLA, Los Angeles, CA.. Other Institution. .
Level:International

(09-2012. )
*Prime ends for non-simply connected domains in Euclidean and metric spaces. *Potential Theory and its Related Fields, RIMS meeting; Kyoto University, Kyoto, Japan. Conference. .
Level:International

RIMS meeting: Potential Theory and its related fields

(03-2012. )
*$\infty$-Poincare inequality on metric measure spaces *.University of South Florida, Tampa, FL.. Professional Meeting. .
Level:National

(10-2011. )
*Regularity of quasiminimal surfaces in metric measure spaces *.Scuola Normale Superiore, Pisa, Pisa, Italy. Conference. .
Level:International

(09-2011. )
*Regularity of sets of quasiminimal boundary surfaces *.Cornell University, Ithaca, NY. Professional Meeting. .
Level:Regional

(08-2011. )
*Regularity of sets of quasiminimal boundary surfaces *.University of Jyvaskyla, Jyvaskyla, Finland. Conference. .
Level:International

(06-2011. )
*Geometric characterization of planar BV extension domains *.Complex analysis and potential theory: a conference in honor of Paul Gauthier and Kohur Gowrisankaran, CRM, University of Montreal, Canada. Conference. .
Level:International

(05-2011. )
*Introduction to Newton-Sobolev spaces in the metric setting *.Universidad Autonoma de Barcelona, Barcelona, Spain. Other Institution. .
Level:International

(05-2011. )
*Sobolev type function spaces for metric measure spaces-a short doctoral course *.University of Sevilla, Sevilla, Spain. Workshop. .
Level:International

(04-2011. )
*De Girogi measure and $1$-capacity in metric setting. *University of Helsinki, Helsinki, Finland. Other Institution. .
Level:International

(04-2011. )
*Geometric characterization of $\infty$-Poincare inequality *.University of Jyvaskyla, Jyvaskyla, Finland. Other Institution. .
Level:International

(03-2011. )
*BV functions and planar BV extension domains *.Linkoping University, Linkoping, Sweden. Other Institution. .
Level:International

(03-2011. )
*BV functions in the metric setting, and De Giorgi measure. *Linkoping University, Linkoping, Sweden. Other Institution. .
Level:International

(02-2011. )
*Geometry of $\infty$-Poincare inequality, some counterexamples *.Aalto University (TKK), Helsinki, Finland. Workshop. .
Level:International

(02-2011. )
*$\infty$-Poincare inequality and geometry. *University of Helsinki, Helsinki, Finland. Other Institution. .
Level:International

(01-2011. )
*Sets of finite perimeter and BV functions in metric measure spaces *.Universidad Complutense de Madrid, Madrid, Spain. Other Institution. .
Level:International

(11-2010. )
*A two-lecture analysis seminar on $\infty$-Poincare inequality *.University of Washington, Seattle, WA. Other Institution. .
Level:National

(10-2010. )
*Geometric characterization of $\infty$-Poincare inequality *.Purdue University, West Lafayette, IN.

(09-2010. )
*A graduate course on analysis in metric spaces, at Beijing Normal University *.Beijing Normal University, Beijing, China.

(08-2010. )
*A series of 3 lectures given at the ICM satellite conference, Harmonic and Quasiconformal Mappings *.Indian Institute of Technology at Madras, Chennai, India.

(05-2010. )
*Geometric and analytic characterizations of quasiconformal mappings *.University of Illinois at Urbana, Urbana-Champaign, IL.

(04-2010. )
*Geometric implications of $\infty$-Poincare inequality *.University of New Mexico, Albuquerque, NM.

(11-2009. )
*Planar BV extension domains *.Colloquium, Georgia Southern University,

(10-2009. )
*Geometric characterizations of planar BV extension domains *.Baylor University, Waco, TX.

(04-2009. )
*Besov spaces in metric setting and interpolation *.Syracuse University (Analysis seminar), Syracuse, NY.. Other Institution. .
Level:National

(03-2009. )
*Introduction to analysis in metric spaces (graduate course) *.Universidad Complutense de Madrid, Madrid, Spain.

(10-2008. )
*DeGiorgi measure and obstacle problems *.Wesleyan University (AMS special session), Wesleyan University, Middletown, CT.. Professional Meeting. .
Level:National

(05-2008. )
*Role of BV functions in geometry of metric measure spaces supporting a Poincare inequality *.Syracuse University, Syracuse, NY..

(06-2007. )
*Mini-course on BV functions in metric spaces *.Helsinki University of Technology,

(05-2007. )
*Boxing inequalities and characterizing 1-hyperbolicity *.International Conference on Harmonic Analysis, Pescara, Italy.

(05-2007. )
*Analysis seminar *.University of Pisa, Pisa, Italy.

(04-2007. )
*Analysis seminar *.University of Jyv¨askyl¨a, Finland.

(11-2006. )
*Boundary Harnack principle and decay estimates for p-harmonic functions *.special session on Subelliptic PDEs and Sub-Riemannian Geometry, AMS Sectional meeting, Fayetteville, Arkansas.

(08-2006. )
*On covering theorems and Hardy-Littlewood maximal functions *.Ramanujan Institute of Mathematical Sciences, Chennai University, Chennai, India.

(08-2006. )
*A series of 5 lectures on Sobolev space theory, fine regularity, and non-linear potential theory *.Indian Institute of Technology at Madras, Chennai, India.

(05-2005. )
*On conformal Martin boundaries of domains in metric measure spaces *.Analysis seminar, University of Helsinki, Finland.

(05-2005. )
*Conformal Martin boundary of Euclidean domains *.Analysis seminar, University of Link¨oping, Sweden.

(02-2005. )
*On equivalence of Dirichlet forms and Newtonian spaces *.Analysis seminar, University of Michigan, Ann Arbor.

(08-2004. )
*Dirichlet forms and Newton-Sobolev spaces for metric spaces supporting Poincar´e inequalities *.International Workshop on Potential Theory, Matsue, Japan.

(07-2004. )
*Domar’s argument and a proof of Carleson estimates for p-quasiminimizers *.conference on analysis on metric spaces at the Banach center, Poland.

(07-2004. )
*Introduction to Dirichlet forms on metric spaces *.analysis seminar, Helsinki University of Technology, Finland.

(04-2004. )
*Domar’s argument in the non-linear setting *.analysis seminar, University of Kentucky, Lexington.

(10-2003. )
*Lipschitz regularity of Cheeger–harmonic functions in metric spaces *.AMS sectional meeting, Boulder, CO.

(07-2003. )
*An introduction to the Dirichlet problem for p-harmonic functions *.Banff International Research Station, Banff, Canada.

Nageswari Shanmugalingam
(07-2016. )
*Besov spaces and traces *.Charles University, Prague., Czech Republic. Conference. .
Level:International

Nageswari Shanmugalingam
(10-2016. )
*Analysis on trees. *SIAM Central States Meeting, University of Arkansas, Little Rock., Little Rock, Arkansas.. Conference. .
Level:National

Nageswari Shanmugalingam
(07-2016. )
*Traces and extensions *.IMPAN, Warsaw, Poland, Other Institution. .
Level:Local

(04-2017. )
*Bounded variation in metric spaces *.Informal Analysis Meeting, Kent State Univ., held 7--9 April 2017., Kent, OH..
Level:International

(06-2017. )
*Short course: Analysis based on upper gradients. *10th School on Analysis and Geometry in Metric Spaces, Levico Terme, Italy. Professional Meeting. .
Level:International

(07-2017. )
*Dirichlet problem for least gradients. *Geometric Measure Theory Conference, Warwick University, Coventry, U.K.. Conference. .
Level:International

(10-2017. )
*Graphs versus metric graphs, and analysis. *SIAM Central States Sectional Meeting, Colorado State University, Fort Collins, CO.. Professional Meeting. .
Level:Regional

(09-2017. )
*Colloquium-Versions of Dirichlet problem for least gradients *.Department of Mathematics, Kansas State University, Manhattan, KS.. Other Institution. .
Level:University

### Colloquium

Nageswari Shanmugalingam, Xining Li
(11-2013).
*Poincare inequality in metric measure spaces; examples. *Linkoping University, Sweden. Other Institution.
Level:International

### Lecture

(03-2013. )
*Short course (4 lectures) on analysis in metric measure spaces *.UCLA, Los Angeles, CA. Workshop.
Level:National

### Event Organized

"Modern Aspects of Complex Geometry" conference organizing committee"Modern Aspects of Complex Geometry" conference organizing committee Conference 01-2014 05-2015 University of Cincinnati Level:International

Modern Aspects of Complex Geometry

Workshop I: Analysis on Metric SpacesWorkshop I: Analysis on Metric Spaces Workshop 03-12-2013 02-15-2013 Institute of Pure and Applied Mathematics (UCLA) Level:International

Interactions between Analysis and Geometry: special semester program

Workshop on Quasiconformal mappings and harmonic mappingsWorkshop on Quasiconformal mappings and harmonic mappings Workshop 08-09-2010 08-17-2010 Chennai, India Level:International

## Honors and Awards

2008 McMicken Dean's Award for Distinguished Scholarship Status:Recipient Level:College Type:Recognition

2017 Fellow of the Graduate School Type:Fellowship

## Service

(PhD dissertation committee of Elefterios Soultanis, University of Helsinki ) Reviewer Type:Other Educational Service Level:International 01-2016 -03-2016

(Masters Oral Examination Committee for Ang Li ) Committee Member Type:Departmental Service Level:Department 01-2016 -04-2016

Taft Foundation (Taft Faculty Fellowships Committee ) Committee Chair Type:University/College Service Level:College 08-2015 -03-2016

Type:Service to Student Groups Level:Department 06-2015 -07-2015

Type:Community Service Level:International 05-2015 -06-2015

Peer Review/Referee Type:Community Service Level:International 01-2015 -11-2015

(Analysis Preliminary Examination Committee ) Committee Member Type:Departmental Service Level:Department 01-2015 -08-2015

American Association of University Professors (UC) (AAUP Associates Council ) Elected Member Type:Service to Professional Associations Level:University 01-2015 -04-2016

Type:Service to Student Groups Level:Department 01-2015 -05-2015

Revista Matematica Complutense (Editorial Board ) Editorial Board Member Type:Community Service Level:International 2015 -2016

(External reader for PhD dissertation ) Reviewer Type:Service to Student Groups Level:International 2015 -2015

(Analysis Preliminary Examination Committee ) Committee Member Type:Departmental Service Level:Department 08-2014 -07-2015

(Departmental Hiring Committee ) Committee Member Type:Departmental Service Level:University 08-2014 -02-2015

Journal "Revista Matematica Complutense" (Editorial Committee ) Editorial Board Member Type:Editorial Service Level:International 08-2014 -07-2015

(Qualifying Examination Committee ) Committee Member Type:Departmental Service Level:Department 03-2014 -08-2014

("Modern Aspects of Complex Geometry" conference organizing committee ) Committee Chair Type:Community Service Level:University 01-2014 -05-2015

Demonstratio Mathematica (Editorial Board ) Editorial Board Member Type:Community Service Level:International 2014 -2016

Electronic Journal of Conformal Geometry and Dynamics (AMS journal) (Editorial Board ) Editorial Board Member Type:Community Service Level:International 2014 -2016

National Science Foundation (Review Panel ) Committee Member Type:Grant Panel Level:National 12-2013 -02-2014

Electronic Journal of Conformal Geometry and Dynamics (American Mathematical Society journal) (Editorial Committee ) Editorial Board Member Type:Editorial Service Level:International 08-2013 -07-2015

Journal "Demonstratio Mathematica" (Editorial Committee ) Editorial Board Member Type:Editorial Service Level:International 08-2013 -07-2015

(Taft Faculty Fellowships Committee ) Committee Member Type:University/College Service Level:College 08-2013 -04-2015

(Reappointment, Promotion and Tenure Committee ) Committee Chair Type:Departmental Service Level:Department 08-2013 -06-2014

Taft Research Center (Taft Faculty Fellowships Committee ) Committee Member Type:University/College Service Level:College 08-2013 -To Present

(Qualifying Examination Committee ) Committee Member Type:Departmental Service Level:Department 08-2013 -To Present

(RPT Committee ) Committee Chair Type:Departmental Service Level:Department 08-2013 -06-2014

National Science Foundation Review Board/Panel Type:Grant Panel Level:National 12-2012 -02-2013

Reviewer Type:Community Service Level:International 08-2012 -11-2012

(Graduate Affairs Committee ) Committee Chair Type:Departmental Service Level:Department 08-2012 -07-2013

Mentor Type:University/College Service Level:College 08-2012 -To Present

(Qualifying Examination Committee ) Committee Member Type:Departmental Service Level:Department 07-2012 -07-2013

(Complex Analysis Preliminary Exam committee ) Committee Member Type:Departmental Service Level:Department 07-2012 -10-2012

Mentor Type:Departmental Service Level:Department 06-2012 -12-2012

(Dissertation committee (Renjin Jiang) ) Reviewer Type:Community Service Level:International 01-2012 -02-2012

Conformal Geometry and Dynamics (Editorial Board ) Board Member Type:Editorial Service Level:International 01-2012 -01-2014

Demonstratio Mathematica (Editorial Board ) Member Type:Editorial Service Level:International 11-2011

(Graduate Student Evaluation Committee ) Committee Member Type:Departmental Service Level:Department 09-2011 -08-2012

International Journal of Mathematics and Mathematical Sciences (Editorial board ) Editorial Board Member Type:Editorial Service Level:International 09-2011

(Reappointment, Promotion, and Tenure committee (RPT committee) ) Committee Member Type:Departmental Service Level:Department 09-2011 -06-2013

Taft Research Center (Conference Committee ) Committee Member Type:University/College Service Level:University 09-2011 -06-2013

(Hiring Committee ) Committee Member Type:Departmental Service Level:Department 09-2011 -04-2012

Academic advisor Mentor Type:Departmental Service Level:Department 09-2011 -06-2012

(Topology preliminary examination committee ) Committee Member Type:Departmental Service Level:Department 08-2011 -06-2012

Taft Research Center (Taft Steering Committee ) Committee Member Type:University/College Service Level:University 06-2011 -08-2012

Proceedings of the American Mathematical Society Peer Review/Referee Type:Editorial Service Level:National 03-2011

Universidad Complutense de Madrid, Spain (Dissertation defense committee (for Estibalitz Durand-Cartagena) ) Committee Member Type:Other Level:International 01-2011 -02-2011

Computers and Mathematics with Applications (journal) Reviewer Type:Editorial Service Level:International 2011

(PhD Dissertation committee for Poranee Kongkha-Julian ) Committee Member Type:Departmental Service Level:Department 09-2010 -11-2012

American Mathematical Society (AMS) (Organizing special session on Geometric Analysis ) Committee Member Type:Service to Professional Associations Level:Regional 03-2010

(Departmental Colloquium Chair ) Committee Chair Type:Departmental Service Level:Department 09-2009 -06-2010

(Topology Preliminary Examination Committee ) Committee Chair Type:Departmental Service Level:Department 08-2009 -08-2010

Taft Research Center (Taft Student Awards Committee ) Committee Chair Type:University/College Service Level:College 08-2009 -08-2010

(International Congress of Mathematicians Satellite Workshop and conference on harmonic and conformal mappings, organizing committee ) Committee Member Type:Community Service Level:International 08-2009 -08-2010

(Hiring Committee ) Committee Member Type:Departmental Service Level:Department 12-2008 -03-2009

NSF (Geometric Function Theory panel ) Review Board/Panel Type:Grant Panel Level:National 11-2008 -02-2009

American Mathematical Society (AMS) (Book and journal donation program committee ) Committee Member Type:Service to Professional Associations Level:National 09-2008 -09-2010

Taft Research Center (Taft Student Awards Committee ) Committee Member Type:University/College Service Level:College 08-2008 -08-2009

Mathematica Scandinavica Peer Review/Referee Type:Editorial Service Level:International

Journal of Functional Analysis Peer Review/Referee Type:Editorial Service Level:International

National Science Foundation (NSF Review Panel ) Committee Member Type:Community Service Level:National 2016

## Post Graduate Training and Education

08-1999-12-1999 Research fellow, Institut Mittag-Leffler,, , Djursholm, Sweden

01-2000-06-2000 Post-doctoral researcher, National University of Ireland at Maynooth,, , Maynooth, Ireland

08-2000-04-2002 Post-doc, University of Texas at Austin,, , Austin, TX

01-2001-04-2001 Visitng Scholar, University of Jyvaskyla,, , Jyvaskyla, Finland

## Keywords

Potential theory in metric measure spaces, geometric analysis

## Professional Affiliation

1999 -2016: Member American Mathematical Society

## Courses Taught

Geometric Function Theory Level:Graduate

Complex Analysis Level:Graduate

-MATH-2063 MULTIVARIABLE CALC Level:Undergraduate

Topology Level:Graduate

-MATH-2063 MULTIVARIABLE CALC Level:Undergraduate

Topology Level:Graduate

-MATH-2076 LINEAR ALGEBRA Level:Undergraduate

Complex Analysis Level:Graduate

Real Analysis Level:Graduate

-MATH-2063 MULTIVARIABLE CALC Level:Undergraduate

Geometric Analysis. Level:Graduate

15-MATH-505 ADVANCED CALCULUS Level:Both

15-MATH-252 CALCULUS II

15-MATH-506 ADVANCED CALCULUS Level:Both

15-MATH-273 DIFFERENTIAL EQNS Level:Undergraduate

Calculus I Level:Undergraduate

Introduction to Complex Analysis Level:Both

15-MATH-504 ADVANCED CALCULUC Level:Both

15-MATH-252 CALCULUS II Level:Undergraduate

Abstract Algebra Level:Both

15-MATH-513 ABSTRACT ALGEBRA Level:Both

15-MATH-253 CALCULUS III Level:Undergraduate

15-MATH-251 CALCULUS I Level:Undergraduate

15-MATH-511 ABSTRACT ALGEBRA Level:Both

## Faculty Development Activities

2011 How to manage large classes CET&L Langsam library Type:Workshop

01-09-2012 -01-13-2012 Mapping Theory in Metric Spaces NSF-funded workshop intended to foster collaboration., American Institute of Mathematics (AIM) Palo Alto, CA. Type:Workshop

10-2013 -12-2013 Semester program on "Evolutionary Problems" Institut Mittag-Leffler Djursholm, Sweden Type:Other

03-2013 -05-2013 Special Semester on Interactions Between Analysis and Geometry Institute of Pure and Applied Mathematics UCLA, Los Angeles, CA. Type:Other