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# People in the Department

# Nageswari Shanmugalingam

Title: Professor

Office: 5428F French Hall

Tel: 513-556-4062

Email: shanmun@ucmail.uc.edu

Web: https://homepages.uc.edu/~shanmun/

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 Information

### Research 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

- (PI), Shanmugalingam, Nageswari,
*Potential theory of functions of bounded variation and quasiconformal maps*, National Science Foundation. (DMS-1500440), $297,800. 07/01/2015 to 06/30/2018. Status: Active. - (PI), Shanmugalingam, Nageswari,
*Metric Geometry and Functions of Bounded Variation*, National Science Foundation. (DMS-1200915), $137,659.00. 06/01/2012 to 05/31/2015. Status: Active. - (PI),
*Metric geometry and functions of bounded variation*, NSF. (DMS-1200915), 237,809. 06-2012 to 05-2015. Status: Active. - (PI), Shanmugalingam, Nageswari,
*Geometry and Potential Theory in Metric Measure Spaces*, Simons Foundation. (200474), $35,000.00. 07/01/2011 to 08/31/2016. Status: Closed. - Nageswari Shanmugalingam,
*Geometry and potential theory in metric measure spaces*, Simons Foundation. (200474), 35000. 07-2011 to 06-2016. Status: Completed. - (PI), Shanmugalingam, Nageswari,
*p-Harmonic Mappings and Quasiconformal Maps*, National Science Foundation. (OISE-1019689), $45,540.00. 06/01/2010 to 05/31/2012. Status: Closed. - (PI), Nageswari Shanmugalingam,
*U.S.-India Workshop and ICM Satelite Conference on p-Harmonic and Quasiconformal Mappings, Chennai, India, August 2010*, NSF. (OISE-1019689), 45540. 06-2010 to 06-2012. Status: Completed. *Taft Research Seminar fund*. 08-2005 to 05-2006.- (PI), Shanmugalingam, Nageswari,
*Potential Theory on Metric Measure Spaces*, National Science Foundation. (DMS-0355027), $98,481.00. 09/01/2004 to 08/31/2008. Status: Closed. *NSF grant*. (DMS–0355027 ), 98481. 08-2004 to 08-2008.- (PI), NSF. (DMS--0355027), 98481. 08-2004 to 08-2008. Status: Completed.
- (PI), Shanmugalingam, Nageswari,
*Harmonic Analysis and Green Functions on Metric Spaces*, National Science Foundation. (DMS-0243355), $38,063.00. 08/20/2002 to 08/31/2004. Status: Closed. - (PI), NSF. (DMS-0243355), 65061. 08-2001 to 08-2004. Status: Completed.
*NSF grant*. (DMS–0100132/0243355 ), 65061. 08-2001 to 08-2004.*European Union CMU grant*, University of Jyv¨askyl¨a. 01-2001 to 05-2001.*Post-doctoral visiting fellowship*, Mittag-Leffler Institute. 09-1999 to 12-1999.*Wilson Scholarship*, University of Rochester. 01-1993 to 05-1994.- (PI), Shanmugalingam, Nageswari,
*Notions of curvature and their role in analysis on metric measure spaces*, National Science Foundation. (DMS-1800161), $240,000.00. 09/01/2018 to 08/31/2021. Status: Awarded.

## 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.[Link] - 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.[Link] - 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.[Link] - 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.[Link] - 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 [Link] - 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[Link] - 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.[Link] - 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[Link] - 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.[Link]- 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.Link] - 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.[Link] - 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.[Link] - 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[Link] - 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

### 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[Link] - 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

### Books

- 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)[Link]

### 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[Link]

### In Press

- Trace and extension theorems for functions of bounded variation,

(with Lukáš Malý and Marie Snipes), to appear in Annali SNS.[Link] **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

### 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

### Under Review

- Trace theorems for functions of bounded variation in metric spaces,

(with Panu Lahti), on CVGMT preprint server.[Link]

## Presentations & Lectures

### 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.. [Link] - Nageswari Shanmugalingam (12-2015).
*Geometry behind the Poincare inequalities in the metric setting*University of Helsinki, Helsinki, Finland. [Link] - Nageswari Shanmugalingam (10-2015).
*Trees and Cantor sets; Sobolev spaces and Besov spaces; rough quasiisometries and quasisymmetries*Loyola University, Chicago, Chicago, IL. [Link] - Nageswari Shanmugalingam (10-2015).
*Traces of BV functions in metric setting*California State University, Fullerton, Fullerton, CA. [Link] - Nageswari Shanmugalingam (10-2015).
*Geometry behind the Poincare inequalities*University of Connecticut, colloquium, mathematics department, UConn, Storrs, CT.. [Link] - Nageswari Shanmugalingam (06-2015).
*Functions of bounded variation in metric setting: three definitions.*ICMAT (Universidad Autonoma de Madrid), Madrid, Spain. [Link] - Nageswari Shanmugalingam (06-2015).
*Trees and ultrametrics, Sobolev spaces and Besov spaces, rough quasiisometries and quasi symmetries.*Aalto University, Helsinki, Finland. [Link] - Nageswari Shanmugalingam (06-2015).
*Sphericalization and flattening transformations of metric measure spaces*Linkoping University, Linkoping, Sweden. [Link] - Nageswari Shanmugalingam (05-2015).
*Introduction to Sobolev spaces in metric setting; a short course*ICMAT (Universidad Autonoma de Madrid), Madrid, Spain. [Link] - Nageswari Shanmugalingam (12-2014).
*Functions of least gradient in the metric setting*Institute of Pure and Applied Mathematics conference, Lake Arrowhead (UCLA conference center). - 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. - 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. - Nageswari Shanmugalingam (03-2014).
*Sphericalization and Flattening*American Math. Soc. Southern Sectional Meeting, University of Tennessee, Knoxville, TN.. - Nageswari Shanmugalingam (02-2014).
*Geometric implications of Poincare inequalities*Conference: Function Theory on Infinite Dimensional Spaces XIII, ICMAT, Madrid, Spain. - Nageswari Shanmugalingam, Xining Li (11-2013).
*Sphericalization and Flattening*University of Linkoping. - (10-2013).
*Prime end boundary and Dirichlet problem*"Evolutionary problems" program, Institut Mittag-Leffler, Djursholm, Sweden. - 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. - Nageswari Shanmugalingam (03-2013).
*Week-long graduate course: Analysis on metric measure spaces*Institute of Pure and Applied Mathematics (UCLA), UCLA, Los Angeles, CA.. - (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. [Link] - (03-2012).
*$\infty$-Poincare inequality on metric measure spaces*University of South Florida, Tampa, FL.. - (10-2011).
*Regularity of quasiminimal surfaces in metric measure spaces*Scuola Normale Superiore, Pisa, Pisa, Italy. - (09-2011).
*Regularity of sets of quasiminimal boundary surfaces*Cornell University, Ithaca, NY. - (08-2011).
*Regularity of sets of quasiminimal boundary surfaces*University of Jyvaskyla, Jyvaskyla, Finland. - (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. - (05-2011).
*Introduction to Newton-Sobolev spaces in the metric setting*Universidad Autonoma de Barcelona, Barcelona, Spain. - (05-2011).
*Sobolev type function spaces for metric measure spaces-a short doctoral course*University of Sevilla, Sevilla, Spain. - (04-2011).
*De Girogi measure and $1$-capacity in metric setting.*University of Helsinki, Helsinki, Finland. - (04-2011).
*Geometric characterization of $\infty$-Poincare inequality*University of Jyvaskyla, Jyvaskyla, Finland. - (03-2011).
*BV functions and planar BV extension domains*Linkoping University, Linkoping, Sweden. - (03-2011).
*BV functions in the metric setting, and De Giorgi measure.*Linkoping University, Linkoping, Sweden. - (02-2011).
*Geometry of $\infty$-Poincare inequality, some counterexamples*Aalto University (TKK), Helsinki, Finland. - (02-2011).
*$\infty$-Poincare inequality and geometry.*University of Helsinki, Helsinki, Finland. - (01-2011).
*Sets of finite perimeter and BV functions in metric measure spaces*Universidad Complutense de Madrid, Madrid, Spain. - (11-2010).
*A two-lecture analysis seminar on $\infty$-Poincare inequality*University of Washington, Seattle, WA. - (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.. - (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.. - (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. [Link] - Nageswari Shanmugalingam (10-2016).
*Analysis on trees.*SIAM Central States Meeting, University of Arkansas, Little Rock., Little Rock, Arkansas.. - Nageswari Shanmugalingam (07-2016).
*Traces and extensions*IMPAN, Warsaw, Poland. - (04-2017).
*Bounded variation in metric spaces*Informal Analysis Meeting, Kent State Univ., held 7--9 April 2017., Kent, OH.. - (06-2017).
*Short course: Analysis based on upper gradients.*10th School on Analysis and Geometry in Metric Spaces, Levico Terme, Italy. - (07-2017).
*Dirichlet problem for least gradients.*Geometric Measure Theory Conference, Warwick University, Coventry, U.K.. - (10-2017).
*Graphs versus metric graphs, and analysis.*SIAM Central States Sectional Meeting, Colorado State University, Fort Collins, CO.. - (09-2017).
*Colloquium-Versions of Dirichlet problem for least gradients*Department of Mathematics, Kansas State University, Manhattan, KS..

### Colloquia

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

### Lectures

- (03-2013).
*Short course (4 lectures) on analysis in metric measure spaces.*long program Interactions Between Analysis and Geometry, at IPAM, UCLA,, UCLA, Los Angeles, CA.

## Honors & Awards

- McMicken Dean's Award for Distinguished Scholarship, 2008.
- Fellow of the Graduate School , 2017.

## Experience & Service

### Post Graduate training and Education

- 08-1999 to 12-1999, Research fellow, Institut Mittag-Leffler,, Djursholm, Sweden.
- 01-2000 to 06-2000, Post-doctoral researcher, National University of Ireland at Maynooth,, Maynooth, Ireland.
- 08-2000 to 04-2002, Post-doc, University of Texas at Austin,, Austin, TX.
- 01-2001 to 04-2001, Visitng Scholar, University of Jyvaskyla,, Jyvaskyla, Finland.

### Events Organized

- Conference. "Modern Aspects of Complex Geometry" conference organizing committee (01-2014 to 05-2015) , University of Cincinnati.
- Workshop. Workshop I: Analysis on Metric Spaces (03/12/2013 to 02/15/2013) , Institute of Pure and Applied Mathematics (UCLA).
- Workshop. Workshop on Quasiconformal mappings and harmonic mappings (08/09/2010 to 08/17/2010) , Chennai, India.

### Service

- Reviewer, PhD dissertation committee of Elefterios Soultanis, University of Helsinki, 01-2016 to 03-2016
- Committee Member, Masters Oral Examination Committee for Ang Li, 01-2016 to 04-2016
- Committee Chair, Taft Foundation Taft Faculty Fellowships Committee, 08-2015 to 03-2016
- 06-2015 to 07-2015
- 05-2015 to 06-2015
- Peer Review/Referee, 01-2015 to 11-2015
- Committee Member, Analysis Preliminary Examination Committee, 01-2015 to 08-2015
- Elected Member, American Association of University Professors (UC) AAUP Associates Council , 01-2015 to 04-2016
- 01-2015 to 05-2015
- Editorial Board Member, Revista Matematica Complutense Editorial Board, 2015 to 2016
- Reviewer, External reader for PhD dissertation, 2015 to 2015
- Committee Member, Analysis Preliminary Examination Committee, 08-2014 to 07-2015
- Committee Member, Departmental Hiring Committee, 08-2014 to 02-2015
- Editorial Board Member, Journal "Revista Matematica Complutense" Editorial Committee, 08-2014 to 07-2015
- Committee Member, Qualifying Examination Committee, 03-2014 to 08-2014
- Committee Chair, "Modern Aspects of Complex Geometry" conference organizing committee, 01-2014 to 05-2015
- Editorial Board Member, Demonstratio Mathematica Editorial Board, 2014 to 2016
- Editorial Board Member, Electronic Journal of Conformal Geometry and Dynamics (AMS journal) Editorial Board, 2014 to 2016
- Committee Member, National Science Foundation Review Panel, 12-2013 to 02-2014
- Editorial Board Member, Electronic Journal of Conformal Geometry and Dynamics (American Mathematical Society journal) Editorial Committee, 08-2013 to 07-2015
- Editorial Board Member, Journal "Demonstratio Mathematica" Editorial Committee, 08-2013 to 07-2015
- Committee Member, Taft Faculty Fellowships Committee, 08-2013 to 04-2015
- Committee Chair, Reappointment, Promotion and Tenure Committee, 08-2013 to 06-2014
- Committee Member, Taft Research Center Taft Faculty Fellowships Committee, 08-2013 to Present
- Committee Member, Qualifying Examination Committee, 08-2013 to Present
- Committee Chair, RPT Committee , 08-2013 to 06-2014
- Review Board/Panel, National Science Foundation 12-2012 to 02-2013
- Reviewer, 08-2012 to 11-2012
- Committee Chair, Graduate Affairs Committee, 08-2012 to 07-2013
- Mentor, 08-2012 to Present
- Committee Member, Qualifying Examination Committee, 07-2012 to 07-2013
- Committee Member, Complex Analysis Preliminary Exam committee, 07-2012 to 10-2012
- Mentor, 06-2012 to 12-2012
- Reviewer, Dissertation committee (Renjin Jiang), 01-2012 to 02-2012
- Board Member, Conformal Geometry and Dynamics Editorial Board, 01-2012 to 01-2014
- Member, Demonstratio Mathematica Editorial Board, 11-2011
- Committee Member, Graduate Student Evaluation Committee, 09-2011 to 08-2012
- Editorial Board Member, International Journal of Mathematics and Mathematical Sciences Editorial board, 09-2011
- Committee Member, Reappointment, Promotion, and Tenure committee (RPT committee), 09-2011 to 06-2013
- Committee Member, Taft Research Center Conference Committee, 09-2011 to 06-2013
- Committee Member, Hiring Committee, 09-2011 to 04-2012
- Mentor, Academic advisor 09-2011 to 06-2012
- Committee Member, Topology preliminary examination committee, 08-2011 to 06-2012
- Committee Member, Taft Research Center Taft Steering Committee, 06-2011 to 08-2012
- Peer Review/Referee, Proceedings of the American Mathematical Society 03-2011
- Committee Member, Universidad Complutense de Madrid, Spain Dissertation defense committee (for Estibalitz Durand-Cartagena), 01-2011 to 02-2011
- Reviewer, Computers and Mathematics with Applications (journal) 2011
- Committee Member, PhD Dissertation committee for Poranee Kongkha-Julian, 09-2010 to 11-2012
- Committee Member, American Mathematical Society (AMS) Organizing special session on Geometric Analysis, 03-2010
- Committee Chair, Departmental Colloquium Chair, 09-2009 to 06-2010
- Committee Chair, Departmental Colloquium Chair, 09-2009 to 06-2010
- Committee Chair, Topology Preliminary Examination Committee, 08-2009 to 08-2010
- Committee Chair, Taft Research Center Taft Student Awards Committee, 08-2009 to 08-2010
- Committee Member, International Congress of Mathematicians Satellite Workshop and conference on harmonic and conformal mappings, organizing committee, 08-2009 to 08-2010
- Committee Member, Hiring Committee, 12-2008 to 03-2009
- Review Board/Panel, NSF Geometric Function Theory panel, 11-2008 to 02-2009
- Committee Member, American Mathematical Society (AMS) Book and journal donation program committee, 09-2008 to 09-2010
- Committee Member, Taft Research Center Taft Student Awards Committee, 08-2008 to 08-2009
- Peer Review/Referee, Mathematica Scandinavica
- Peer Review/Referee, Journal of Functional Analysis
- Committee Member, National Science Foundation NSF Review Panel, 2016

### Other Experience and Professional Memberships

- 1999 to 2016 ,Member, American Mathematical Society

### Courses Taught

- Geometric Function Theory

Geometric Function Theory*Level:*Graduate*Term:*16SS - Complex Analysis

Complex Analysis*Level:*Graduate*Term:*15SS*Comments:*Prelim Exam course - -MATH-2063 MULTIVARIABLE CALC
*Level:*Undergraduate*Term:*15FS - Topology

Topology*Level:*Graduate*Term:*15FS - -MATH-2063 MULTIVARIABLE CALC
*Level:*Undergraduate*Term:*15FS - Topology

Topology*Level:*Graduate*Term:*15FS - -MATH-2076 LINEAR ALGEBRA
*Level:*Undergraduate*Term:*14SS - Complex Analysis

Complex Analysis*Level:*Graduate*Term:*14SS*Comments:*Taught this course as a part-reading, part lecture course, as an overload of my teaching (1 credit towards workload) - Real Analysis

Real Analysis*Level:*Graduate*Term:*14FS*Comments:*Prelim exam course - -MATH-2063 MULTIVARIABLE CALC
*Level:*Undergraduate*Term:*14FS - Geometric Analysis.

Geometric Analysis.*Level:*Graduate*Term:*13SS - 15-MATH-505 ADVANCED CALCULUS
*Level:*Both*Term:*12W - 15-MATH-252 CALCULUS II
*Term:*12W - 15-MATH-506 ADVANCED CALCULUS
*Level:*Both*Term:*12S - 15-MATH-273 DIFFERENTIAL EQNS
*Level:*Undergraduate*Term:*12S - Calculus I

Calculus I*Level:*Undergraduate*Term:*12FS - Introduction to Complex Analysis

Introduction to Complex Analysis*Level:*Both*Term:*12FS - 15-MATH-504 ADVANCED CALCULUC
*Level:*Both*Term:*11A

[Link] - 15-MATH-252 CALCULUS II
*Level:*Undergraduate*Term:*10W - Abstract Algebra

Abstract Algebra*Level:*Both*Term:*10W - 15-MATH-513 ABSTRACT ALGEBRA
*Level:*Both*Term:*10S - 15-MATH-253 CALCULUS III
*Level:*Undergraduate*Term:*10S - 15-MATH-251 CALCULUS I
*Level:*Undergraduate*Term:*09A - 15-MATH-511 ABSTRACT ALGEBRA
*Level:*Both*Term:*09A

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