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Nageswari Shanmugalingam

Title: Professor
Office: 5428F French Hall
Tel: 513-556-4062
Email: shanmun@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://math.uc.edu/~nages/.

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), $185,525.00. 07/01/2015 to 06/30/2018. Status: Active.
  • (PI), Potential Theory of Functions of Bounded Variation and Quasiconformal Maps, National Science Foundation. (DMS 1500440 ), 75,707 (1st year. Total over 3 years: $230,000). 07-2015 to 06-2018. 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.

Publications

Peer Reviewed Publications

Peer Reviewed Conference/Workshop Proceedings

Books

Conference/Workshop Proceedings

In Press

Invited Publication

Under Review

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.

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.

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