# David * Minda

## Emeritus

## Charles Phelps Taft Professor

### French Hall

4103

A&S Math Scs Emeriti - 0025

## Education

PhD: University of California San Diego San Diego, CA, 1970 (Mathematics; complex analysis)

MS: University of Cincinnati Cincinnati, OH, 1966 (Mathematics, complex analysis)

BS: University of Cincinnati Cincinnati, OH, 1965 (Mathematics)

## Research and Practice Interests

My research interests lie within complex analysis, broadly interpreted. In the past quater century my work has focused on the role of conformal metrics, especially the hyperbolic metric, within complex analysis. Roughly speaking, the idea is to obtain a conformal geometric understanding of classical parts of complex analysis, and then use this new geometric insight to generalize the classical results to new contexts. Many classical results are conformal and two-dimensional; as such they do not readily extend to other contexts. On the other hand, a geometric formulation frequently does extend.

## Positions and Work Experience

01-08-2013 -04-07-2013 Visiting Researcher, African Institute for Mathematical Sciences, Muizenberg, South Africa

01-05-2011 -04-05-2011 Visiting Researcher, African Institute for Mathematical Sciences, Muizenberg, South Africa

11-2004 -04-2005 Visiting Scholar , University of Cambridge, Cambridge, England

01-2000 -04-2000 Visiting Scholar , University of Cambridge, Cambridge, England

02-1997 -04-1997 Research Visitor, University of Tennessee, Knoxville, Knoxville, TN

09-1988 -12-1988 Visiting Professor of Mathematics, University of California, San Diego, San Diego, CA

03-1983 -07-1983 Visiting Professor of Mathematics, University of California, San Diego, San Diego, CA

09-1980 -12-1980 Visiting Associate Professor of Mathematics, University of California, San Diego, San Diego, CA

## Research Support

Investigators:PI (H. Jackson) and several co-PIs including D. Minda 09-2010 -09-2013 NSF STEM grant DUE - CCLI-Phase 2 A Coherent Multi-disciplinary Initiative to Enhance Student Learning in STEM Courses Role:Co-PI $250,000 Active Type:Grant

Grant: #DUE-1022563 Investigators:Ault, Bruce; Cameron, Guy; Huff, Warren; Jackson, Howard; Minda, Carl 08-15-2010 -07-31-2014 National Science Foundation A Coherent Cross-Disciplinary Learning Initiative in STEM Role:Collaborator $249,648.00 Completed

Grant: #OBR COF 09-07 Investigators:Cameron, Guy; Escoe, Gisela; Gaffney, James; Keener, Timothy; Kukreti, Anant; Minda, Carl; Montrose, Marshall 07-01-2009 -06-30-2014 Ohio Board of Regents Master Degrees as Conduits to Recruiting, Retaining and Upgrading Ohio's STEM Workforce Role:Collaborator $670,500.00 Completed

Grant: #IAS-EHR-0314808 Investigators:Minda, Carl 09-01-2003 -08-31-2005 National Science Foundation Park City Mathematics Institute: Cincinnati Public Schools Role:PI $645,399.00 Closed Level:Federal

Investigators:Groetsch 2003 -2006 Institute for Advanced Study, University of Cincinnati for Math and Science Partnership with Cincinnati Public Schools National Science Foundation Education Grant 600,000 Type:Grant

Grant: #OSP01159 Investigators:Minda, Carl 06-15-2001 -09-15-2001 Department of Education Geometry for Middle School Teachers Including Coordinates and Transformations Role:PI $9,000.00 Closed Level:Federal

Investigators:Groetsch 1998 -1999 OBR Eisenhower grant Type:Grant

Investigators:Groetsch 1997 -2003 University of Cincinnati (Park City Mathematics Institute) National Science Foundation Education Grant Type:Grant

1986 -1996 University of Cincinnati National Science Foundation Research Grant Type:Grant

1982 -1983 University of Cincinnati National Science Foundation Research Grant Type:Grant

1978 -1979 University of Cincinnati National Science Foundation Research Grant Type:Grant

1973 -1975 University of Cincinnati National Science Foundation Research Grant Type:Grant

1971 University of Minnesota National Science Foundation Research Grant Type:Grant

1967 -1969 NSF Graduate Fellow Type:Fellowship

1965 -1967 NSF Cooperative Graduate Fellow Type:Fellowship

AMS-NSF Travel Grant to attend ICM-90 in Kyoto, Japan Type:Grant

AMS-NSF Travel Grant to attend ICM-94 in Zurich, Switzerland

AMS-NSF Travel Grant to attend ICM-98 in Berlin, Germany

Grant: #DUE-1022563 Investigators:Ault, Bruce; Cameron, Guy; Huff, Warren; Jackson, Howard; Minda, Carl 08-15-2010 -07-31-2014 National Science Foundation A Coherent Cross-Disciplinary Learning Initiative in STEM Role:Collaborator $249,648.00 Closed Level:Federal

## Abbreviated Publications

### Peer Reviewed Publications

Normal families: a geometric perspective (with A.F. Beardon), Comput. Methods Funct. Theory, Gehring Memorial Volume, (2014), 331-355.

The hyperbolic metric and uniformly perfect regions (with W. Ma), J. of Analysis., 20 (2012), 59-70.

Bounded Schwarzian and two-point distortion (with W. Ma and D. Mejia), Comput. Methods Funct. Theory, 13 (2013), 705-715.

Two-point distortion for Nehari functions (with W. Ma and D. Mejia), Complex Anal. Oper. Theory, 8 (2014), 213-225.

Schwarzian norm and two-point distortion (with M. Chuaqui, P. Duren, W. Ma, D. Mejia and B. Osgood), Pacific J. Math., 254 (2011), 101-116.

The divergence of two hyperbolic geodesics (with A.F. Beardon), Comput. Methods Funct. Theory, 12 (2012), 101-104.

Conformal images and the angle of parallelism (with A.F. Beardon), Comput. Methods Funct. Theory, 12 (2012), 87-100.

Convex sets of constant width and constant diameter (with P. Hasto and Z. Ibragimov), Houston J. Math., 38 (2012), 421-443.

Hyperbolic distortion for holomorphic maps, J. Analysis, 18 (2010), 317--336.

The diameter of a hyperbolic disc (with A.F. Beardon), Proceedings of the12th Romanian-Finnish Seminar (Turku), Complex Analysis and Operator Theory, 5 (2011), 881-887.

Large deviations for the leaves in some random trees (with W. Bryc and S. Sethuraman), Appl. Probab. 41 (2009), 845--873.

Geodesics and curvature of Mobius invariant metrics (with D. Herron and Z. Ibragimov), Rocky Mountain J. Math., 38(2008), 891--921.

Dieudonne points of holomorphic self{maps of regions (with A.F. Beardon), Comput. Methods Funct. Theory, 8(2008), 409-432.

Mobius invariant metrics which are bilipschitz equivalent to the hyperbolic metric (with D. Herron and W. Ma), Conform. Geom. Dyn. 12(2008), 67-96.

Conformal automorphisms of finitely connected plane regions (with A.F. Beardon), Transcendental Dynamics and Complex Analysis, ed. by P. J. Rippon and G. M. Stallard, London Math. Soc. Lecture Note Series, no. 368, 2008, pp. 37-73.

Triangles, ellipses and cubic polynomials (with S. Phelps), Amer. Math. Monthly, 115(2008), 679--689.

Isometries of some hyperbolic-type path metrics, and the hyperbolic medial axis (with P. Hasto, Z. Ibragimov, S. Ponnusamy and S.K. Sahoo), In the Tradition of Ahlfors-Bers, IV, Contemporary Math., 432(2007), 63-74.

Euclidean properties of hyperbolic coordinates (with W. Ma), Comput. Methods Funct. Theory, 6(2006), 223-242.

Estimates for conformal metric ratios (with D. Herron and W. Ma), Comput. Methods Funct. Theory, 5(2005), 323-345.

Hyperbolically 1-convex functions (with W. Ma and D. Mejia), Ann. Polon. Math., 84(2004), 185-202.

Random iteration of analytic functions (with A.F. Beardon, T.K. Carne and T.W. Ng), Ergod. Th. & Dynam. Sys., 24(2004), 659--675.

Two-point distortion theorems for hyperbolically convex functions (with W. Ma and D. Mejia), Rev. Roumaine Math. Pures Appl., 49(2004), 461-479.

A multi-point Schwarz-Pick lemma (with A.F. Beardon), J. Analyse Math., 92(2004), 81-104.

The three derivatives of z^2 (with A.F. Beardon), Journal of Analysis, accepted for publication 12/29/14.

Domain constants and quasiconformal maps (with W. Ma), Journal of Analysis, submitted, 13 pages.

The Hurwitz metric, Complex Anal. Oper. Theory, submitted, 12 pages.

Harmonic quasiconformal maps and the hyperbolic metric (with W. Ma), Journal of Analysis, submitted, 15 pages.

### Electronic Journal

Area, capacity and diameter versions of Schwarz's Lemma (with Burckel, Marshall, Poggi-Corradini and Ransford), Conform. Geom. Dyn. 12(2008), 133--152.

### Book Chapter

The hyperbolic metric and geometric function theory (with A.F. Beardon), Quasiconformal Mappings and their Applications, ed. by S. Ponnusamy, T. Sugawa and M. Vuorinen, Narosa Publishing House, New Delhi, 2007, 9-56.

Geometric properties of hyperbolic geodesics (with W. Ma), Quasiconformal Mappings and their Applications, ed. by S. Ponnusamy, T. Sugawa and M. Vuorinen, Narosa Publishing House, New Delhi, 2007, 165-187.

## Presentations

### Invited Presentations

D. Minda
(09-16-2013. )
(In Progress. )
*Normal families - a conformal geometric approach *.Technische Universitat Bergakademie Freiberg, Freiberg, Germany. Workshop. .
Level:International

David Minda
(06-03-2012. )
*Conformal Geometry and Related Fields *.Summer 2012 meeting of the Canadian Mathematical Society, Regina, Saskatchewan, canada. Professional Meeting. .
Level:International

David Minda
(05-2010. )
*Holomorphic functions with bounded Schwarzian norm *.Conference on Complex Analysis, University of Illinois at Urbana-Champaign.
Level:International

David Minda
(12-2009. )
*Short course on ``Conformal metrics in complex analysis'' consisting of four one-hour lectures *.International Workshop on Harmonic Mappings and Hyperbolic Metrics, Indian Institute of Technology Madras, Chennai, India.
Level:International

David Minda
(10-17-2009. )
*Polygons, ellipses and polynomials *.1051st meeting of AMS, Baylor University, Waco.
Level:Regional

David Minda
(08-2009. )
*Hyperbolic distortion for holomorphic maps of regions *.12th Romanian-Finnish Seminar, University of Turku, Turku, Finland.
Level:International

David Minda
(03-28-2009. )
*The hyperbolic metric and real affine mappings *.1047th meeting of AMS, University of Illinois Urbana-Champaign.
Level:Regional

David Minda
(02-2009. )
*A short course consisting of three lectures on "Revitalizing the Teaching of Geometry From High Schools Through Universities'' *.Seminario: Un acercamiento entre las Matematicas del colegio y las Matematicas de la Universidad, Medellin, Colombia.
Level:International

D. Minda
(11-01-2007. )
*"Hyperbolic distortion for holomorphic maps of plane regions'' *.Conformal Mapping, Circle Packing and Applications, 7th Annual Red Raider Mini--Symposium, exas Tech University, Lubbock, TX.
Level:National

David Minda
(07-2007. )
*Two semi-plenary lectures, "Conformal automorphisms of plane regions" and "Teaching geometry for pre-service math teachers" *.XVI Congreso Nacional de Matematicas, Medellin, Colombia.
Level:International

David Minda
(05-2007. )
*"Geometric variations of Schwarz's Lemma" *.CMS-MITACS Joint Conference 2007, Winnepeg, Manitoba, Canada.
Level:International

David Minda
(01-2006. )
*"Holomorphic self-maps and Euclidean contractions" *.International Conference on Geometric Function Theory, Special Functions and Applications, Pondicherry, India.
Level:International

David Minda
(12-2005. )
*Presented three one-hour lectures, "The hyperbolic metric and geometric function theory" *.International Workshop on Quasiconformal Mappings and Their Applications, Indian Institute of Technology Madras, Chennai, India.
Level:International

D. Minda
(10-17-2003. )
*Some geometric gems via Mobius transformations *.Fall Meeting of the Ohio Section of the MAA, Ohio Northern University, Ada, OH. Professional Meeting. .
Level:State

(05-2003. )
*A Mobius invariant metric, Conformal Geometry of Surfaces: Theory, Computation and Application *.Townsend, Tennessee.

D. Minda
(10-08-2002. )
*``Mobius invariant metrics'' *.Complex Analysis Conference, Kyoto Institute of Technology, Japan.
Level:International

D. Minda
(08-01-2002. )
*"Mobius invariant metrics - a survey'' *.10th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Silla University, Pusan, South Korea.
Level:International

D. Minda
(07-24-2001. )
*"Holomorphic self-maps of a plane region'' *.Japan-Korea Joint Workshop in Mathematics 2001, Yamaguchi University, Yamaguchi,.
Level:International

D. Minda
(08-16-2000. )
*"Hyperbolic geometry and complex analysis,'' *.Congreso Nacional de Matematicas 2000, Bogota, Colombia.
Level:International

D. Minda
(08-15-2000. )
*``Consequences of negative curvature in complex analysis'' and "Self-maps of a hyperbolic region.'' *.Simposo de Variable Compleja y Funciones Especiales, Escuela, Colombiana de Ingenieria, Bogota, Colombia.
Level:International

David Minda
(04-11-2014. )
*Rescaling non-Lipschitz families of analytic functions. *1100th meeting of Amer. Math. Soc., Texas Tech University, Lubbock, TX. Professional Meeting. .
Level:Regional

David Minda
(06-08-2014. )
*Rescaling non-uniformly Lipschitz sequences *.Summer Meeting 2014 of the Canadian Mathematical Society, Winnipeg, Manitoba, Canada. Professional Meeting. .
Level:International

David Minda
(11-07-2014. )
*Is it geometric function theory or conformal geometry? *.Complex Analysis, Potential Theory, Special Functions & Applications, Honoring the Retirement of Roger W. Barnard, Texas Tech University, Lubbock, TX. Conference. .
Level:International

### Colloquium

D. Minda
(09-25-2013).
*Conformal automorphisms of plane regions *. Universitat Wuerzburg, Wuerzburg, Germany. Other Institution.
Level:International

D. Minda
(03-12-2013).
*Hyperbolic geometry and conformal images *. African Institute for Mathematical Sciences, Muizenberg, South Africa. Other Institution.
Level:International

D Minda
(03-18-2011).
*Conformal automorphisms of plane regions *. University of the Witwatersrand, Johannesburg, South Africa. Other Institution.
Level:University

D. Minda
(03-17-2011).
*The three classical geometries with constant curvature *. University of the Witwatersrand, Johannesburg, South Africa. Other Institution.
Level:University

David Minda
(02-22-2011).
*Geometry and curvature *. African Institute for Mathematical Sciences, Muizenberg, South Africa.
Level:University

David Minda
(12-2009).
*Automorphisms of plane regions *. Sri Jayendra Saraswathi Swamiji Viswa Mahavidyalaya University, Kanchipuram, India.
Level:University

D. Minda
(04-29-2009).
*Conformal automorphisms of plane regions *. University of Manitoba, Winnipeg, Manitoba, Canada. Other Institution.
Level:University

(09-08-2005).
*Mobius automorphisms of circular regions *. San Diego State University, San Diego, CA.

(03-02-2005).
*Conformal automorphisms of finitely connected plane regions *. York University, York, England.

(02-16-2005).
*Variations on Dieudonne’s Lemma *. University of Cambridge, England.

D. Minda
(12-17-2003).
*Solving Euclidean problems with inversive geometry *. San Diego State University, San Diego, CA. Other Institution.
Level:University

(02-25-2000).
*Hyperbolic coordinates in convex regions *. Imperial College of Science and Technology, London, England.

(02-2000).
*Polarization and the hyperbolic metric *. University of Cambridge, England.

## Honors and Awards

01-08-2013 -04-08-2013 AIMS Research Fellowship for Visiting Researchers This fellowship paid for my round-trip airfare, Cincinnati - Cape Town, South Africa, and helped defray lodging expenses in Muizenberg, South Africa while conducting research at AIMS (African Institute for Mathematical Sciences) African Institute for Mathematical Sciences, Status:Recipient Level:International Type:Fellowship

01-01-2011 -04-01-2011 AIMS Research Fellowship for Visiting Researchers This fellowship paid for my round-trip airfare, Cincinnati - Cape Town, South Africa, and helped defray lodging expenses in Muizenberg, South Africa while conducting research at AIMS (African Institute for Mathematical Sciences) African Institute of Mathematical Sciences Status:Recipient Level:International Type:Fellowship

09-2001 -06-2003 U.C. Honors Program Teacher of the Year 2002 UC Honors program Status:Recipient Level:University Type:Recognition

06-1999 Charles Phelps Taft Professor of Mathematics Taft Foundation Status:Recipient Level:College Type:Recognition

06-1994 Fellow of the Graduate School Graduate Fellows at UC Status:Recipient Level:University Type:Recognition

Dolly Cohen Award for Excellence in Teaching UC Status:Recipient Level:University Type:Monetary

2002 Ohio Section MAA Award for Distinguished College or University Teaching of Mathematics Ohio section of MAA Status:Recipient Level:State Type:Recognition

McMicken Dean's Award for Distinguished Scholarship, 1997 Status:Recipient Level:College Type:Recognition

## Post Graduate Training and Education

09-1970-08-1971 Postoc in Mathematics, University of Minnesota, , Minneapolis, MN

## Professional Affiliation

01-09-2013: Executive Editor Complex Analysis and its Synergies Springer Verlag, New York

## Courses Taught

Probability and Statistical Inference Level:Graduate

Algebra & Number Theory II Level:Graduate

Technology for Statistics Level:Graduate

MAT Project Level:Graduate

INTRO GEOMETRIES II Level:Undergraduate

15-MATH-252 CALCULUS II Level:Undergraduate

15-MATH-256 CALC II LAB Level:Undergraduate

TECH FOR CALC Level:Graduate

15-MATH-798 M A T PROJECT I Level:Graduate

15-MATH-799 M A T PROJECT II Level:Graduate

MATH MODELS Level:Graduate

ANALYSIS I Level:Graduate

15-MATH-253 CALCULUS III Level:Undergraduate

15-MATH-257 CALC III LAB Level:Undergraduate

Geometric Function Theory Level:Graduate

Introduction to Complex Analysis Level:Both

Technology for Geometry Level:Graduate

Linear Algebra For Geometry Level:Graduate

Geometry 2 Level:Graduate

Geometry 2 Level:Graduate