## Open Positions |

View Opportunities |

# People in the Department

< Back to list

# David * Minda

Title: Charles Phelps Taft Professor

Office: 4103 French Hall

Tel: 513-556-4079

Email: david.minda@uc.edu

## 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 Information

### Research 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.

### Research Support

- (Co-PI), PI (H. Jackson) and several co-PIs including D. Minda,
*A Coherent Multi-disciplinary Initiative to Enhance Student Learning in STEM Courses*, NSF STEM grant DUE - CCLI-Phase 2. $250,000. 09-2010 to 09-2013. Status: Active. - (Collaborator), Ault, Bruce; Cameron, Guy; Huff, Warren; Jackson, Howard; Minda, Carl,
*A Coherent Cross-Disciplinary Learning Initiative in STEM*, National Science Foundation. (DUE-1022563), $249,648.00. 08/15/2010 to 07/31/2014. Status: Completed. - (Collaborator), Cameron, Guy; Escoe, Gisela; Gaffney, James; Keener, Timothy; Kukreti, Anant; Minda, Carl; Montrose, Marshall,
*Master Degrees as Conduits to Recruiting, Retaining and Upgrading Ohio's STEM Workforce*, Ohio Board of Regents. (OBR COF 09-07), $670,500.00. 07/01/2009 to 06/30/2014. Status: Completed. - (PI), Minda, Carl,
*Park City Mathematics Institute: Cincinnati Public Schools*, National Science Foundation. (IAS-EHR-0314808), $645,399.00. 09/01/2003 to 08/31/2005. Status: Closed. - Groetsch,
*National Science Foundation Education Grant*, Institute for Advanced Study, University of Cincinnati for Math and Science Partnership with Cincinnati Public Schools. 600,000. 2003 to 2006. - (PI), Minda, Carl,
*Geometry for Middle School Teachers Including Coordinates and Transformations*, Department of Education. (OSP01159), $9,000.00. 06/15/2001 to 09/15/2001. Status: Closed. - Groetsch,
*OBR Eisenhower grant*. 1998 to 1999. - Groetsch,
*National Science Foundation Education Grant*, University of Cincinnati (Park City Mathematics Institute). 1997 to 2003. *National Science Foundation Research Grant*, University of Cincinnati. 1986 to 1996.*National Science Foundation Research Grant*, University of Cincinnati. 1982 to 1983.*National Science Foundation Research Grant*, University of Cincinnati. 1978 to 1979.*National Science Foundation Research Grant*, University of Cincinnati. 1973 to 1975.*National Science Foundation Research Grant*, University of Minnesota. 1971.*Graduate Fellow*, NSF. 1967 to 1969.*Cooperative Graduate Fellow*, NSF. 1965 to 1967.*Travel Grant to attend ICM-90 in Kyoto, Japan*, AMS-NSF.*Travel Grant to attend ICM-94 in Zurich, Switzerland*, AMS-NSF .*Travel Grant to attend ICM-98 in Berlin, Germany*, AMS-NSF .- (Collaborator), Ault, Bruce; Cameron, Guy; Huff, Warren; Jackson, Howard; Minda, Carl,
*A Coherent Cross-Disciplinary Learning Initiative in STEM*, National Science Foundation. (DUE-1022563), $249,648.00. 08/15/2010 to 07/31/2014. Status: Closed.

## 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.

### 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.

### Electronic Journal

- Area, capacity and diameter versions of Schwarz&39;s Lemma (with Burckel, Marshall, Poggi-Corradini and Ransford), Conform. Geom. Dyn. 12(2008), 133--152.

## Presentations & Lectures

### Invited Presentations

- D. Minda (09/16/2013).
*Normal families - a conformal geometric approach*Technische Universitat Bergakademie Freiberg, Freiberg, Germany. - David Minda (06/03/2012).
*Conformal Geometry and Related Fields*Summer 2012 meeting of the Canadian Mathematical Society, Regina, Saskatchewan, canada. - David Minda (05-2010).
*Holomorphic functions with bounded Schwarzian norm*Conference on Complex Analysis, University of Illinois at Urbana-Champaign. - 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. - David Minda (10/17/2009).
*Polygons, ellipses and polynomials*1051st meeting of AMS, Baylor University, Waco. - David Minda (08-2009).
*Hyperbolic distortion for holomorphic maps of regions*12th Romanian-Finnish Seminar, University of Turku, Turku, Finland. - David Minda (03/28/2009).
*The hyperbolic metric and real affine mappings*1047th meeting of AMS, University of Illinois Urbana-Champaign. - 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. - 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. - 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. - David Minda (05-2007).
*"Geometric variations of Schwarz's Lemma"*CMS-MITACS Joint Conference 2007, Winnepeg, Manitoba, Canada. - David Minda (01-2006).
*"Holomorphic self-maps and Euclidean contractions"*International Conference on Geometric Function Theory, Special Functions and Applications, Pondicherry, India. - 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. - 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. - (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. - 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. - D. Minda (07/24/2001).
*"Holomorphic self-maps of a plane region''*Japan-Korea Joint Workshop in Mathematics 2001, Yamaguchi University, Yamaguchi,. - D. Minda (08/16/2000).
*"Hyperbolic geometry and complex analysis,''*Congreso Nacional de Matematicas 2000, Bogota, Colombia. - 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. - David Minda (04/11/2014).
*Rescaling non-Lipschitz families of analytic functions.*1100th meeting of Amer. Math. Soc., Texas Tech University, Lubbock, TX. - David Minda (06/08/2014).
*Rescaling non-uniformly Lipschitz sequences*Summer Meeting 2014 of the Canadian Mathematical Society, Winnipeg, Manitoba, Canada. - 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.

### Colloquia

- D. Minda (09/25/2013).
*Conformal automorphisms of plane regions.*Universitat Wuerzburg, Wuerzburg, Germany. - D. Minda (03/12/2013).
*Hyperbolic geometry and conformal images.*African Institute for Mathematical Sciences, Muizenberg, South Africa. - D Minda (03/18/2011).
*Conformal automorphisms of plane regions.*University of the Witwatersrand, Johannesburg, South Africa. - D. Minda (03/17/2011).
*The three classical geometries with constant curvature .*University of the Witwatersrand, Johannesburg, South Africa. - David Minda (02/22/2011).
*Geometry and curvature.*African Institute for Mathematical Sciences, Muizenberg, South Africa. - David Minda (12-2009).
*Automorphisms of plane regions.*Sri Jayendra Saraswathi Swamiji Viswa Mahavidyalaya University, Kanchipuram, India. - D. Minda (04/29/2009).
*Conformal automorphisms of plane regions.*University of Manitoba, Winnipeg, Manitoba, Canada. - (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. - (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 & Awards

- AIMS Research Fellowship for Visiting Researchers, African Institute for Mathematical Sciences,, 01/08/2013 to 04/08/2013. 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).
- AIMS Research Fellowship for Visiting Researchers, African Institute of Mathematical Sciences, 01/01/2011 to 04/01/2011. 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).
- U.C. Honors Program Teacher of the Year 2002, UC Honors program, 09-2001 to 06-2003.
- Charles Phelps Taft Professor of Mathematics, Taft Foundation, 06-1999.
- Fellow of the Graduate School, Graduate Fellows at UC, 06-1994.
- Dolly Cohen Award for Excellence in Teaching, UC .
- 2002 Ohio Section MAA Award for Distinguished College or University Teaching of Mathematics, Ohio section of MAA.
- McMicken Dean's Award for Distinguished Scholarship, 1997.

## Experience & Service

### Work Experience

- 01/08/2013 to 04/07/2013, Visiting Researcher, African Institute for Mathematical Sciences, Muizenberg, South Africa.
- 01/05/2011 to 04/05/2011, Visiting Researcher, African Institute for Mathematical Sciences, Muizenberg, South Africa.
- 11-2004 to 04-2005, Visiting Scholar , University of Cambridge, Cambridge, England.
- 01-2000 to 04-2000, Visiting Scholar , University of Cambridge, Cambridge, England.
- 02-1997 to 04-1997, Research Visitor, University of Tennessee, Knoxville, Knoxville, TN.
- 09-1988 to 12-1988, Visiting Professor of Mathematics, University of California, San Diego, San Diego, CA.
- 03-1983 to 07-1983, Visiting Professor of Mathematics, University of California, San Diego, San Diego, CA.
- 09-1980 to 12-1980, Visiting Associate Professor of Mathematics, University of California, San Diego, San Diego, CA.

### Post Graduate training and Education

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

### Other Experience and Professional Memberships

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

### Courses Taught

- Probability and Statistical Inference

Probability and Statistical Inference*Level:*Graduate*Term:*13SS*Comments:*The emphasis of this course is on the probability and statistics needed by secondary math teachers. Steve Pelikan and I each taught half of the course. He prepared the notes for the course and I supplemented them with additional material. - Algebra & Number Theory II

Algebra & Number Theory II*Level:*Graduate*Term:*13SS*Comments:*This course focusses on polynomials over rings and emphasizes analogies with number theory. Steve Pelikan prepared the notes and I wrote up some supplementary material. - Technology for Statistics

Technology for Statistics*Level:*Graduate*Term:*13SS*Comments:*The course uses GeoGebra to explore data and distributions. It is project-oriented with cooperative learning. Steve Peikan and I shared instruction. - MAT Project

MAT Project*Level:*Graduate*Term:*13SS*Comments:*Steve Pelikan and I share the work of advising MAT students about the preparation and presentation of their MAT projects. - INTRO GEOMETRIES II

INTRO GEOMETRIES II*Level:*Undergraduate*Term:*12W*Comments:*I have prepared extensive printed notes that I distribute free to the students in place of a textbook. Each time I teach the course I modify the notes. In Winter I added about 30 pages to the notes. In addition, I assign and grade 2 homework problems (all proofs) at each class meeting (M,W,F). This gives the course an extensive writing component. This writing component is especially important for the students who intend to become secondary math teachers, the majority of the class. In addition, I have included possible classroom activities in the notes for these prospective teachers. Only a few UC math classes have such a strong connection with the preparation of teachers. - 15-MATH-252 CALCULUS II
*Level:*Undergraduate*Term:*12W*Comments:*Sections 031 and 032 were combined in one room for 3 one-hour lectures and then met separately for 1-hour recitations in groups of size 23. I prepared recitation worksheets and the TA helped the students do the worksheets in groups. - 15-MATH-256 CALC II LAB
*Level:*Undergraduate*Term:*12W*Comments:*Weekly Mathematica projects were assigned. Students were expected to complete the work outside of class. Assistance was available during office hours. - TECH FOR CALC

TECH FOR CALC*Level:*Graduate*Term:*12U*Comments:*I prepared 10 GeoGebra worksheets for the half of the course that I taught. The goal was to help the in-service teachers learn GeoGebra and reinforce the material that the teachers were learning in their other MAT courses. - 15-MATH-798 M A T PROJECT I
*Level:*Graduate*Term:*12U*Comments:*Steve Pelikan and I shared the work in advising and guiding MAT students in the preparation of their MAT projects. The MAT project serves the roll of a master's thesis in the MAT program. - 15-MATH-799 M A T PROJECT II
*Level:*Graduate*Term:*12U*Comments:*Steve Pelikan and I shared the work in advising and guiding MAT students in the preparation of their MAT projects. The MAT project serves the roll of a master's thesis in the MAT program. - MATH MODELS

MATH MODELS*Level:*Graduate*Term:*12U*Comments:*The primary emphasis of this course is elementary applications of calculus to physics. Steve Pelikan and I each taught half of the course. He prepared most of the notes for this course, but I supplemented them with additional material - ANALYSIS I

ANALYSIS I*Level:*Graduate*Term:*12S*Comments:*Over the years I have prepared class notes for Analysis I, so a textbook is not needed. In the summer of 2012, I revised the notes and added over 30 pages of new material - 15-MATH-253 CALCULUS III
*Level:*Undergraduate*Term:*12S*Comments:*Sections 031 and 032 were combined into 3 one-hour lectures and then met separately in groups of 22 for 2 one-hour recitations. I prepared worksheets for the recitations. - 15-MATH-257 CALC III LAB
*Level:*Undergraduate*Term:*12S*Comments:*Weekly Mathematica projects were available. - Geometric Function Theory

Geometric Function Theory*Level:*Graduate*Term:*14SS - Introduction to Complex Analysis

Introduction to Complex Analysis*Level:*Both*Term:*14FS - Technology for Geometry

Technology for Geometry*Level:*Graduate*Term:*14US*Comments:*The course emphasized the use of GeoGebra in geometry; team taught with Professor Pelikan - Linear Algebra For Geometry

Linear Algebra For Geometry*Level:*Graduate*Term:*14US*Comments:*taught half of the house; Professor Pelikan taught the other half - Geometry 2

Geometry 2*Level:*Graduate - Geometry 2

Geometry 2*Level:*Graduate*Term:*14US

## Update Personal Profile |

eProfessional |