# Talks given

**Papers presented/invited/seminars/invited talks:**

(Note: B.T.M.C.= British Theoretical Mechanics Colloquium)

- "Magnetoacoustic‑gravity waves in the presence of a horizontal magnetic field". 1973, Symposium on Solar Physics, University College London.

- "Wave propagation problems in solar physics" 1974, University of Sussex, Department of Astronomy.

- "Asymptotic solutions of a magnetoatmospheric wave equation" 1975, University of St.Andrews, Dept. of Applied Mathematics.

- "Some results in magnetoatmospheric stability theory", March 1977, University of Hull(B T.M.C.).

- "Magnetohydrodynamic wave energy flux" April 1977, Symposium, University of Edinburgh.

6/7 "Shear instabilities in chromospheric flow systems" and "Magnetoatmospheric wave heating of a chromospheric plasma", September 1977, Royal Society meeting (London) on Solar Physics .

- "The space‑time evolution of resonant wave triads ‑ the pump wave approximation" April1978, University of Sheffield (B.T.M.C.)

- "Mathematical theory of Alfven wave reflection" May 1978, New University of Ulster: Irish Astronomical Society Meeting.

- "Asymptotic solutions of astrophysical wave equations" 1978, University College Dublin,Dept. of Mathematical Physics.

- "Wave reflection and stability in astrophysics", 1979, Dept. Applied Mathematics, Queen'sUniversity, Belfast.

- "On the nature of mathematical statements" 1980, Dept. of Mathematics, Ulster Polytechnic,Belfast.

- "Some comments of magnetoatmospheric critical levels" 1981 University of St. Andrews, Seminar to Solar Physics Group.

- "Yet another paper on Howard's semicircle theorem: a semidumbell theorem", March 1980,University of Cambridge (B.T.M.C.).

- "Mechanical wave energy flux in magnetoatmospheres", April 1981, University of Bradford(B.T.M.C.).

- "Some mathematical aspects of wave motion", Department of Mathematics, Rochester Institute of Technology, 1983.

- "Singular differential equations and critical levels", Department of Mechanical Engineering,University of Rochester, 1983.

- "Singular differential equations and complex eigenvalues in hydrodynamics," Department of Mathematics, University of Rochester, 1983.

THIS TALK WAS ALSO PRESENTED AT:

- "Department of Mathematical Sciences, Old Dominion University, Norfolk, Virginia, 1983.
- "Some singular differential equations in magentohydrodynamics", Department of Mathematics, Clarkson College, New York, 1983.

- "Photospheric and chromospheric penumbral waves", American Astronomical SocietyMeeting, Pasadena, California, 1983.
- "Mathematical models of solid tumor growth by diffusion", Eastern Virginia Medical School,May 1984.
- "Magnetoatmospheric waves from a localized source" SIAM National Meeting, University of Washington, June 1984.

- "Mathematical models of solid tumor growth by diffusion", University of Rochester Cancer Center, January 1985.

- "A nonlinear eigenvalue problem in astrophysical magnetohydrodynamics", University of Alabama, Birmingham, 1986, International Conference on Differential Equations and Mathematical Physics.

- "Some singular differential equations in plasma physics and magnetohydrodynamics",Mathematics Department, Virginia Tech. October 1986.

- " Mathematical Model of Tumor Growth by Diffusion". 6th International Conference on Mathematical Modelling, St. Louis, August, 1987.

- " Mathematical Model of Tumor Growth by Diffusion" Combined Mid‑West‑South East Conference on Differential Equations, Vanderbilt University October 1987.

- 'Some Properties of the Spectrum of a Differential Operator in Solar Magnetohydrodynamics". Combined Mid‑West‑SouthEast Conference on Differential Equations, Vanderbilt University, October, 1987.

- "Acoustic‑Gravity Waves in a Spherically Stratified Atmosphere: Generalized Schrodinger Equation." 8th Regional Conference on Differential Equations. University of Georgia, Fall 1988.

- "Diffusion Models of Prevascular and Vascular Tumor Growth ‑ Review". 2nd International Conference on Mathematical Population Dynamics, Rutgers University May 1989.

- "Nonlinear Diffusion Problem in Cancer Biology". 9th S.E. Atlantic Conference on Differential Equations". UNC Charlotte. Fall 1989.

- "Modeling Growth Inhibitory/Stimulatory Factors in Cancerous/Normal Tissue". SIAM Annual Meeting, Chicago, July 1990.

- "Magnetoacoustic‑Gravity Waves and their (Ir)relevance to Solar Physics: an overview". ODU Department of Physics Colloquium, October 1990.

- "Nonlinear Model of Self‑Activation and Inhibition". 10th S.E. Atlantic Regional Conferenceon Differential Equations, Virginia Tech. November 1990.

- "Mangasarian's Multisurface Method of Pattern Separation for Medical Diagnosis applied to Breast Cytology" . Clinical Cancer Research Group, ODU, January 1991.

- "Mathematical Modeling in Biology with Applications to Cancer Research". Stanford Research Institute, January 1991.

- "Self Activation and Inhibition of Tissue Growth". ICIAM, Washington D.C., July 1991.

- "Non‑Radial Stellar Oscillations: A Quantum Mechanical Approach", International Conference on Differential Equations and Mathematical Physics, Georgia Tech, March 1992.

- "Estimation, Critical Thinking, and the Teaching of Mathematical Modellng". Conference on Post‑Secondary Pedagogy, Albany, N.Y. November 1992.

This lecture was also presented at the following conferences:

- V‑QUEST Second Annual Conference, Norfolk, Va., February 1993.

- "Making Math Connections" Conference, Thomas Nelson Community College, Hampton,Va., February 1993.

- "Dimensional Analysis in Mathematical Modeling: The Buckingham Pi Theorem and some of its Applications". Presented at "Making Math Connections II" Conference, Thomas Nelson Community College, January 1994.

44 "Teaching for a World of Technology" Featured Speaker for the Maury High School "Tech‑Prep" Conference, Airport Hilton, Norfolk, March 1994.

- "Mathematical Models and Metaphors of Tumor Growth: A Speculative Overview. " InvitedTalk at the International Centre for Mathematical Sciences Workshop on Tumor Growth and Development, Edinburgh, Scotland. February 1995.

- "Mathematical Models and Metaphors of Tumor Growth and Vascularization. "M.A.A.Regional Meeting, Thomas Nelson Community College, Hampton, Va. April 1995.

- "Catastrophe and Chaos ‑ The Mathematicians Contribution to Biology" ODU Biology Dept.Seminar, November 1995.

- "Some Aspects of Wave Motion in Astrophysics" Center for Coastal Physical Oceanography Seminar (ODU), January 1995.

- "Mathematical Models and Metaphors in Cancer Research", to faculty in the Department of Molecular Biology, Mayo Clinic, Rochester, Minn., April 1996.

- "Quantity, Uncertainty and Change", Keynote Speaker at the Peninsular NCTM Spring Banquet, April 1996.

- "Modeling with Difference Equations, and How I Came to Love Them", presented at the Ocean Lakes High School Math Teachers' Workshop, Virginia Beach, June 1996.

- A series of three workshops on Mathematical Modeling for Norfolk Public H.S. Math teachers, Summer 1996.

- "Mathematical Models and Metaphors in Cancer Biology", at the Society for Mathematical Biology Annual Meeting, U. of W., Seattle, WA, August 1996.

- “A Cusp-Catastrophe Model of Rapid Metastatic Tumor Growth/Remission”, at the MD/DC/VA Section of the MAA Spring Meeting, College of William and Mary, April 1997.

- Paper 55 was also presented at the International Conference on Mathematical Models in Medicine and the Health Sciences, Vanderbilt University, Nashville, TN in May 1997.

- A variant of paper 55 was presented at the Annual meeting of the Society for Mathematical Biology, UNC Raleigh, August 1997.

- “A Simple Nonlinear Ordinary Differential Equation Model of Rapid Tumor Growth/Remission via a Cusp Catastrophe”, at the Annual Ocean Lakes HS Conference on “Mathematical Connections”, Va. Beach, October 1997.

- “Estimation: Its Importance and Methods”, to CHROME students at Tallwood HS, Va. Beach, February 1998.

- “A Simple Mathematical Model with Profound Consequences”, to the School of Science, Pennsylvania State University, Erie Campus, May 1998.

- “Mathematical Modeling of Tumor Growth: Synopsis, Simile and Speculation.” Invited Presentation at the Cancer Minisymposium, University of Minnesota Institute of Mathematics and its Applications, Minneapolis, MN, November 1998.

- “Modeling Cancer Progression”, at the Mathematical Institute, Oberwolfach, Germany, February 1999.

- “Model Building in Cancer Biology: Are Conceptual Models Useful?”. At the Center for Mathematical Biology, Mathematical Institute, University of Oxford, March 1999.

64/65. “The Mathematical Physics of Rainbows”, at the High Altitude Observatory, Boulder, Colorado, October 1999. This was also presented at the Richard Barry Mathematics Colloquium in November 1999.

- “A mathematical model of wound healing in bone.” At the 2000 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS ’00), Las Vegas, June 2000.
- “Mathematical models of tumor growth: from empirical description to biological mechanism”. Invited talk at the 7
^{th}workshop on Mathematical Modeling in Nutrition and Health Sciences, Penn State, July 2000.

- “Human blood, melting ice and rainfall: the arithmetic of fluidity and the fluidity of arithmetic”. Presented at the Virginia Beach Higher Education Center, January 2001, invited by the Virginia Geographic Alliance (this was a workshop for Middle and High School Mathematics and Geography teachers).
*Also presented at the same workshop:*

- “Meteor impacts and hurricanes: how to waste a lot of energy….”

- “The mathematical physics of rainbows and glories”. Invited seminar to the Department of Mathematics & Computer Science, Georgia Southern University, February 2001.

- “Mathematical models of tumor growth: from empirical description to biological mechanism”. Invited colloquium at the Department of Mathematics & Computer Science, Georgia Southern University, February 2001.

- “Human blood, melting ice and rainfall: the arithmetic of fluidity and the fluidity of arithmetic”. Invited presentation to faculty and students at Thomas nelson Community College, Hampton, VA, February 2001.
- “Paper folding, growth of bacteria and other simple applications of exponential functions” to students and staff at Bayside Middle School, February 2001.

- “The effect of surface curvature on wound healing in bone: II. The critical size defect” at a workshop on Mathematical Models in Cancer, organized by the Department of Mathematics, Vanderbilt University, May 2002.

- “Inside Mathematical Modeling: Building Models in the Context of Wound Healing in Bone” to the Department of Electrical & Computer Engineering, Old Dominion University, September 2002.

- “Mathematics in Nature” at the CHROME* annual Sponsor Launch Program at NSU. The theme of the program was “Math & Science Across the Curriculum”. * Cooperating Hampton Roads Organizations for Minorities in Engineering. October 2002.
- “Math in Nature” at the Friends of the Library Fall Forum (jointly with Dr. Martina Doblin whose topic was “Art in Science”). November 2002.

78/79. “Introductory Applied Mathematics I & II” to Elementary School Teachers and their NSF-appointed ODU graduate assistants at Douglass Park Elementary School, November & December 2002.

- “Mathematics in Nature” to science faculty and students at Norfolk State University, April 2003.

- “Patterns, Principles and Poetry in Nature: Some Observations” to faculty and graduate students in the department of Ocean, Earth and Atmospheric Sciences at Old Dominion University, April 2003. (Jointly with Dr. Martina Doblin, whose topic was “Art in Science”.)

- "Patterns, Principles and Poetry in Nature: Some Observations" to faculty and students at the Math and Science Colloquium of St. Mary's College, MD, October 2003.

- "Can "Tunneling" Occur Between Cancer-Free and Cancerous States? Some Pre-Modeling Speculation" at the American Mathematical Society Special Session on Mathematical Modeling in Physiology and Medicine, UNC Chapel Hill, October 2003.

- Invited presentation entitled "Developing Mathematical Models in Cancer Biology: Some Personal Reflections" at a workshop on Mathematical Oncology at the Fields Institute for Research in Mathematical Sciences, University of Toronto, April 2004.

- "Mathematics in Nature: Some Thoughts on Course Development” at the 327th WE-Heraeus Seminar, the title of the workshop being "Atmospheric Optics". The meeting took place at the "Physikzentrum Bad Honnef", located near Bonn/Germany, in June 2004.

- Invited after-dinner speaker for ODU Photonics Conference: “The Rainbow: a Historico-Mathematical Synopsis”, June 2004.

- "A Simple Mathematical Model of the Rainbow" to Norfolk Public School mathematics teachers at their annual workshop, November 2004.

- "Patterns in Nature" to the Institute for Learning in Retirement (ILR) at the Virginia Beach Higher Education Center, February 2005.

- Keynote Speaker at the Elizabeth City State University Spring Arts Festival with the theme
*The Art in Science*. My two talks were: ”Mathematical Patterns in Nature: Some General Notions” and “Mathematical Patterns in Nature: Some Theoretical Concepts”, April 15/16 2005.

- "Patterns Around Us - Life at the Base of the Atmosphere". HACE (Hourly and Classified Employees) 29th Annual Luncheon, ODU, May 2005.

- "Modeling Nature's Patterns". Invited speaker, PenCTM (Peninsula Council of Teachers of Mathematics) annual dinner, CNU, Newport News, May 2005.

- Invited speaker at the National Cancer Institute's Integrative Cancer Biology Program Mini-Symposium, held in Berkeley, CA from May 16 - 18. The title of my talk was "Mathematical Models in Cancer Biology: Philosophy, Methodology, Utility and Limitations."

- "Rainbows, Halos and Glories" to students and parents at the Jones Magnet Middle School Planetarium, Hampton. June 2005.

- “Patterns in Nature” to the Lakewood Gardening Club, Norfolk, VA., February 2006.

- “Patterns in Nature”: invited speaker at the Mid-Atlantic Regional Conference of the National Institute for Learning Disabilities, Portsmouth, VA, February 2006.

- "Nature's Beauty: Some Reflections and Refractions": invited speaker at the St. Mary's College of Maryland Natural Science and Mathematics Colloquium Series, March 2006.

- "A Simplified Mathematical Model for Growth Factor Induced Wound Healing." ODU/NSU/EVMS Research Expo 2006, Constant Convocation Center, April 2006.
- "On Rainbows from Inhomogeneous Transparent Spheres: A Ray-Theoretic Approach." ODU/NSU/EVMS Research Expo 2006, Constant Convocation Center, April 2006.

- "Mathematics - its Beauty, Power and Applicability; Elementary Examples from Nature and Life." Invited speaker at the Anja S. Greer Conference on Mathematics, Science & Technology at Phillips Exeter Academy, Exeter, NH, June 2006.

- "Mathematics in Nature"; an invited presentation at the Fall meeting of the Tidewater Council of Teachers of Mathematics, Virginia Beach Higher Education Center, November 2006.

- "Mathematics - its Beauty, Power and Applicability; Elementary Examples from Nature and Life." Invited seminar speaker, Aerospace Engineering Department, Old Dominion University, November 2006.

- "Mathematics in Nature"; an invited presentation at the Fall meeting of the Tidewater Council of Teachers of Mathematics, Virginia Beach Higher Education Center, November 2006;

- "Patterns in Nature" to the University of Nevada (Las Vegas) Forum; March 2007.

- “Patterns in nature” to "Z-Arts!", the Zion Canyon Arts & Humanities Council, Springdale, Utah; also March 2007.

- "Mathematics in Nature" to the 2007 VMATYC conference (the Virginia Mathematical Association of Two Year Colleges), Hampton, VA; April 2007.

- "The Rainbow: Portraits in Art, Culture and Science", to the students and faculty at Phillips Exeter Academy, NH. April 2007.

- "Noah's Arc: Asin in the Sky" at the 9th International Meeting on Light and Color in Nature. Montana State University, Bozeman, Montana, June 2007.

- "Mathematical Models for Wound Healing on a Hemi-spherical Calvarium: The Critical Size Defect" at the Spring South East Meeting of the American Mathematical Society at LSU, Baton Rouge, LA., March 2008.

- "Mathematical Patterns in Nature" to math students and faculty in the Mathematics Department at VCU, Richmond, VA., April 2008.

- "Mathematical Patterns in Nature" to students and faculty in the Department of Mathematics at the College of William and Mary, April 2008.

- "Patterns in Nature”, in the Scientific Colloquium Series at the NASA/Goddard Space Flight Center, Greenbelt, MD., May 2008.

- "A "Toy" ODE Model For the Onset of Cancer, and Guesstimation: Orders of Magnitude and The Goldilocks Principle. This was a lecture in the Mathematics Undergraduate Lecture Series at UVA, Charlottesville, May 2008.
- “Mathematical Patterns in Nature”; as a “featured speaker” at the 34
^{th}Annual Conference of the American Mathematical Association of Two-Year Colleges, Washington DC, November 2008.

- “Guesstimation: Fermi Problems, Orders of Magnitude and the Goldilocks Principle” at Johns Hopkins Applied Physics Laboratory A.I. Mahan Colloquium, January 2009.

- “Using Mathematical Models of Bird Eggs as a ‘Case Study’ across the Calculus Syllabus (I,II,III)” at the 2009 joint meeting of the Florida Section of the Mathematical Association of America and the Florida Two-Year College Mathematics Association meeting at Florida Gulf Coast University, Ft. Myers, FL, February 2009.

- Also at the Virginia Council of Teachers of Mathematics 30th Annual Mathematics Conference, Virginia Beach, March 2009. The title was “Mathematical models of birds eggs: a case study for Calculus III students.”

- “Guesstimation” at CNU Math Department Pi Mu Epsilon induction ceremony. March 2009.

- “Guesstimation”, at Broward College “Math Awareness Week”, Davie, Florida, April 2009.

- “Fermi problems, Guesstimation and the Goldilocks Principle”, at the Amerigroup Corporation, Virginia Beach, VA (this was broadcast on the internet for their other sites in the US.)

- “Guesstimation, Fermi Problems and the Goldilocks Principle” at the Engineers' Club of the Virginia Peninsula, Newport News, VA, August 2009.

- A combined book-signing and talk given at the Noblis organization in Falls Church, VA. The talk was "Mathematical Patterns in Nature", and the book signing was sponsored by "Hooks Book Events" (Bethesda, MD), September 2009.

- At the Delft Symposium on Mathematical Models for Wound Healing, held at the Technical University of Delft, The Netherlands. The title of my paper was
*‘Waves’ of healing, the critical size defect and keloid scars: some speculation.*October 2009.

- The Keynote Speaker for the Greater Richmond Council of Teachers of Mathematics (GRCTM) in Midlothian, VA. The title of my talk was
*“A Mathematical Nature Walk”.*October 2009.

- Norfolk Chapter of the American Association of University Women entitled “Noticing Nature’s Wonderful Patterns”, November 2009.

125a/b. I was a featured speaker at the NILD (National Institute for Learning Development) 2009 Northeast Regional Conference, in Lancaster, PA. I spoke on “Noticing Mathematical Patterns in Nature”. Also, I conducted a workshop for teachers at the same conference, entitled “Guesstimation: “Ballpark” Numbers, the Geometric Mean and the Goldilocks Principle.” December 2009.

- Keynote speaker at the Maggie L. Walker Governor’s School Mu Alpha Theta induction ceremony, Richmond VA, February 2010. The title of my talk was “Mathematical Patterns in Nature.”

- Keynote speaker at the Pi-Mu-Epsilon Math Honor Society Induction ceremony at CNU, Newport News, March 2010. The title of my talk was Mathematical Patterns in Nature.

- Utah Valley University, Orem, Utah, where I gave a talk entitled “A Mathematical Nature Walk” and led a ‘mathematical nature walk’ at Robert Redford’s Sundance Resort, Sundance, Utah! (March 2010).

**The Atmosphere Exposed:**Photographs of Halos, Mirages, Iridescent Clouds,... & More! Five of my nature photographs have been accepted for display, including two in the brochure. The**June 2010**exhibition opens in conjunction with the International Light and Color in the Open Air Conference being hosted on the campus of St. Mary's College of Maryland. For the first time in the thirty-year history of the conference, a gallery exhibition is included! The display will be on view from 12 June through 30 September 2010.

- A talk/book signing at Noblis, Inc., Falls Church, VA (June 2010). The title of the talk was: Fermi problems and estimation: The power of arithmetic: the Goldilocks Principle and the geometric mean.

- At the 10th International Conference on Light and Color in the Atmosphere at St. Mary's College, St. Mary's City, MD, I presented a paper entitled "On the existence of single and twin primary zero-order rainbows in radially inhomogeneous spheres." (June 2010).

- At the "Math/Science Innovation Center" in Richmond, VA. The talks were "Guesstimation, Fermi Problems and the Goldilocks Principle", and "Mathematical Patterns in Nature". (June 2010).

- A talk/book signing at the 26th Anja S. Greer Conference on Mathematics, Science & Technology, held at Philips Exeter Academy, Exeter, NH. The title of my talk was "A Mathematical Nature Walk". (June 2010).

- At the 1065th meeting of the American Mathematical Society, held at the University of Richmond, VA, in a special session on Mathematical Models in Biology and Medicine, a talk entitled "Waves" of healing, the critical size defect and keloid scars: some speculation.” (November 2010).

135/6. I was a keynote speaker at the ASCI (Association of Christian Schools International) 2010 New England Educator Convention in Sturbridge, MA. The title of my talk was Majestic Themes in Nature and Scripture: Mathematical Patterns in Nature. Also at the same convention I gave a seminar entitled Guesstimation, "Ballpark" Numbers, the Geometric Mean and the Goldilocks Principle. (November 2010).

137/8. At the Annual Meeting of the Pacific Northwest Section of the Mathematical Association of America, at the University of Alaska Southeast, Juneau, AK, June 2011, the following invited events:

*(i)* A mini-course entitled" Teaching Mathematical Modeling Through Patterns in Nature", and.

*(ii))* A Public Lecture entitled" Mathematical Patterns in Nature".

- At the School of Mathematical Sciences, Rochester Institute of Technology, an invited lecture at the 4th Annual Summer Mathematics Institute, entitled "Mathematical Patterns in Nature". (June 2011).

140/141. “Guesstimation: ‘Ballpark’ Numbers, the Geometric Mean and the Goldilocks Principle”, and “Noticing Mathematical Patterns in Nature”; at the 30^{th} Anniversary Conference of the National Institute for Learning Development, held in Orlando, FL. (February 2012).

- “Direct and Inverse problems for Radially Inhomogeneous Spheres, with applications to Rainbow Refractometry and Optical Fiber studies.” Virginia State University. (March 2012).

143/144. “Quantitative Reasoning and Mathematical Modeling at the Undergraduate Level”, and was for faculty at both the University of Washington (UWB – the Bothell campus) and Cascadia Community College. I also gave a public lecture at UWB on “Mathematical Patterns in Nature”. (April 2012).

- At ODU: The Provost’s Conversations on Teaching and Learning: “Using Humor in the Classroom: Does it Aid Understanding?” (April 2012)

- “Noticing Mathematical Patterns in Nature” – Keynote speaker at the 10
^{th}Annual Colonial Academic Alliance U/G Research Conference, ODU. (April 2012).

- “Noticing Mathematical Patterns in Nature”; Hampden-Sydney University, Virginia. (April 2012).

- I spoke at the RSA (Royal Society for the encouragement of Arts, Manufactures and Commerce); the lecture was entitled “X and the City: The mathematics of urban life.” (May 2012). The RSA is located on John Adam Street in London!

- “X and the City: The mathematics of urban life.” A BBC World Service interview for “The World Today” program. (May 2012). Also radio interviews about X and the City on BBC Europe and “Big Science” (in San Francisco).

- “Zero-order 'rainbows', electromagnetic wave equations and poles of the scattering matrix: what's all that about?” (contributed talk) at MathFest 2012, the annual meeting of the Mathematical Association of America, Madison, WI (August 2012).

- “’Rainbows’ in homogeneous and radially inhomogeneous spheres: connections with ray, wave and potential scattering theory” (contributed talk) at the 2012 South-Eastern Regional Conference on Differential Equations, Wake Forest University, Winston-Salem, NC. (October 2012).

- “X and the City” talk and book-signing at the ODU-VBHEC, February 2013.

- “X and the City: Modeling Aspects of Urban Life” to faculty and students in the mathematics department at Fairfield University, CT, April 2013.

- VSU Math Dept. (Petersburg, VA), at talk entitled
*The Mathematical Basis of a Universal ‘Law of Quarter Powers’ for Critters, Large and Small.*April 2013.

- A paper (with co-author Philip Laven) entitled “
*The Heiligenschein*” at the 2013 International Light and Color in Nature: Conference, this time held in Fairbanks, AK, August 2013.

*X and the City: "Arithmetic" Applied to Urban Life.*This public lecture was given at Hofstra University as part of their Science Evenings with IDEAS (Institute for the Development of Education in the Advanced Sciences. October 2013.

*Mathematical Patterns in Nature.*This was a keynote address at the Annual Conference of the Association for Constructivist Teaching, held at the National Museum of Mathematics, NYC, October, 2013.

*Rays, Waves and Rainbows*, to the Mathematics Department at UMBC, December 2013.

*Guesstimation, Fermi problems and the geometric mean*to faculty and students at Tidewater Community College (Norfolk campus), March 2014.

- Keynote address at the TCTM (Tidewater Council of Teachers of Mathematics) conference at Kempsville HS (July 2014). Title: ‘Natural Mathematics: Can we ‘use’ Nature to interest Students in Mathematical Patterns?”

*Rays, Waves and Rainbows*to the department of Mathematics, UNCG, February 2015.

- "
*Mathematical Patterns in Nature: A Talk Your Mother Would Love*". To faculty and students in the Dept. of Informatics, University of Ulster, Coleraine Campus, N. Ireland, April 2015.

*NOTE: nearly all of the above, over the last several years, have been invited presentations.*

- Presented at Regent University Center for Renewal Studies – Faith & Science Conference, March 18
^{th}, 2016:*Teaching Mathematical Science from Nature’s ‘Book’ in a Secular Environment.*

- Presented at the Regional MAA meeting, Spring 2016: Rays, Waves and Rainbows:
*A brief tour through some mathematical history.* *Patterns in Nature: A Treasure Trove for the Curious*. Keynote address for an undergraduate conference “Claim Your Curiosity” at Middle Georgia State University (Macon campus), Macon, GA. April 2017.*Patterns in Nature: A Treasure Trove for the Curious*. Modern Technology and Management Institute Keynote Address, September 2017 (Virginia Beach).*Patterns in Nature: A Treasure Trove for the Curious*. ODU Science Club Café, Slover Library, Norfolk, VA. July 2017.*Mountain Shadows and Glitter Paths Revisited*. ODU Mathematics Awareness SIAM Conference, April 21, 2018.*Patterns in Nature: A Treasure Trove for the Curious*. Norfolk State University, October 13^{th}, 2018.*Patterns in Nature: A Treasure Trove for the Curious*. Dean’s Distinguished Lecture, University of Wisconsin, Milwaukee, October 23^{rd}, 2018. https://uwm.edu/letters-science/event/patterns-in-nature-a-treasure-trove-for-the-curious/*Mathematical Patterns in Nature*. Invited talk for the Chesapeake Section of the AAPT, November 10^{th}, 2018.*Mathematical Patterns in Nature*to the VCTM 2019 meeting, Longwood U. March 9^{th}, 2019.*Patterns in Nature*to students and faculty in the School of Sciences, Regent U. March 22^{nd}2019.*Fibonacci Numbers: Deriving the Binet Formula, Golden Spirals and Other Foibles*, April 6, 2019 ODU Math Awareness Conference.*Patterns in Nature: A Treasure Trove for the Curious*. George W. Jeffers Memorial Lecture, VJAS General Session, May 22, 2019.*Light and Colo(u)r in Nature: A Personal Journey.*Keynote talk for the 15^{th}International Light and Color in Nature meeting, Bar Harbor, Maine, July 15 – 18, 2019.*Patterns in Nature I: A Treasure Trove for the Curious – Beer Mats, Rainbows, Halos, Sundogs and Glories; Optical Beauty in the Skies.*Talk #1 on Seabourn Odyssey Cruise, August 6^{th,}2019.*Patterns in Nature II: A Treasure Trove for the Curious – Shadows, Sunflowers (again!), Butterflies, Clouds, Waves (and a whole lot more).*Talk #2 on Seabourn Odyssey Cruise, August 8^{th}, 2019.*The Greeks’ fascination with Symmetry and Proportion: Pythagoras, Archimedes, The Golden Number, Fibonacci of Pisa, Spirals, Leaves, Pinecones and Sunflower Seeds.*Talk #3 on Seabourn Odyssey Cruise, August 10^{th}, 2019.*Fractals - an entirely new Geometry: Trees, Ferns, Lightning, Lungs, Heartbeats,**River Deltas, the Coastline of Britain**and the art of Jackson Pollock – What*Talk #4 on Seabourn Odyssey Cruise, August 12__would__Pythagoras think?^{th}, 2019.*Patterns in Nature: A Treasure Trove for the Mathematically Curious.*Keynote address for the 33rd Virginia Mathematical Association of Two-Year Colleges (VMATYC) Conference, November 1^{st}2019, John Tyler Community College.