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I am a senior researcher at Euclid Lab, an Associate Professor in the Mathematics Department at the University of Georgia, and the lead mentor for Camp Euclid.  My main area of research is 4-dimensional geometry and topology. I obtained my Ph.D. in mathematics from the University of California, Berkeley under the supervision of Robion Kirby and have worked as a research mathematician since 1999.

If you see a green light in the left panel, that means I am online and you can click on the webcam/microphone/chat icons to visit me in my virtual office.

  • Curriculum Vitae: This is a link to a pdf version of my CV.
  • Research: I have been working since 1996 on problems related to constructions of smooth 4-manifolds with additional geometric structures related to symplectic and contact geometry. I am currently wrapped up in an active collaboration with Rob Kirby, thinking about using generic maps from 4-manifolds to the 2-sphere to get at a combinatorial/topological understanding of smooth 4-manifold invariants. Using these techniques we recently discovered the right way to generalize the notion of a Heegaard splitting in dimension 3 to the 4-dimensional setting; where 3-manifolds are split into two handlebodies, 4-manifolds are now trisected into 3 4-dimensional 1-handlebodies. Other recent, more-or-less ongoing and/or potential collaborators include Joan LicataMargaret Symington, Andras Stipsicz, Aaron Abrams, Valerie HowerOlguta Buse, Bruce Bartlett and Thomas Mark.
  • UGA Topology: The University of Georgia has been a great place for topology since way back when, and the Georgia Topology Conference has been "serving topologists since 1961". Here's the web page for the UGA Topology Group.
  • Students: I have two PhD students, Eric Burgess and Nick Castro.
  • Blog: You can read my research blog here.
  • Teaching: I have taught a wide range of university-level mathematics courses, ranging from graduate courses in knot theory and algebraic topology to college algebra courses and courses for future elementary and high school teachers. I am currently teaching a graduate topics course, "Knots, 3-manifolds and 4-manifolds".
  • Outreach: I have given many mathematics enrichment talks at local high schools in communities as diverse as rural Quebec and the townships of Cape Town. I am currently helping the University of Georgia MathCounts Outreach program run an Athens Math Circle, although in truth all the work is done by UGA undergraduate and graduate students.
  • Publications: Below is a list of my publications in reverse chronological order:

David Gay



Euclid Lab


David Gay
Euclid Lab
160 Milledge Terr.
Athens, GA 30606-4936

Office Hours:

By appointment


507B Boyd Hall, University of Georgia or on line via google hangout (email me to set up an appointment).