Fascinating. This actually makes sense to me. Consider the various and vast implications of this . . .
William Thurston’s son . . . Followed in his low-dimensional topology (and knotted) foot steps . . .
About Dylan Thurston
Main Research Group: Topology
Affiliated Groups: Logic / Complex Analysis / Geometry
Research Interests: geometric and quantum low-dimensional topology and related fields; including Heegaard Fleor homology and its extension to 3-manifolds with boundary; rigidity of graphs in space; cluster algebras; geometric intersection numbers for curves on surfaces; finite-type invariants
Dylan Paul Thurston
Department of Mathematics
University of Indiana, Bloomington
Low-dimensional topology and related fields.
Fellowships and awards
Professor, Indiana University, Bloomington, Spring 2013–present. Chancellor’s Professor, University of California at Berkeley, Fall 2012. Visiting Professor, Tokyo Institute of Technology, Spring 2012. Visiting Professor, Cornell University, Fall 2011.
Assistant Professor, Barnard College, Columbia University, 2005–2012.
Benjamin Peirce Assistant Professor, Harvard University, 2002–2005.
NSF Postdoctoral Research Fellow, Harvard University, 2000–2002.
JSPS Postdoctoral Fellowship (Short Term), Research Institute for Mathematical Sciences,
Kyoto University, Japan, Sept–Nov 2001.
Ph.D., University of California at Berkeley, 2000. Dissertation: “Wheeling: A diagrammatic analogue of the Duflo isomorphism” under Vaughan Jones. arXiv:math.QA/0006083.
A.B. cum laude, Harvard University, 1995. Thesis: “Integral expressions for the Vassiliev knot invariants”, under Raoul Bott. arXiv:math.QA/9901110.
NSF grant DMS-1507244, “Rubber Bands to Rational Maps”, 2015–present.
NSF grant DMS-1358638, “Homology theories for tangles and bordered 3-manifolds”, 2010–
Presidential Research Award, Barnard College, 2009. Project: “Homology theories of knots and links”.
Most Cited Paper Award for Computer Aided Geometric Design, 2009, for “Discrete one-forms on meshes and applications to 3D mesh parametrization” with Steven Gortler and Craig Gotsman.
Sloan Research Fellow, 2006–2010.
NSF Postdoctoral Research Fellow, Harvard University, 2000–2002.
Bordered Heegaard Floer homology: Invariance and pairing. With R. Lipshitz and P. Ozs- váth. Memoirs of the American Mathematical Society, accepted for publication, 2016. arXiv:0810.0687.
Bimodules in bordered Heegaard Floer homology. With R. Lipshitz and P. Ozsváth. Geometry and Topology, 19:525–724, 2015. arXiv:1003.0598.
A tour of bordered Floer theory. With R. Lipshitz and P. Ozsváth. Proceedings of the National Academy of Sciences, 108(20):8085–8092, May 17, 2011. arXiv:1107.5621.
Slicing planar grid diagrams: a gentle introduction to bordered Heegaard Floer homology. With R. Lipshitz and P. Ozsváth. Proceedings of Gökova Geometry-Topology Conference 2008, Gökova, 2009. arXiv:0810.0695.
Heegaard Floer homology as morphism spaces. With R. Lipshitz and P. Ozsváth. Quantum Topology, 2(4):381–449, 2011. arXiv:1005.1248.
A faithful linear-categorical action of the mapping class group of a surface with boundary. With R. Lipshitz and P. Ozsváth. Journal of the European Mathematical Society, 15(4):1279–1307, 2013. arXiv:1012.1032.
Bordered Floer homology
Heegaard Floer homology: Other papers
Conformal geometry and rational maps
Finite type and quantum invariants
Computing HF by factoring mapping classes. With R. Lipshitz and P. Ozsváth. Geometry and Topology, 18:2547–2681, 2014. arXiv:1005.2550.
Bordered Floer homology and the spectral sequence of a branched double cover I. With R. Lipshitz and P. Ozsváth. Journal of Topology, 7(4):1155–1199, 2014. arXiv:1011. 0499.
Notes on bordered Floer homology. With R. Lipshitz and P. Ozsváth. In Contact and Symplectic Topology, 275–355, Bolyai Society Mathematical Studies 26, 2014. arXiv: 1211.6791.
Relative Q-gradings from bordered Floer theory. With R. Lipshitz and P. Ozsváth. Preprint, 2012. arXiv:1211.6990.
Bordered Floer homology and the spectral sequence of a branched double cover II: The spectral sequences agree. With R. Lipshitz and P. Ozsváth. Journal of Topology, accepted for publication, 2015. arXiv:1404.2894.
On combinatorial link Floer homology. With C. Manolescu, P. Ozsváth, and Z. Szabó. Geometry and Topology, 11:2339–2412, 2007. arXiv:math.GT/0610559.
Legendrian knots, transverse knots and combinatorial Floer homology. With P. Ozsváth and Z. Szabó. Geometry and Topology, 12:941–980, 2008. arXiv:math.GT/0611841.
Transverse knots distinguished by knot Floer homology. With L. Ng and P. Ozsváth. Journal of Symplectic Geometry, 6:461–490, 2008. arXiv:math.GT/0703446.
Grid diagrams and Heegaard Floer invariants. With C. Manolescu and P. Ozsváth. Preprint, 2009. arXiv:0910.0078.
Naturality and mapping class groups in Heegaard Floer homology. With A. Juhász. Preprint, 2012. arXiv:1210.4996.
The algebra of knotted trivalent graphs and Turaev’s shadow world. In Invariants of knots and 3-manifolds (Kyoto 2001), 337–362, Geometry and Topology Monographs 4, 2002– 2004. arXiv:math.GT/0311458.
Appendix to “The volume of hyperbolic alternating link complements” by M. Lackenby. With I. Agol. Proc. London Math. Soc., 3d ser., 88(1):204–224, 2004. arXiv:math.GT/ 0012185.
A random tunnel number one 3-manifold does not fiber over the circle. With N. Dunfield. Geometry and Topology, 10:2431–2499, 2006. arXiv:math.GT/0510129.
3-manifolds efficiently bound 4-manifolds. With F. Costantino. Journal of Topology, 1(3): 703–745, 2008. arXiv:math.GT/0506577.
Grid diagrams, braids, and contact geometry. With L. Ng. Proceedings of Gökova Geometry- Topology Conference 2008, Gökova, 2009. arXiv:0812.3665.
A shadow calculus for 3-manifolds. With F. Costantino. Draft available online. On geometric intersection of curves in surface. Draft available online.
From rubber bands to rational maps: A research report. Research in the Mathematical Sciences, accepted for publication, 2016. arXiv:1502.02561.
Conformal surface embeddings and extremal length. With J. Kahn and K. Pilgrim. Preprint, 2015. arXiv:1507.05294.
Wheels, wheeling, and the Kontsevich integral of the unknot. With D. Bar-Natan, S. Garoufalidis, and L. Rozansky. Israel J. Math. 119:217–237, 2000. arXiv:q-alg/9703025.
The Århus invariant of rational homology 3-spheres I: A highly non-trivial flat connection on S3. With D. Bar-Natan, S. Garoufalidis, and L. Rozansky. Selecta Math., n.s., 8(3):315–339, 2002. arXiv:q-alg/9706004.
Cluster algebras, representation theory
The Århus invariant of rational homology 3-spheres II: Invariance and universality. With D. Bar-Natan, S. Garoufalidis, and L. Rozansky. Selecta Math., n.s., 8(3):341–371, 2002. arXiv:math.QA/9801049.
The Århus invariant of rational homology 3-spheres III: The relation with the Le-Murakami- Ohtsuki invariant. With D. Bar-Natan, S. Garoufalidis, and L. Rozansky. Selecta Math., n.s., 10(3):305–324, 2004. arXiv:math.QA/9808013.
Two applications of elementary knot theory to Lie algebras and Vassiliev invariants. With D. Bar-Natan and T. Le. Geometry and Topology 7(1):1–31, 2003. Published version of my Ph.D. dissertation. arXiv:math.QA/0204311.
On the existence of finite type link homotopy invariants. With B. Mellor. J. Knot Theory Ramifications 10(7):1025–1039, 2001. arXiv:math.GT/0010206.
Hyperbolic volume and the Jones polynomial. Lecture notes from a series at summer school “Invariants des nœuds et de variétés de dimension 3”, Grenoble, France, 1999. Notes available online.
Perturbative 3-manifold invariants by cut-and-paste topology. With G. Kuperberg. Preprint, 1999. arXiv:math.GT/9912167.
The F4 and E6 families have only a finite number of points. Draft available online.
From dominoes to hexagons. Preprint, 2004. arXiv:math.CO/0405482.
Cluster algebras and triangulated surfaces. I. Cluster complexes. With S. Fomin and M.
Shapiro. Acta Mathematica, 201:83–146, 2008. arXiv:math.RA/0608367.
Cluster algebras and triangulated surfaces. Part II: Lambda lengths. With S. Fomin. Memoirs of the American Mathematical Society, accepted for publication, 2016. arXiv:1210.
Positive basis for surface skein algebras. Proceedings of the National Academy of Sciences,
111(27):9725–9732, 2014. arXiv:1310.1959.
The complex volume of SL(n, C) representations of 3-manifolds. With S. Garoufalidis and
C. Zickert. Duke Mathematical Journal, 164(11):2099–2160, 2015. arXiv:1111.2828.
Discrete one-forms on meshes and applications to 3D mesh parametrization. With S. Gortler and C. Gotsman. Computer Aided Geometric Design, 23:83–112, 2006.
Characterizing generic global rigidity. With S. Gortler and A. Healy. American Journal of Mathematics, 132(4):897–939, 2010. arXiv:0710.0926.
Sensor network localization using sensor perturbation. With Y. Zhu and S. Gortler. Transactions on Sensor Networks, 7(4), Article 36, 2011.
On affine rigidity. With S. Gortler, C. Gotsman, and L. Liu. Journal of Computational Geometry 4(1):160–181, 2013. arXiv:1011.5553.
Generic global rigidity in complex and pseudo-Euclidean spaces. With S. Gortler. In Rigidity and Symmetry, 131–154, Fields Institute Communications 70, 2014. arXiv:1212.6685. Characterizing the universal rigidity of generic frameworks. With S. Gortler. Discrete and
Computational Geometry, 51(4):1017–1036, 2014. arXiv:1001.0172.
Measurement isomorphism of graphs. With S. Gortler. Preprint, 2012. arXiv:1212.6551.
A bulk inflaton from large volume extra dimensions. With B. Greene, D. Kabat, and J. Levin. Physics Letters B, 694(4):485–490, 2011. arXiv:1001.1423.
Markup optimisation by probabilistic parsing. With C.-c. Shan. Draft available online.
Selected invited talks
“Elastic graphs and degenerations of complex structures”
Special session on Holomorphic Dynamics, AMS sectional meeting, Stony Brook, March 2016
“Discrete measured foliations”
Oberwolfach workshop on Computational Geometric and Algebraic Topology, Oct 2015 Tech Topology Conference, Georgia Tech, Oct 2015
“Rubber bands, square tilings, and rational maps”
Dynamical Developments: a conference in Complex Dynamics and Teichmüller theory, Bremen University, Aug 2015
Invited address, AMS sectional meeting, University of Wisconsin—Eau Claire, Sept 2014
“Bordered Heegaard-Floer homology”
Lecture course at XIXth Oporto meeting on Geometry, Topology and Physics, Faro, Por- tugal, July 2010
“Combinatorial Heegaard-Floer homology and transverse knots.” Notes available online. Workshop on Cluster Algebras and Related Topics (4 lectures), Morelia, Mexico, Decem- ber 2008
“Wheels and wheeling” and “Hyperbolic volume and the Jones polynomial”
Summer school at conference Invariants des nœuds et de variétés de dimension 3, Greno- ble, France, June 1999.
Topology II, graduate course, IU Bloomington, Spring 2016.
Complex Analysis, upper-level undergraduate course, Harvard, Fall 2003; Barnard, Fall
2009; IU Bloomington, Spring 2016.
Geometric Topology, graduate course, IU Bloomington, Fall 2016; Harvard, Spring 2005. Rational Maps, graduate topics course, IU Bloomington, Spring 2015.
Topology, upper-level undergraduate course, IU Bloomington, Spring 2015; Harvard, Spring
Geometric Topology II, graduate course, IU Bloomington, Spring 2014.
Metric Geometry, graduate course, IU Bloomington, Fall 2013.
Intuitive Topology, undergraduate course, IU Bloomington, Spring 2013.
Curves on Surfaces, graduate topics course, Berkeley, Fall 2012.
Calculus I, Cornell, Fall 2011; Calculus II, Harvard, Spring 2003; Calculus III, Barnard,
Fall 2005, Spring 2006, Fall 2010.
Graph rigidity undergraduate research project, Barnard, Summer 2009–2011. Led to sev-
eral papers by the students, including S. Frank and J. Jiang, “New classes of counterexamples to Hendrickson’s global rigidity conjecture”>, Discrete and Computational Ge- ometry, 45(3):574–591.
Honors Linear Algebra, introductory course for majors, Barnard, Fall 2009.
Perspectives in Mathematics, introductory course for non-majors, Barnard, Fall 2009, Fall
- With D. MacDuff and D. Bayer.
Algebraic Topology I, Harvard, Fall 2004; Algebraic Topology II, Barnard, Spring 2008,
Spring 2009, Spring 2011.
Introduction to Algebraic Topology, undergraduate course, Barnard, Spring 2009. Symmetry, first-year seminar, Barnard, Fall 2006 and Spring 2008.
Geometry and Topology seminar, Barnard, multiple semesters, Spring 2007–present. Combinatorics, undergraduate course, Barnard, Spring 2007.
Undergraduate seminar, Barnard, Spring 2007.
Modern Analysis II, undergraduate course, Barnard, Spring 2006.
Teaching and undergraduate research
Lie Algebras, upper-level undergraduate course, Harvard, Fall 2002.
Algebra, informal upper-level undergraduate course, Harvard, Fall 2002.
Elliptic Functions, upper level undergraduate course, Geneva, Fall 1998. With P. de la
Co-organizer, Special Session on Random Spaces, AMS sectional meeting, University of Wisconsin—Eau Claire, Sept 2014.
Co-organizer, Conference “What’s next? The mathematical legacy of Bill Thurston”, at Cornell University, June 2014.
Organizer of semester on “Homology Theories of Knots and Links” at MSRI, Spring 2010, including organizing the introductory workshop.
Founding editor, Quantum Topology, 2009–present.
Referee for Acta Mathematica, Algebraic Geometry and Topology, Compositio Mathemat-
ica, Duke Mathematical Journal, Experimental Mathematics, Geometry and Topology,
Topology, National Science Foundation, inter alia. Member, Association for Women in Mathematics. Member, American Mathematical Society.
Sensor Network Localization Using Sensor Perturbation
Yuanchen Zhu Harvard University
Steven J. Gortler Harvard University
Dylan Thurston Columbia University