Mike Sullivan

Professor

Faculty,
Full Professor
2024
Contact
Email
Email
Phone
Location
LGRT 1323G

Education

PhD, Stanford University, 1999

RESEARCH INTERESTS

Symplectic Geometry & Topology

Publications

Geometry and Topology

  • “C0-limits of Legendrians and positive loops,” To appear in Compositio Mathematica (with G. Dimitroglou Rizell).
  • “C0-limits of Legendrian knots,” Trans. Amer. Math. Soc. Ser. B 11 (2024), 798 – 825 (with G. Dimitroglou Rizell).
  • “The persistence of a relative Rabinowitz-Floer complex,” Geom. Topol. 28 (2024), no. 5, 2145 – 2206. (with G. Dimitroglou Rizell).
  • “Sheaves via augmentations of Legendrian surfaces,” J. Homotopy Relat. Struct. 16 (2021), no. 4, 703 – 752 (with D. Rutherford)
  • “The persistence of the Chekanov-Eliashberg algebra.” Selecta Math. (N.S.) 26 (2020), no. 5, Paper No. 69, 32 pages (with G. Dimitroglou Rizell).
  • “An energy-capacity inequality for Legendrian submanifolds.” J. Topol. Anal. 12 (2020), no. 3, 547–623. (with G. Dimitroglou Rizell)
  • “Cellular Legendrian contact homology for surfaces, part I.” Adv. Math. 374 (2020), 107348, 71 pp (with D. Rutherford)
  • “Cellular Legendrian contact homology for surfaces, part II.” Internat. J. Math. 30 (2019), no. 7, 1950036, 135 pp. (with D. Rutherford)
  • “Cellular Legendrian contact homology for surfaces, part III.” Internat. J. Math. 30 (2019), no. 7, 1950037, 111 pp. (with D. Rutherford)
  • “Generating families and augmentations for Legendrian surfaces.” Algebr. Geom. Topol. 18 (2018), no. 3, 1675–1731 (with D. Rutherford)
  • “Families of Legendrian submanifolds via generating families.” Quantum Topol. 7 (2016), no. 4, 639–668. (with J. Sabloff)
  • “Transverse open string topology and the cord algebra” Journal of Symplectic Geometry 13 (2015), no. 1, 1-16 (with S. Basu, J. McGibbon, D. Sullivan).
  • “A bordered Legendrian contact algebra,” Journal of Symplectic Geometry 12 (2014), no. 2, 237-255 (with A./J. Harper).
  • “Filtrations on the knot contact homology of transverse knots,” Mathematische Annalen 355 (2013), no. 4, 1561-1591 (with T. Ekholm, J. Etnyre, L. Ng).
  • “Knot contact homology,” Geometry and Topology 17 (2013), no. 2, 975-1112 (with T. Ekholm, J. Etnyre, L. Ng).
  • “Symplectic field theory and quantum backgrounds,” Journal of Symplectic Geometry 6 (2008), no. 4, 379-405 (with J. Terilla and T. Tradler).
  • “Legendrian contact homology for P × R,” Transactions of the AMS, 359 (2007), 3301-3335 (with T. Ekholm, J. Etnyre).
  • “Rounding corners of polygons and the embedded contact homology of T3,” Geometry and Topology 10 (2006) 169-266 (with M. Hutchings).
  • “The contact homology of Legendrian submanifolds in R2n+1,” Journal of Differential Geometry 71 (2005) 177-305 (with T. Ekholm, J. Etnyre).
  • “Non-isotopic Legendrian submanifolds in R2n+1,” Journal of Differential Geometry 71 (2005) 85-128 (with T. Ekholm, J. Etnyre).
  • “The periodic Floer homology of a Dehn twist,” Algebraic and Geometric and Topology 5 (2005) 301-354 (with M. Hutchings).
  • “Orientations in Legendrian contact homology and exact Lagrangian immersions,” International Journal of Mathematics 16 (2005) 453-532 (with T. Ekholm, J. Etnyre).
  • “K-theoretic invariants for Floer homology,” Geometric and Functional Analysis 12 (2002) 810-872. 

Financial Math

  • “A Multi-dimensional Transform for Pricing American Options with Stochastic Volatility” to appear in Journal of Computational Finance (with  N. Believa, Y. Chen, S. Nawalhka and S. Zreik )
  • “Pricing American Options under Levy Jump Models: A Multidimensional Transform Method.”  The Journal of Derivatives, 2023, 31 (2) 9 –35 (with N. Beliaeva, Y. Chen, S. Nawalkha).
  • “A computational scheme for the optimal strategy in an incomplete market,” Journal of Economic Dynamics and Control, 31 (2007) 3591-3613 (with J. Keppo, X. Meng).
  • “Convergence to Black-Scholes for ergodic volatility models,” European Journal of Applied Mathematics 16 (2005) 385-409 (with J. Conlon).

Grants

  • 2025-2030, $42,000, Simons Foundation “Legendrian submanifolds: quantitative geometry and the Nearby Lagrangian Conjecture” (Sole Principal Investigator)
  • 2020-2025, $42,000, Simons Foundation “The success and failure of holomorphic curves and Legendrian sub- manifolds” (Sole Principal Investigator)
  • 2014-2019, $35,000, Simons Foundation “Holomorphic curves and contact geometry” (Sole Principal Investiga- tor)
  • 2010-2013, $112,036, NSF-DMS 1007260 (Sole Principal Investigator)
  • 2010-2011 $22,436, Mass Mutual Foundation “The Actuarial Connection” (Principal Investigator)
  • 2009-2010 $21,374 ,Mass Mutual Foundation “The Actuarial Connection” (Principal Investigator)
  • 2008-2011, $1,500,000, NSF-DMS 0757245, 0757253, 0757312, 0757293, 0757277, “How the algebraic topology of closed manifolds relates to strings and 2D quantum field theory” (Participant in collaborative FRG grant)
  • 2007-2010, $97,149, NSF-DMS 0707091, “Contact homology and string topology” (Sole Principal Investigator)
  • 2003-2006, $84,128, NSF-DMS 0305825/0450115, “Computations and applications of periodic Floer homology and contact homology in symplectic geometry” (Sole Principal Investigator)
  • Summer 2005, $3,000, NSF-DMS 0542290 (for REU student)
  • 2000-2003, $N/A, NSF-DMS 9977371 (VIGRE Postdoc)