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Maksim Maydanskiy

maksimm@math.stanford.edu or maydanskiy@math.jussieu.fr

I have moved to Institut de Mathématiques de Jussieu in Paris.

I was a student of Denis Auroux at MIT, and then a researcher at MSRI, Cambridge University, and Stanford University.

Teaching:

In the Spring 2013 quarter I taught Math 53 - Ordinary Differential Equations with Linear Algebra.

In the Fall of 2012 I taught Math 115, Functions of a Real Variable and in the Spring 2012 I taught Math 51, Linear Algebra and Multivariable Differential Calculus.

I sometimes give talks at Berkeley Math Circle and Stanford Math Circle and San Jose Math Circle.

Based on one of the sessions, I have written an exposition on the Baby Hummer card trick, a trick from the Magical Mathematics book by Persi Diaconis and Ron Graham.

I was a mentor at 2008 Research Science Institute.

Research:

My research is in symplectic geometry, with a focus on Floer-theoretic invariants of open symplectic manifolds.

Here are the slides from the special session on Symplectic and Contact geometry at the AMS meeting in Rochester (here are also some old slides from the meeting in Worchester in 2009).

And here are notes on spectral flow in Morse theory. These are to be updated and supplemented with notes on spectral flow in Hamiltonian and Lagrangian Floer homologies.

Papers:

  • The symplectic topology of some rational homology balls, with Yankı Lekili, preprint, 2012, arxiv:1202.5625, accepted, Comm. Math. Helvetici.
  • A dictionary between Legendrian contact homology and Fukaya-Seidel categories, with Sheel Ganatra, published as an appendix to Effect of Legendrian surgery by Frédéric Bourgeois, Tobias Ekholm and Yakov Eliashberg, Geom. Topol. 16 (2012) 301–389.
  • Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres, with Paul Seidel, J. Topol. 3 (2010), no. 1, 157-180.
  • Non-degeneracy of superpotential and semisimplicity of quantum cohomology of smooth toric Fano varieties with facet symmetric associated polytopes, with Benjamin Mirabelli, ERA AMS, 18 (2011), 131 - 143.
  • Exotic symplectic manifolds via Lefschetz Fibrations, preprint, 2009, arxiv:0906.2224, accepted J. Symplectic Geom.
  • The incidence coloring conjecture for graphs of maximum degree 3, Discrete Math. 292 (2005) 131-141.