Yevgeny Liokumovich

I am a Postdoctoral Associate / Pure Math Instructor at MIT. My postdoctoral mentor is Larry Guth. My research is partially supported by NSF DMS-1711053 (2017-2020).

Previously I was a Chapman Fellow at Imperial College London for one year. My postdoctoral mentor at Imperial was Andre Neves. I also was a short-term visitor at Max Planck Institute in Bonn for two months.

I got my PhD in June 2015 from the University of Toronto under the supervision of Alexander Nabutovsky and Regina Rotman.

I am working on problems in Almgren-Pitts Min-Max Theory, Quantitative Topology, Metric Geometry.

Papers

- “On the existence of unstable minimal Heegaard surfaces” (with D. Ketover), math arXiv:1709.09744

- “Area of convex disks” (with G.R. Chambers, C. Croke and H. Wen), to appear in Proc. Amer. Math. Soc., math arXiv:1701.06594

- “Existence of minimal hypersurfaces in complete manifolds of finite volume” (with G.R. Chambers), math arXiv:1609.04058

- “Weyl law for the volume spectrum” (with F. C. Marques and A. Neves), to appear in Annals of Mathematics, math arXiv:1607.08721.

- “Determinantal variety and bilipschitz equivalence” (with K.U. Katz, M.G. Katz and D. Kerner), to appear in J. Topol. Anal., math arXiv:1602.01227

- “Optimal sweepouts of a Riemannian 2-sphere” (with G. R. Chambers), to appear in J. Eur. Math. Soc., math arXiv:1411.6349

- “Splitting a contraction of a simple curve traversed m times” (with G. R. Chambers), J. Topol. Anal. Vol. 9, No. 3 (2017) 409–418.

- “Lengths of three simple periodic geodesics on a Riemannian 2-sphere” (with A. Nabutovsky and R. Rotman), Math. Ann. (2017) 367:831–855, math arXiv:1410.8456

- “Width, Ricci curvature and minimal hypersurfaces” (with P. Glynn-Adey), J. Diff. Geom. Vol. 105 (2017), 33-54.

- “Sweeping out 3-manifold of positive Ricci curvature by short 1-cycles via estimates of min-max surfaces” (with X. Zhou), Int. Math. Res. Not. (IMRN) (2016), math arXiv:1510.02896

- “Families of short cycles on Riemannian surfaces”, Duke Math. J. 165 (2016), no. 7, 1363-1379.

- “Contracting the boundary of a Riemannian 2-disc” (with A. Nabutovsky and R. Rotman), Geom. Funct. Anal. (GAFA), Vol. 25 (2015), 1543-1574.

- “Slicing a 2-sphere”, J. Topol. Anal. Vol. 06 (2014), No. 04, 573-590.

- “Converting homotopies to isotopies and dividing homotopies in half in an effective way” (with G. R. Chambers), Geom. Funct. Anal. (GAFA) Vol. 24 (2014), 1080-1100.

- “Surfaces of small diameter with large width”, J. Topol. Anal. Vol. 06 (2014), No. 03, 383-396, 2013.

- “Spheres of small diameter with long sweep-outs”, Proc. Amer. Math. Soc. 141 (2013), 309-312.

Teaching

Fall semester of 2017: Multivariable Calculus 18.02

Fall semester of 2016: Multivariable Calculus 18.02