Stefan Müller

Train to Blue Mountains, Australia
Assistant Professor of Mathematics


Office: Math/Physics 2320 (map)

Phone: (912) 478-0874
Fax: (912) 478-0654 (math office)

Email: smueller at georgiasouthern dot edu

About me

I am on leave at Stanford University for the academic year 2017/18. I keep this website up-to-date, so please read on.

I am an Assistant Professor in the Department of Mathematical Sciences at Georgia Southern University. After earning my Ph.D. from the University of Wisconsin-Madison in 2008 under the supervision of my advisor Yong-Geun Oh, I held positions as Research Fellow (Postdoc) in the School of Mathematics at Korea Institute for Advanced Study (KIAS) in Seoul, as Assistant Professor of Mathematics at Penn State University in Altoona, and as Visiting Assistant Professor at the University of Illinois at Urbana-Champaign. I joined Georgia Southern University in 2015. My research is in symplectic and contact geometry, and more specifically, in topological Hamiltonian dynamics and topological contact dynamics, and I am interested in all facets of C^0-symplectic and contact topology. I currently serve on the Colloquium Committee and the Grants and Scholarships Committee in the Department of Mathematical Sciences, and I am an Undergraduate Committee Alternate on the COSM Senate. During the spring 2017 semester, I taught Calculus II and Ordinary Differential Equations, and was a regular speaker in the geometry/topology seminar. See below for details on my research and (current) teaching.

Research and interests

«Mathematics can only be understood backwards; but it must be lived forwards.»
— freely adapted from Søren Kierkegaard, Journals IV A 164 (1843)

Topological Hamiltonian dynamics and topological contact dynamics were developed over the past few years by myself in collaboration with my thesis advisor Yong-Geun Oh and later with Peter Spaeth, partly in an effort to understand the deeper topological structure underlying symplectic and contact topology. These theories have applications to other branches of mathematics including topological dynamics and Riemannian geometry. Most recently, I am interested in a C^0-characterization of symplectic and contact (embeddings) and in J-holomorphic curve methods. To learn more, refer to (the abstracts of) my publications and preprints listed below. At some point I wrote an annotated publications list (pdf) that contains a summary of much of my research (up to that point in time).

Publications and preprints

«The truth is... to overcome the terrible inhibitions that almost every writer faces when he has to stop vaguely talking and dreaming about his work; when the time comes to sit down and write definite text whose short-comings stare bleakly back at their creator...»
— Hans Selye, From Dream to Discovery

Preprints

  • Epsilon-non-squeezing and C^0-rigidity of epsilon-symplectic embeddings, arXiv:1805.01390, 17 pages
  • J-holomorphic disks with pre-Lagrangian boundary conditions, arXiv:1704.02655, 13 pages
  • C^0-characterization of symplectic and contact embeddings and Lagrangian rigidity, arXiv:1607.03135, 45 pages

Publications

Mathematical Reviews for my published papers can be found on MathSciNet. My MR Author ID is 831538. My ORCID identifier (and link to my public record) is 0000-0002-7228-604X.
  • Topological contact dynamics III: uniqueness of the topological Hamiltonian and C^0-rigidity of the geodesic flow, with Peter Spaeth, J. Symplectic Geom. 14 (2016), no. 1, 1–29.
  • Topological contact dynamics I: symplectization and applications of the energy-capacity inequality, with Peter Spaeth, Adv. Geom. 15 (2015), no. 3, 349–380.
  • Gromov's alternative, Eliashberg's shape invariant, and C^0-rigidity of contact diffeomorphisms, with Peter Spaeth, Internat. J. Math. 25 (2014), no. 14, 1450124, 13 pp.
  • Uniform approximation of homeomorphisms by diffeomorphisms, Topology Appl. 178 (2014), 315–319.
  • Topological contact dynamics II: topological automorphisms, contact homeomorphisms, and non-smooth contact dynamical systems, with Peter Spaeth, Trans. Amer. Math. Soc. 366 (2014), no. 9, 5009–5041.
  • Helicity of vector fields preserving a regular contact form and topologically conjugate smooth dynamical systems, with Peter Spaeth, Ergodic Theory Dynam. Systems 33 (2013), no. 5, 1550–1583.
  • On properly essential classical conformal diffeomorphism groups, with Peter Spaeth, Ann. Global Anal. Geom. 42 (2012), no. 1, 109–119.
  • The group of Hamiltonian homeomorphisms in the L^∞-norm, J. Korean Math. Soc. 45 (2008), no. 6, 1769–1784.
  • The group of Hamiltonian homeomorphisms and C^0-symplectic topology, with Yong-Geun Oh, J. Symplectic Geom. 5 (2007), no. 2, 167–219.

Notes

  • A note on the volume flux of smooth and continuous strictly contact isotopies, arXiv:1107.4869, 8 pages

Ph.D. thesis

  • The group of Hamiltonian homeomorphisms and C^0-symplectic topology, Ph.D. thesis, the University of Wisconsin-Madison, 2008, 104+v pages

Recent talks and travel

«When [Erwin Schrödinger] went to the Solvay conferences in Brussels, he would walk from the station to the hotel where the delegates stayed, carrying all his luggage in a rucksack and looking so like a tramp that it needed a great deal of argument at the reception desk before he could claim a room.»
— Paul A. M. Dirac, quoted in Robert L. Weber, Pioneers of Science: Nobel Prize Winners in Physics (1980)

Teaching

«I hear and I forget. I see and I remember. I do and I understand.»
— Chinese Proverb

Calvin & Hobbes doing Math
Teaching is an important part of my job, and I enjoy it very much. If you are a student in one of my MATH 21 classes at Stanford, go the course website at Stanford for more information. Click here for MATH 52 (winter 2018) or MATH 19 (autumn 2017). During the spring 2017 semester, I taught MATH 2242 (Calculus II) Section J and MATH 3230 (Ordinary Differential Equations) Section F. If you were a student in one of these classes, log into Folio and find your course for more information (including the syllabus).

Do you ever struggle with learning/studying? The book Make It Stick is a nice resource for anyone and any subject matter (not only mathematics). If you are a current student at Georgia Southern, you have free access to an online copy through the university's library. (You are encouraged to download up to one chapter at a time and then log out so that others can access the book as well.)