Jiří's UIUC Page

Jiří Lebl
J.L. Doob Research Assistant Professor

Jump to: [Teaching] [Research Interests] [Publications] [Software] [Random Stuff]

Office: 105 Altgeld Hall
Office hours: MW 11:00am-11:50am and at other times by appointment
Office Phone: (217) 333-3143
Email: jle...@math.uiuc.edu

Postdoc (i.e. grad student emeritus) in mathematics at UIUC. Wearer of hats (hat in fact, I only have one) and silly colored socks. Degrees and such nonsense: BA is from SDSU (2001), MA from SDSU (2003), PhD from UCSD (2007). Notice that I frequent universities with 4-letter acronyms. Here is my partial mathematics genealogy. And finally, Markéta's page.

Teaching

Current:
Math 444 Fall 2009

Past:
Math 380 Fall 2007, Math 124 Spring 2008, Math 286 Fall 2008, Math 286 Spring 2009, Math 225 Spring 2009.

Research Interests, CV, etc...

Current interests: Complex analysis, CR geometry and also applications of computers to research. In particular, real analytic CR submanifolds, Levi-flat hypersurfaces, singular real and complex varieties, proper holomorphic mappings between balls. MSC: 32, 14. I am also interested in and/or have published papers which touched on 5, 11, 30, 35, 68.

See my Research Statement and my Curriculum Vitae. May be slightly out of date. For up to date publication list, see below.

I hold the NSF grant DMS-0900885 for 2009-2012 titled Singularities and Complexity in CR Geometry.

Mathematics Publications and Preprints

Jiří Lebl and Han Peters, Polynomials constant on a hyperplane and CR maps of hyperquadrics, preprint arXiv:0910.2673.

Jiří Lebl, Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics, preprint arXiv:0906.0325.

Jiří Lebl, Pullback of varieties by finite maps, preprint arXiv:0812.2498.

Jiří Lebl and Daniel Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, preprint arXiv:0808.0284.

Jiří Lebl, Singular Levi-flat hypersurfaces in complex projective space, preprint arXiv:0805.1763.

John P. D'Angelo and Jiří Lebl, On the complexity of proper holomorphic mappings between balls, Complex Variables and Elliptic Equations, 54 (2009), nos. 2-3, 187-204, MR2513534, DOI:10.1080/17476930902759403, arXiv:0802.1739.

Jiří Lebl, Levi-flat hypersurfaces with real analytic boundary, to appear in Transactions of the American Mathematical Society, preprint arXiv:0710.3801.

John P. D'Angelo and Jiří Lebl, Complexity results for CR mappings between spheres, International Journal of Mathematics, 20 (2009), no. 2, 149-166, MR2493357, DOI:10.1142/S0129167X09005248, arXiv:0708.3232.

Jiří Lebl, Singularities and complexity in CR geometry, PhD thesis, University of California at San Diego, Spring 2007.

Jiří Lebl, Extension of Levi-flat hypersurfaces past CR boundaries, Indiana University Mathematical Journal, 57 (2008), no. 2, 699-716, MR2414332, DOI:10.1512/iumj.2008.57.3203, arXiv:math.CV/0612071. Further notes / additions

John P. D'Angelo, Jiří Lebl, and Han Peters, Degree estimates for polynomials constant on a hyperplane, Michigan Mathematical Journal, 55 (2007), no. 3, 693-713, MR2372622, arXiv:math.CV/0609713. Further notes / additions

Jiří Lebl, Nowhere minimal CR submanifolds and Levi-flat hypersurfaces, Journal of Geometric Analysis, 17 (2007), no. 2, 321-342, MR2320166, arXiv:math.CV/0606141.

Jiří Lebl, Quasiconformal extensions of quasisymmetric mappings, Masters thesis, SDSU, Spring 2003.

[List of my papers on arXiv] [Recent papers in Complex Variables on arXiv]

Textbooks/Notes

Notes on Diffy Qs: Differential Equations for Engineers. The notes follow the syllabus of Math 286 at UIUC (but they also include a chapter on Laplace transform which is not covered in Math 286). These notes can be used as a stand alone textbook. 252 pages, available as a PDF download (free) or get it as cheap paperback. It is also browsable as webpages.

Human Publications

Maia Karolína Lebl (coauthored with Markéta), 3.2kg (7.1 lb), July 27th 2006.

Mathematics Presentations

(Only conference talks here)

Uniqueness of certain polynomials constant on a hyperplane, Applications of Computer Algebra 2009, Montréal, Canada.

Singular Levi-flat hypersurfaces in complex projective space, Conference on Complex and CR Geometry, Partial Differential Equations and Invariant Theory in honor of Joseph J. Kohn, July 2008, Prague, Czech Rep.

Singular Levi-flat hypersurfaces in complex projective space, CIRM - CR-Geometry and PDE's - III, June 2008, Levico Terme, Italy.

Levi-flat hypersurfaces with real analytic boundary, Special session CMS meeting, December 2007, London, ON.

Extensions of Levi-flat hypersurfaces past CR boundaries, Special session AMS meeting, October 2007, Chicago, IL.

Singularities of Levi-Flat Hypersurfaces, International Conference in PDE, Complex Analysis, and Differential Geometry, June 2006, Notre Dame, IN.

Mathematics Computer Software

Genius - A free software (GPL) mathematics package for Unix/Linux (also works on MacOS X). See the website for more information and the latest release. Some sort of release is usually included in most linux software repositories (e.g. universe in Ubuntu). I have been working on this since about '97 and it is quite capable nowdays.

Not Really Publications

Seminar notes: Several Complex Variables are Better than One. Here are the notes from the seminar on Hartogs theorem and some of its consequences given in Food for Thought seminar on Feb 2nd '06. Get the notes in PDF here. Large font was for me, if you want smaller font get the tex file.

After my masters thesis defense I had some free time and dabbled crypto for a bit (I was taking a crypto class at SDSU) and there was a final project, so I wrote up a short paper where I came up with two new toy public key crypto systems (not useful, but perhaps the ideas could be refined). Anyway this is from May 2003 "Toy Public Key Cryptography" (PDF) (or as postscript)

I went on a holiday in Hawaii with Markéta (we married after we got back from there) and so obviously I brought the MAA Monthly and solved a few problems. Here's 10998 as postscript or latex (appeared in the December 2004 issue), and 11002 as postscript or latex (both done circa spring 2003). We've been to Hawaii since, but I didn't really spend much time at all on math then, maybe I'm not such a huge geek after all.

Some unfinished (and never will be finished) research on counting b-nary fraction sequences summing to 1. Here as postscript file (circa summer 2002). Unfortunately after I did the main counting result I then found that this was already published in the 70's (MR 50:1767) (concentrating on b=2 and done with simpler formulas). I haven't actually found anything really new beyond that. Thus endeth my brief excursion into combinatorics and info theory.

Also I've written quite a few of the encyclopedia entries on Planetmath. Unfortunately it has been overrun by cranks and there doesn't seem to be the will to kick them off. I am thinking of forking planetmath to save the good parts of the encyclopedia (90% is good I would say) but the presence of inaccurate, nonsensical, or sometimes just plain wrong entries undermines credibility of the website.

Random Things, Pictures, Etc...

I always used to write a blog, before it was called a blog. I tend to write things very sporadically. I've recently opened a blog at wordpress instead of advogato since they allow latex. So go read my blog.

If you are interested in a dead tree version of my thesis, some of my strange czech poetry, or some photobooks, or whatever else I've put on lulu ... see my lulu page.

Here are some pictures from the MSRI, CR Geometry workshop in 2005. Not really pictures from the workshop, but more from walking around Berkeley. And here are some pictures from the AIM workshop on CR complexity in Septermber 2006. In similar spirit. There are some other pictures from conferences and random other things at our galleries: old gallery, new gallery

If you ever wondered what a five-legged goat looks like, see Goat Love, Inc.

See my non-math home page for other boring info including some more math stuff.