Office: 711 Van Vleck
Office hours: Tue 2:25pm-3:55pm, Thu 2:25pm-3:30pm, or by appointment at other times
Office phone: (608) 262-3298
Email: lebl at math dot wisc dot edu
Mathematician at UW-Madison, wearer of hats and colored socks (odd pairs only). Degrees: PhD from UCSD (2007), my BA and MA are from SDSU (2001, 2003). I spent 2007-2010 as a postdoc at UIUC, and the 2010-2011 year visiting UCSD. Here is my partial mathematics genealogy. I usually write my name without the diacritical signs as Jiri Lebl. I sometimes use the name George to ease pronunciation.
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 that touched on 5, 11, 30, 35, 68.
I hold the NSF grant DMS-0900885 for 2009-2013 titled Singularities and Complexity in CR Geometry ($99,898).
Math 322 Fall 2012, Math 621 Fall 2012, UW Math 522 Spring 2012, UW Math/CS 240 Spring 2012, UW Math 521 Fall 2011, UW Math 213 Fall 2011, UCSD Math 140B Spring 2011, UCSD Math 20B Spring 2011, UCSD Math 10C Winter 2011, UCSD Math 140A Winter 2011, UCSD Math 20C Fall 2010, UCSD Math 20D Fall 2010, UIUC Math 285 Spring 2010, UIUC Math 595 Spring 2010, UIUC Math 444 Fall 2009, UIUC Math 225 Spring 2009, UIUC Math 286 Spring 2009, UIUC Math 286 Fall 2008, UIUC Math 124 Spring 2008, UIUC Math 380 Fall 2007.
Jiří Lebl, André Minor, Ravi Shroff, Duong Son, and Yuan Zhang, CR singular images of generic submanifolds under holomorphic maps, preprint arXiv:1205.5309.
Dusty Grundmeier, Jiří Lebl, and Liz Vivas, Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics, preprint arXiv:1110.4082.
Jennifer Halfpap and Jiří Lebl, Signature pairs of positive polynomials, to appear in Bulletin of the Institute of Mathematics, Academia Sinica, New Series, arXiv:1211.0997.
Orest Bucicovschi and Jiří Lebl, On the continuity and regularity of convex extensions, to appear in Journal of Convex Analysis, arXiv:1012.5796.
Jiří Lebl and Han Peters, Polynomials constant on a hyperplane and CR maps of spheres, to appear in Illinois Journal of Mathematics, arXiv:1105.2343.
John P. D'Angelo and Jiří Lebl, Pfister's theorem fails in the Hermitian case, Proceedings of the American Mathematical Society, 140 (2012), 1151-1157, MR2869101, DOI:10.1090/S0002-9939-2011-10841-4, arXiv:1010.3215.
Jiří Lebl, Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics, Michigan Mathematical Journal, 60 (2011), no. 3, 603-628, MR2861091, DOI:10.1307/mmj/1320763051, arXiv:0906.0325.
Jiří Lebl and Daniel Lichtblau, Uniqueness of certain polynomials constant on a line, Linear Algebra and its Applications, 433 (2010), no. 4, 824-837, MR2654111, DOI:10.1016/j.laa.2010.04.020, arXiv:0808.0284. See also the addendum arXiv:1302.1441.
John P. D'Angelo and Jiří Lebl, On the complexity of proper holomorphic mappings between balls, Complex Variables and Elliptic Equations, 54 (2009), nos. 3-4, 187-204, MR2513534, DOI:10.1080/17476930902759403, arXiv:0802.1739.
Jiří Lebl, Levi-flat hypersurfaces with real analytic boundary, Transactions of the American Mathematical Society, 362 (2010), no. 12, 6367-6380, MR2678978, DOI:10.1090/S0002-9947-2010-04887-1, 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, 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, DOI:10.1307/mmj/1197056463, arXiv:math.CV/0609713. Further notes / additions
Jiří Lebl, Addendum to Uniqueness of certain polynomials constant on a line, arXiv:1302.1441.
Jiří Lebl, Pullback of varieties by finite maps, arXiv:0812.2498. Note: A stronger theorem is "in the works."
Jiří Lebl, Singularities and complexity in CR geometry, PhD thesis, University of California, San Diego, Spring 2007.
Jiří Lebl, Quasiconformal extensions of quasisymmetric mappings, Masters thesis, SDSU, Spring 2003.
|Notes on Diffy Qs: Differential Equations for Engineers. A textbook for an undergraduate level course on differential equations broadly aimed at engineers or other technical fields. Covers first and second order ODE, systems of linear ODEs, Fourier series methods and PDEs, boundary and eigenvalue problems, Laplace transform, power series methods. Grew out of my notes for Math 286 at UIUC. It has been and is being used at a number of different schools from community college level, to top research schools. It has been adopted as a standard book at UC-Irvine. 315 pages, available as a PDF download (free) or get it as cheap paperback. It is also browsable as web pages.|
|Basic Analysis: Introduction to Real Analysis. A textbook for a proof-based undergraduate real analysis course. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces. It started its life as my notes for Math 444 at UIUC. It has been and is being used at a number of different schools and even been adopted as a standard book at a few. 192 pages, available as a PDF download, or get it as cheap paperback.|
|Hermitian Forms Meet Several Complex Variables: Minicourse on CR Geometry Using Hermitian Forms. A set of notes for a half-semester graduate mini-course on Hermitian forms and CR geometry given at UIUC in the spring of 2010. Should serve as a quick introduction to the subject of CR geometry from a somewhat different viewpoint than is usual. 62 pages, available as a PDF download.|
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 nowadays.
Signature pairs of positive polynomials, Joint Mathematical Meetings, AMS special session, January 2013, San Diego, CA. (slides)
Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics, International Workshop on Several Complex Variables and Complex Geometry, July 2012, Taipei, Taiwan. (slides with typos corrected)
Polynomials constant on a hyperplane and CR maps of spheres, RTG Workshop on Complex Analysis, October 2011, Ann Arbor, MI. (slides)
Poster Singular set of a Levi-flat hypersurface is Levi-flat, VI Workshop on Geometric Analysis of PDE and Several Complex Variables, August 2011, Serra Negra, Brazil. (the poster in pieces)
Hermitian forms and rational maps of hyperquadrics, CIRM - CR-Geometry and PDE's - IV, June 2010, Levico Terme, Italy.
Polynomials constant on a hyperplane and CR maps of spheres, Special session AMS meeting, March 2010, Lexington, KY.
Hermitian forms and rational maps of hyperquadrics, RTG Workshop on Holomorphic Maps and Iterations, March 2010, Ann Arbor, MI. (slides)
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.
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 into cryptography 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 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).
Some very old unfinished (and never will be finished) research on counting b-nary fraction sequences summing to 1. Here as postscript file (circa summer 2002). After I got the main counting result I found it 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.
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 was thinking of forking planetmath to save the good parts of the encyclopedia, but have not had (and likely will not have) the time to do so. 90% is good I would say, but the presence of inaccurate, nonsensical, or sometimes just plain wrong entries undermines credibility of the website.
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 hardcopy version of some of the notes above, 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 September 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.