

1995  PhD, Yale University, New Haven, CT, USA  1995  1998  Assistant Professor, CAU Kiel  1998  2000  Assistant Professor, University of California, Los Angeles, CA, USA  1999  Habilitation, Kiel  2000  2002  Associate Professor, University of California, Los Angeles, CA, USA  2002  Professor, University of California, Los Angeles, CA, USA  2003  2005  Graduate Vice Chair, Department of Mathematics, University of California, Los Angeles, CA, USA  2006  2009  Chair, Department of Mathematics, University of California, Los Angeles, CA, USA  2010  2011  Visiting Professor, University of Bonn  Since 2012  Hausdorff Chair (W3), Bonn 


My research revolves around basic inequalities in harmonic analysis, in particular inequalities which either possess a large amount of symmetries or have some semblance of such symmetries. Singular integrals and many maximal operators relate to translation and dilation symmetries. Many objects appearing in my work have in addition modulation symmetries, which necessitates to study them with a tool called time frequency analysis. Early examples of this theory are Carleson's theorem on almost everywhere convergence of Fourier series and Lp bounds on the bilinear Hilbert transform. More recently, time frequency analysis was recognized as closely connected with an Lp theory of outer measures.
In recent years I have developed with collaborators twisted technology, a new tool to estimate multi parameter singular integrals with generalized modulation symmetries. A recent highlight of this theory was a result on quantitative norm convergence of ergodic averages relative to two commuting transformations.
Another focus in recent years was on directional operators such as the directional Hilbert transform and directional maximal operators. Major conjectures in the field are named after Stein and Zygmund. With my research group we have studied a multiparameter approach to these problems, which relates them with time frequency anaylsis.
A beautifully symmetric and very difficult object in higher dimensions is the simplex Hilbert transform, the smallest nontrivial example being the triangular Hilbert transform. Lp bounds for these transforms are a major open problem, such bounds would unify many results in harmonic analysis. It appears that one needs to develop a multiscale analysis for arbitrary frames, I expect that the recent breakthrough on the circle of ideas of the Kadison Singer and Feichtinger conjectures might help with that.
Further topics of my interest include nonlinear Fourier analysis and Fourier restriction theorems.


Project “Multilinear estimates in geometric Fourier Analysis”,
within Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”
Annual summer schools on topics in analysis
Organizer, since 2000


Research Area A Analysis means understanding objects as built up from elementary building blocks. In Harmonic Analysis, these building blocks are elementary wave forms. Most of my work is on scaling critical problems in harmonic analysis, where blocks at all possible length scales are present and equally strong. In time frequency analysis, waves at all frequencies are of equal strength as well. My research in time frequency analysis has applications in abstract questions in harmonic analysis as well as in the related areas of differential equations, scattering theory, and ergodic theory, and  since harmonic analysis is very foundational science  more vague connections to a host of other areas in mathematics. 


[ 1] Michael Lacey, Christoph Thiele
L^{p} estimates on the bilinear Hilbert transform for 2<p<∞ Ann. of Math. (2) , 146: (3): 693724 1997 DOI: 10.2307/2952458[ 2] Camil Muscalu, Terence Tao, Christoph Thiele
Multilinear operators given by singular multipliers J. Amer. Math. Soc. , 15: (2): 469496 2002 DOI: 10.1090/S0894034701003794[ 3] Christoph Thiele
A uniform estimate Ann. of Math. (2) , 156: (2): 519563 2002 DOI: 10.2307/3597197[ 4] Camil Muscalu, Jill Pipher, Terence Tao, Christoph Thiele
Biparameter paraproducts Acta Math. , 193: (2): 269296 2004 DOI: 10.1007/BF02392566[ 5] Michael Christ, Xiaochun Li, Terence Tao, Christoph Thiele
On multilinear oscillatory integrals, nonsingular and singular Duke Math. J. , 130: (2): 321351 2005[ 6] Ciprian Demeter, Michael T. Lacey, Terence Tao, Christoph Thiele
Breaking the duality in the return times theorem Duke Math. J. , 143: (2): 281355 2008 DOI: 10.1215/001270942008020[ 7] Richard Oberlin, Andreas Seeger, Terence Tao, Christoph Thiele, James Wright
A variation norm Carleson theorem J. Eur. Math. Soc. (JEMS) , 14: (2): 421464 2012 DOI: 10.4171/JEMS/307[ 8] Michael Bateman, Christoph Thiele
L^{p} estimates for the Hilbert transforms along a onevariable vector field Anal. PDE , 6: (7): 15771600 2013 DOI: 10.2140/apde.2013.6.1577[ 9] Yen Do, Christoph Thiele
L^{p} theory for outer measures and two themes of Lennart Carleson united Bull. Amer. Math. Soc. (N.S.) , 52: (2): 249296 2015 DOI: 10.1090/S027309792014014740[ 10] P. Durcik, V. {Kova\v c}, C. Thiele
Powertype cancellation for the simplex Hilbert transform to appear in J. Anal. Math. 2017



• Illinois Journal of Mathematics (Editor, since 2003)
• Mathematical Research Letters (Editor, 2004  2006)
• Collectanea Mathematica (Editor, since 2006)
• Mathematische Zeitschrift (Editor, since 2014)


1987  Participant of the International Physics Olympiad, Jena, GDR  1987  Bundeswettbewerb Mathematik, Germany, 1. Prize  1989  1993  Scholarship of the German National Scholarship Foundation  2000  Salem Prize  2005  Faculty/Staff Partnership Award  2010  Humboldt Research Award 


2002  Invited speaker, ICM, Beijing, China  2004  Invited speaker, AMS Western Sectional Meeting, Los Angeles, CA, USA  2004  CBMS conference series, main lecturer, May 2004, Atlanta, GA, USA 



Stephanie Molnar (2005): “Sharp Growth Estimates for T(b) Theorems”,
now Associate Professor and Chair, University of Portland, OR, USA
Silvius Klein (2005): “Spectral Theory for Discrete OneDimensional QuasiPeriodic Schrödinger Operators”,
now Postdoc IMPA and tenure track PUC, Rio de Janeiro, Brasil
YaJu Tsai (2005): “SU(2) Nonlinear Fourier Transform”,
now Assistant Professor, National Taiwan University
Victor Lie (2009): “Relational Timefrequency Analysis”,
now Assistant Professor, Purdue University, IN, USA
Zubin Gautam (2009): “Two Geometric Obstruction Results in Harmonic Analysis”,
now Associate at WilmerHale
Yen Do (2010): “A nonlinear stationary phase method for oscillatory RiemannHilbert problems”,
now Assistant Professor, University of Virginia, VA, USA
Vjekoslav Kovac (2011): “Applications of the Bellman Function Technique in Multilinear and Nonlinear Harmonic Analysis”,
now Assistant Professor, University of Zagreb, Croatia
Shaoming Guo (2015): “Hilbert transforms and maximal operators along planar vector fields”,
now Postdoc, Indiana University, Bloomington, IN, USA


 Master theses: 3
 PhD theses: 7, currently 5


Download Profile 