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| 1995 | PhD, Yale University, New Haven, CT, USA | | 1995 - 1998 | Assistant, University of 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 |
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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 multi-parameter 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 non-trivial 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 multi-scale 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.
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Project “Multilinear estimates in geometric Fourier Analysis”,
within Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”
Principal Investigator
Annual summer schools on topics in analysis
Organizer, since 2000
DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Principal Investigator
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[ 1] Michael Lacey, Christoph Thiele
Lp estimates on the bilinear Hilbert transform for 2<p<â??
Ann. of Math. (2) , 146: (3): 693--724
1997
DOI: 10.2307/2952458[ 2] Camil Muscalu, Terence Tao, Christoph Thiele
Multi-linear operators given by singular multipliers
J. Amer. Math. Soc. , 15: (2): 469--496
2002
DOI: 10.1090/S0894-0347-01-00379-4[ 3] Christoph Thiele
A uniform estimate
Ann. of Math. (2) , 156: (2): 519--563
2002
DOI: 10.2307/3597197[ 4] Camil Muscalu, Jill Pipher, Terence Tao, Christoph Thiele
Bi-parameter paraproducts
Acta Math. , 193: (2): 269--296
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): 321--351
2005[ 6] Ciprian Demeter, Michael T. Lacey, Terence Tao, Christoph Thiele
Breaking the duality in the return times theorem
Duke Math. J. , 143: (2): 281--355
2008
DOI: 10.1215/00127094-2008-020[ 7] Richard Oberlin, Andreas Seeger, Terence Tao, Christoph Thiele, James Wright
A variation norm Carleson theorem
J. Eur. Math. Soc. (JEMS) , 14: (2): 421--464
2012
DOI: 10.4171/JEMS/307[ 8] Michael Bateman, Christoph Thiele
Lp estimates for the Hilbert transforms along a one-variable vector field
Anal. PDE , 6: (7): 1577--1600
2013
DOI: 10.2140/apde.2013.6.1577[ 9] Yen Do, Christoph Thiele
Lp theory for outer measures and two themes of Lennart Carleson united
Bull. Amer. Math. Soc. (N.S.) , 52: (2): 249--296
2015
DOI: 10.1090/S0273-0979-2014-01474-0[ 10] P. Durcik, V. Kovac, C. Thiele
Power-type cancellation for the simplex Hilbert transform
to appear in J. Anal. Math.
2017 |
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• Illinois Journal of Mathematics (Editor, 2003 - 2009)
• Mathematical Research Letters (Editor, 2004 - 2006)
• Collectanea Mathematica (Editor, since 2006)
• Mathematische Zeitschrift (Editor, since 2014)
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| 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 |
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| 2002 | Invited speaker, International Congress of Mathematicians, Beijing, China | | 2004 | Invited speaker, AMS Western Sectional Meeting, Los Angeles, CA, USA | | 2004 | CBMS conference series, main lecturer, May, Atlanta, GA, USA | | 2011 | Stein Conference, Prinecton, NJ, USA | | 2014 | EMS Summer School, Santalo, Spain | | 2015 | IMPA Conference on Current Trends in Analysis & PDEs, Rio de Janeiro, Brazil | | 2017 | Harmonic Analysis and Related Areas, Clay Research Workshop, Oxford, England, UK |
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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 One-Dimensional Quasi-Periodic Schrödinger Operators”,
now Assistant Professor, PUC, Rio de Janeiro, Brasil
Victor Lie (2009): “Relational Time-frequency Analysis”,
now Assistant Professor, Purdue University, IN, USA
Yen Do (2010): “A nonlinear stationary phase method for oscillatory Riemann-Hilbert 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
Polona Durcik (2017): “The continuous analysis of entangled multilinear forms and applications”,
now Postdoc, California Institute of Technology, CA, USA
Gennady Uraltsev (2017): “Time-Frequency Analysis of the Variational Carleson Operator using outer-measure Lp spaces”,
now Postdoc, Cornell University, NY, USA
Joris Roos (2017): “Singular integrals and maximal operators related to Carleson's theorem and curves in the plane”,
now Postdoc, UW Madison, WI, USA
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- Master theses: 4
- PhD theses: 11, currently 4
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