Profile
Profile

Prof. Dr. Christoph Thiele

Hausdorff Chair

E-mail: thiele(at)math.uni-bonn.de
Phone: +49 228 73 62254
Homepage: http://www.math.uni-bonn.de/people/thiele/
Room: 3.010
Location: Mathematics Center
Institute: Mathematical Institute
Research Area: Research Area A
Mathscinet-Number: 336659

Academic Career

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

Research Profile

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.

Research Projects and Activities

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

Contribution to Research Areas

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.

Selected Publications

[1] Michael Lacey, Christoph Thiele
Lp estimates on the bilinear Hilbert transform for 2<p<∞
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

Publication List

Editorships

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

Awards

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

Selected Invited Lectures

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

Habilitations

Mariusz Mirek (2016)

Selected PhD students

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 Postdoc IMPA and tenure track PUC, Rio de Janeiro, Brasil

Ya-Ju Tsai (2005): “SU(2) Non-linear Fourier Transform”,
now Assistant Professor, National Taiwan University

Victor Lie (2009): “Relational Time-frequency 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 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

Supervised Theses

  • Master theses: 3
  • PhD theses: 7, currently 5
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