Homepage for Ingo Witt
Postal address
Prof. Dr. Ingo Witt
Mathematical Institute
University of Göttingen
Bunsenstraße 3-5
D-37073 Göttingen
GERMANY
Phone: +49-551-397769
Email: iwitt AT mathematik.uni-goettingen.de
Office hours:
Wednesdays, 4-5 p.m., or by appointment.
My office is located in room 103.
Honors
Scientific interests
Analysis of partial differential equations, microlocal analysis, spectral and scattering theory.
Doctoral students
- Rayhana Darwich: Propagation of polarization sets (starts Oct 2019).
- Santiago Correa: Weakly regular hyperbolic boundary problems of real type.
- Gvantsa Shavardenidze: TBA (joint with Ushagi Goginava, Tbilisi).
- Lasha Baramidze: Generalized bounded variation on Vilenkin groups and convergence of multiple Vilenkin-Fourier series (joint with Ushagi Goginava, Tbilisi).
- Robin Spratte: Paradifferential calculus and conormal distributions.
Master students
A list of my former master and diploma students is here.
Current research projects
Books edited
- Open Quantum Systems - A Mathematical Perspective. Tutor. Sch. Workshops Math. Sci., Birkhäuser/Springer, Cham, 2019 (with D. Bahns and A. Pohl).
- Quantization, PDEs, and Geometry. The Interplay of Analysis and Mathematical Physics. Oper. Theory Adv. Appl., vol. 251, Birkhäuser/Springer, Basel, 2015 (with D. Bahns and W. Bauer).
- Partial Differential Equations and Spectral Theory. Oper. Theory Adv. Appl., vol. 211, Birkhäuser, Basel, 2011 (with M. Demuth and B.-W. Schulze).
- Aspects of Boundary Problems in Analysis and Geometry. Oper. Theory Adv. Appl., vol. 151, Birkhäuser, Basel, 2004 (with J. Gil and T. Krainer).
Recent papers and preprints
- Discrete Morse flow for Ricci flow and porous medium equation. Commun. Nonlinear Sci. Numer. Simul. 59 (2018), 158-164 (with Ma Li).
- Minimal regularity solutions of semilinear generalized Tricomi equations. Pacific J. Math. 296 (2018), 181-226 (with Ruan Zhuoping and Yin Huicheng).
- Global multidimensional shock waves for 2-D and 3-D unsteady potential flow equations. SIAM J. Math. Anal. 50 (2018), 933-1009 (with Li Jun and Yin Huicheng).
- On semilinear Tricomi equations with critical exponents or in two space dimensions. J. Differential Equations 263 (2017), 8102-8137 (with He Daoyin and Yin Huicheng).
- Small data solutions of 2-D quasilinear wave equations under null conditions, Acta Math. Sci. Ser. B Engl. Ed. 38 (2018), 125-150 (with Liu Yingbo).
- On the global existence and blowup of smooth solutions of 3-D compressible Euler equations with time-dependent damping. Pacific J. Math. 292 (2018), 389-426 (with Hou Fei and Yin Huicheng).
- On the global solution problem for semilinear generalized Tricomi equations, I. Calc. Var. Partial Differential Equations 56 (2017), 56:21 (with He Daoyin and Yin Huicheng).
- Blowup time and blowup mechanism of small data solutions to general 2-D quasilinear wave equations. Commun. Pure Appl. Anal. 16 (2017), 719-744 (with Ding Bingbing and Yin Huicheng).
- The small data solutions of general 3-D quasilinear wave equations. II. J. Differential Equations 261 (2016), 1429-1471 (with Ding Bingbing and Yin Huicheng).
- On the existence of low-regularity solutions of semilinear generalized Tricomi equations in mixed-type domains. J. Differential Equations 259 (2015), 7406-7462 (with Ruan Zhuoping and Yin Huicheng).
- The existence and singularity structure of low regularity solutions to higher order degenerate hyperbolic equations. J. Differential Equations 256 (2014), 407-460 (with Ruan Zhuoping and Yin Huicheng).
- The global smooth symmetric solution to 2-D full compressible Euler system of Chaplygin gases. J. Differential Equations 258 (2015), 445-482 (with Ding Bingbing and Yin Huicheng).
- Blowup of classical solutions for a class of 3-D quasilinear wave equations with small initial data. Differential Integral Equations 28 (2015), 941-970 (with Ding Bingbing and Yin Huicheng).
- Liouville theorem for the nonlinear Poisson equation on manifolds. J. Math. Anal. Appl. 416 (2014), 800-804 (with Ma Li).
- On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data. Commun. Contemp. Math. 17 (2015), 1450028, 49 pp. (with Ruan Zhuoping and Yin Huicheng).
- On the lifespan and the blowup mechanism of smooth solutions to a class of 2-D nonlinear wave equations with small initial data. Quart. Appl. Math. 73 (2015), 773-796 (with Ding Bingbing and Yin Huicheng).
- On the blowup and lifespan of smooth solutions to a class of 2-D nonlinear wave equations with small initial data. Quart. Appl. Math. 73 (2015), 219-251 (with Li Jun and Yin Huicheng).
- On the global existence and stability of a multi-dimensional supersonic conic shock wave. Comm. Math. Phys. 329 (2014), 609-640 (with Li Jun and Yin Huicheng).
- On 1-D semilinear generalized Tricomi equations (with He Daoyin and Yin Huicheng).
- On the global solution problem for semilinear generalized Tricomi equations, II, arXiv:1611.07606 (with He Daoyin and Yin Huicheng).
Most preprints are available on the arXiv.
Colloquia and seminars meeting every (or every second) week
Reseach seminars
- Oberseminar "Analysis of Partial Differential Equations."
- In SoSe 2019, we read J. Speck "Shock formation in small-data solutions to 3D quasilinear wave equations."
Math. Surveys Monogr., 214. Amer. Math. Soc., Providence, RI, 2016. (This extends work by D. Christodoulou on the formation of shocks.)
- In WiSe 2018/19, we study the paradifferential calculus in some detail (e.g., harmonic analysis aspects, paralinearization, symbolic calculus)
and also discuss applications.
- Oberseminar "Mathematical Foundations of Quantum Mechanics" (with D. Bahns).
- In SoSe 2019, we read D. Borthwick "Spectral theory of infinite-area hyperbolic surfaces." 2nd ed., Progr. Math., 318.
Birkhäuser/Springer, Cham, 2016. (Not really quantum mechanics, but still related.)
Recent and upcoming events
- Workshop on Partial Differential Equations (on the occasion of Reinhard Racke's 60th birthday), Konstanz, Apr 9-11, 2019.
- Conference "Microlocal and Global Analysis, Interactions with Geometry," Potsdam, Mar 4-8, 2019 (Organizers: S. Azzali, J. Gil, T. Krainer, S. Paycha, E. Schrohe, J. Seiler, I. Witt).
- Summer School on "Operator Algebras, Spectral Theory, and Applications to Topological Insulators," Tbilisi, Sep 17-21, 2018 (Organizers: M. Bakuradze, R. Botchorishvili, U. Goginava, G. Jaiani, R. Meyer, I. Witt).
- Summer School on "Microlocal Methods in Global Analysis," Göttingen, Aug 27-30, 2018 (Organizers: D. Bahns, E. Schrohe, I. Witt). Third in a series of summer schools "Dynamical Approaches in Spectral Geometry" within the framework of the Göttingen SPIRIT Program.
- Conference "MicroLocal and Time-Frequency Analysis 2018" (MLTFA18), Turin, Jul 2-6,2018.
- Walkshop "Mathematical Physics," Brunswick, May 24-25, 2018.
- Lecture series "Weakly stable discontinuities of solutions to multi-dimensional hyperbolic conservation laws," Nanjing Normal University, March 7-21, 2018. Lecture notes will be made available soon.
- Conference "Geometric and Singular Analysis," Potsdam, Feb 19-24, 2018 (Organizers: S. Azzali, W. Bauer, P. Carrillo, S. Coriasco, K. Furutani, S. Paycha, R. Schulz, B.-W. Schulze, B.Vertman, I. Witt).
- Lecture series "Stability of M-D shock waves," Nanjing Normal University, Sep 29 - Oct 11, 2017. Lecture notes will be made available soon.
- Walkshop 2017: Mathematical Physics, LMU München, Jul 6-7, 2017.
- Analysis/Stochastic Analysis Intercontinental, Imperial College London, Jun 26-30, 2017.
- Workshop "Geometric and Singular Analysis," Potsdam, Feb 20-25, 2017 (Organizers: S. Azzali, W. Bauer, S. Coriasco, K. Furutani, S. Paycha, R. Schulz, B.-W. Schulze, J. Seiler, I. Witt).
- Winter School on "Dynamical Methods in Open Quantum Systems," Göttingen, Nov 16-19, 2016 (Organizers: D. Bahns, A. Pohl, I. Witt).
Second in a series of summer schools "Dynamical Approaches in Spectral Geometry" within the framework of the Göttingen SPIRIT Program.
Teaching/Lehre
Im WiSe 2017/18 und SoSe 2018 werde ich die "Differenzial- und Integralrechnung I&II" lesen.
Im Wesentlichen werde ich meinen alten Skripten folgen (mit einigen kleinen Änderungen). Bei dieser Gelegenheit werden auch die Skripten korrekturgelesen und auf einen aktuellen Stand gebracht.
Mit der "Differenzial- und Integralrechung III" im WiSe 2018/19 beginnt dann für Interessierte die Spezialausbildung im Bereich der mathematischen Analysis, die mit dem Zyklus "Analysis of Partial Differential Equations" im Schwerpunkt 1 (WiSe 2019/20 bis SoSE 2021) fortgeführt wird. Dieser Prozess wird durch verschiedene Seminarangebote begleitet werden. Der Stand der Planung, der regelmäßig aktualisiert wird, findet sich hier.
- Skript zur Vorlesung "Differenzial- und Integralrechnung I", WiSe 2011/12
- Skript zur Vorlesung "Differenzial- und Integralrechnung II", SoSe 2012
- Skript zur Vorlesung "Differenzial- und Integralrechnung III", WiSe 2008/09
Frühere Veranstaltungen