Monika Ludwig
Professor
Mathematics
- Phone: (718) 260-3095
- Email: mludwig@duke.poly.edu
- Location: Rogers Hall 321F
Education
Technische Universität Wien, Class of 1994
Doctor of Technical Sciences, Mathematics
Technische Universität Wien, Class of 1990
Master degree (Dipl.-Ing.), Mathematics
Experience
Polytechnic Institute of NYU
Professor
From: March 2007 to present
Technische Universität Wien
Associate Professor
From: July 2001 to March 2007
Universität Bern
Visiting Professor
From: February 2002 to July 2002
Polytechnic University
Visiting Scholar
From: September 2000 to July 2001
University College London
Visiting Scholar
From: September 1999 to September 2000
Technische Universität Wien
Assistant Professor
From: March 1994 to September 1999
Courses Taught
- MA2012: Linear Algebra
- MA6403: Differential Geometry
- MA7043: Linear Algebra II
- MA7333: Measure Theory I
- MA7343: Measure Theory II
- MA7683: Topics in Geometry I
- MA7693: Topics in Geometry II
Research Interests
Convex geometry, geometric and analytic inequalities
Awards + Distinctions
- 1998: Hlawka-Prize of the Austrian Academy of Sciences
- 2004: Förderungspreis of the Austrian Mathematical Society
- since 2011: Corresponding Member of the Austrian Academy of Sciences
Event Participation
- Invited address at the Joint Meeting of the Austrian and German Mathematical Societies, Graz, 2009
- Invited address at the AMS Sectional Meeting, Wesleyan University, 2008
Memberships
Grants
NSF DMS-0963819 "Asymptotic geometric analysis", (Coordinator)
Support for US participants of the program "Asymptotic geometric analysis" at the Fields Institute in Toronto.
NSF DMS-0901911 "The State of Geometry and Functional Analysis", (Coordinator)
Travel grant for US participants of the conference "The State of Geometry and Functional Analysis" Tel Aviv University
NSF DMS-0805623 "Affine geometric analysis", (Principle Investigator)
"Valuations on Convex Bodies", (Principle Investigator)
"Phenenoma in High Dimensions", (Coordinator)
Coordinator of the Austrian node of the Research and Training Network "Phenenoma in High Dimensions" supported by the European Community
"Affinely associated bodies", (Principle Investigator)
Journal Articles
- Valuations on Sobolev spaces,
AMERICAN JOURNAL OF MATHEMATICS, in press. - Fisher information and matrix-valued valuations,
ADVANCES IN MATHEMATICS 226, 2700 - 2711 (2011). - Sharp convex Lorentz-Sobolev inequalities,
MATHEMATISCHE ANNALEN 350, 169 - 197 (2011).
Jointly with Jie Xiao and Gaoyong Zhang. - Minkowski areas and valuations,
JOURNAL OF DIFFERENTIAL GEOMETRY 86, 133 - 161 (2010). - A classification of SL(n) invariant valuations,
ANNALS OF MATHEMATICS 172, 1223 -1271 (2010).
Jointly with Matthias Reitzner. - General affine surface areas,
ADVANCES IN MATHEMATICS 224, 2346 - 2360 (2010). - Intersection bodies and valuations,
AMERICAN JOURNAL OF MATHEMATICS 128, 1409 - 1428 (2006). - A characterization of Lp intersection bodies,
INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2006, Art ID 10548, 1 - 29 (2006).
Jointly with Christoph Haberl. - Elementary moves on triangulations,
DISCRETE & COMPUTATIONAL GEOMETRY 35, 527 - 536 (2006).
Jointly with Matthias Reitzner. - Valuations in the affine geometry of convex bodies,
PROCEEDINGS OF THE CONFERENCE ''INTEGRAL GEOMETRY AND CONVEXITY'',
Wuhan 2004, World Scientific, Singapore, 49 - 65 (2006). - Approximation of the Euclidean ball by polytopes,
STUDIA MATHEMATICA 173, 1 - 18 (2006).
Jointly with Carsten Schütt and Elisabeth Werner. - Minkowski valuations,
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 357, 4191 - 4213 (2005). - Ellipsoids and matrix valued valuations,
DUKE MATHEMATICAL JOURNAL 119, 159 - 188 (2003). - Projection bodies and valuations,
ADVANCES IN MATHEMATICS 172, 158 - 168 (2002). - Moment vectors of polytopes,
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO (2) Suppl. 70, part II, 123 - 138 (2002). - Valuations on polytopes containing the origin in their interiors,
ADVANCES IN MATHEMATICS 170, 239 - 256 (2002). - On the semicontinuity of curvature integrals,
MATHEMATISCHE NACHRICHTEN 227, 99 - 108 (2001). - Upper semicontinuous valuations on the space of convex discs,
GEOMETRIAE DEDICATA 80, 263 - 279 (2000). - A characterization of affine surface area,
ADVANCES IN MATHEMATICS 147, 138 - 172 (1999).
Jointly with Matthias Reitzner. - A characterization of affine length and asymptotic approximation of convex discs,
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITÄT HAMBURG 69, 75 - 88 (1999). - Asymptotic approximation of smooth convex bodies by general polytopes,
MATHEMATIKA 46, 103 - 125 (1999). - Approximation of convex bodies and a momentum lemma for power diagrams,
MONATSHEFTE DER MATHEMATIK 127, 101 - 110 (1999).
Jointly with Karoly Böröczky, jr. - Asymptotic approximation by quadratic spline curves,
ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS. SECTIO MATHEMATICA 42, 133 - 139 (1999). - Asymptotic approximation of convex curves; the Hausdorff metric case,
ARCHIV DER MATHEMATIK 70, 331 - 336 (1998). - A Helmholtz-Lie type characterization of ellipsoids, II,
DISCRETE & COMPUTATIONAL GEOMETRY 16, 55 - 67 (1996).
Jointly with Peter M. Gruber. - Asymptotic approximation of convex curves,
ARCHIV DER MATHEMATIK 63, 377 - 384 (1994).
Other Publications
Convex geometry and its applications. Abstracts from the workshop held November 29–December 5, 2009. Organized by Keith Ball, Martin Henk and Monika Ludwig. Oberwolfach Reports. Vol. 6, no. 4. Oberwolfach Rep. 6 (2009), no. 4, 2851–2926
- Valuations on Sobolev spaces,
Biography
- 1990: Master degree (Dipl.-Ing.), Vienna University of Technology
- 1990 - 1994: Vertragsassistentin, Vienna University of Technology
- 1994: Doctor of Technical Sciences sub auspiciis praesidentis, Vienna University of Technology
- 1994 - 2000: Assistant Professor, Vienna University of Technology
- 1998: Hlawka-Prize of the Austrian Academy of Sciences
- 1999 - 2000: Visiting Scholar, University College London
- 2000: Habilitation, Vienna University of Technology
- 2000 - 2001: Visiting Scholar, Polytechnic University New York
- 2000 - 2007: Associate Professor, Vienna University of Technology
- 2002: Visiting Professor, University of Bern
- 2004: Förderungspreis of the Austrian Mathematical Society
- since 2007: Professor of Mathematics, Polytechnic Institute of New York University
- since 2011: Corresponding Member of the Austrian Academy of Sciences