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MK/RC Integralgeometrie

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Ort: 69/E23
Zeiten: Mo. 10:00 - 12:00 (wöchentlich), Mi. 10:00 - 12:00 (wöchentlich)
Erster Termin: Mo , 01.04.2019 10:00 - 12:00, Ort: 69/E23
Veranstaltungsart: Reading Course (Offizielle Lehrveranstaltungen)

Studienbereiche

  • Mathematik > Masterkurse/Reading Courses
  • Mathematik > Master Lehramt an Gymnasien
  • Mathematik > Master Mathematik

Short CV

  • 1990: Master degree (Dipl.-Ing.), Vienna University of Technology
  • 1993: Doctor of Technical Sciences, Vienna University of Technology
  • 1993 - 1999: Vertragsassistent, Vienna University of Technology
  • 1996: Actuary, full member of the Aktuarvereinigung Österreich
  • 1999 - 2001: Assistant Professor, Vienna University of Technology
  • 2001: Habilitation, Vienna University of Technology
  • 2001 - 2009: Associate Professor, Vienna University of Technology
  • 2001 - 2003: Visiting Scholar, University of Freiburg
  • 2003 - 2007: Guest lecturer for Actuarial Mathematics at Universität Salzburg
  • since 2009: Professor of Mathematics, University of Osnabrück
  • since 2011: Director of the Institute of Mathematics
  • 2013 - 2019: Spokesman DFG-Graduiertenkolleg Combinatorial Structures in Geometry
  • since 2016: DAV-Correspondent at the University of Osnabrück

Research Interests

I am interested in problems on the borderline between stochastic and geometry:

  • convex geometry
  • geometric valuation theory
  • stochastic geometry and geometric probabilites
  • random convex hulls and extreme points
  • random mosaics and tessellations
  • random CW-complexes
  • random graphs

Projects

  • 2020 - 2021: Innovation plus (MWK-Nds.) “MaKe WiWi” (jointly with H. Döring, A. Salle, J. Wilde)
  • 2013 - 2018: DFG Graduiertenkolleg “Combinatorial Structures in Geometry”
  • 2008 - 2010: FWF Project “Combinatorial Properties of Random Mosaics”
  • 2007 - 2008: Scientist in charge of the Austrian node of the Marie Curie Research Training Network "Phenomena in High Dimensions"
  • 2005 - 2007: FWF Project "Valuations on convex bodies" (jointly with Monika Ludwig)

  • 2001 - 2003: FWF Project “The geometric structure of random polytopes”

Recent Talks

  • Stars of Empty Simplices. Oberwolfach, December 2018
  • Concentration of Poisson U-Statistics: Subgraph Counts in Random Geometric Graphs. BIRS, Banff, March 2018
  • Monotonicity of Random Polytopes. Convex and Integral Geometry 2017, Frankfurt, September 2017
  • Random Points on a Halfsphere. AMS sectional meeting, Univ. Athens, USA, März 2016
  • Voronoi trifft Poisson: Zufällige Approximation von Mengen, Weihnachtskolloquium, Universität Bochum, Dezember 2013
  • Large deviation inequality for the Gilbert Graph, Oberwolfach, Februar 2013

Publications

Expected mean width of the randomized integer convex hull. Submitted (jointly with B. Hong Ngoc)

The convex hull of random points on the boundary of a simple polytope. Submitted (jointly with C. Schütt, E. Werner)

Stars of Empty Simplices. Submitted (jointly with D. Temesvari)

Facets of high-dimensional Gaussian polytopes. Submitted (jointly with K. Böröczky, G. Lugosi)

Multivariate Central Limit Theorems for Random Simplicial Complexes. Adv. Appl. Math., to appear (jointly with G. Akinwande)

Asymptotic normality for random simplices and convex bodies in high dimensions. Proc. Amer. Math. Soc., to appear (jointly with D. Alonso-Gutiérrez, F. Besau, J. Grote, Z. Kabluchko, C. Thäle, B. Vritsiou, E. Werner)

Gigantic random simplicial complexes. Homology Homotopy Appl. 22, 297-318 (2020) (jointly with J. Grygierek, M. Juhnke-Kubitzke, T. Römer, O. Röndigs)

On the cells in a stationary Poisson hyperplane mosaic. Adv. Geom. 19, 145-150 (2019), (jointly with R. Schneider)

Crossing Numbers and Stress of Random Graphs. In: Biedl. T. and Kerren, A. (eds.): Graph Drawing and Network Visualization. LNCS 11282, p. 255-268 (2018). Springer, Cham (jointly with M. Chimani, H. Döring)

Production Shock Distribution and Risk Aversion in Multi-Agent-Tournaments. Submitted (jointly with B. Hartig)

Concentration for Poisson U-Statistics: Subgraph Counts in Random Geometric Graphs. Stochastic Process. Appl., 128, 3327-3352 (2018), (jointly with S. Bachmann)

Cells with many facets in a Poisson hyperplane tessellation. Adv. Math. 324, 203-240 (2018) (jointly with G. Bonnet, P. Calka)

Random Approximation of Convex Bodies: Monotonicity of the Volumes of Random Tetrahedra.Discrete Comput. Geom. 59, 165-174 (2018) (jointly with S. Kunis und B. Reichenwallner)

Monotonicity of functionals of random polytopes. In: Ambrus, G., Böröczky, K., and Füredi, Z. (eds.): Discrete Geometry and Convexity. p. 23-28 (2017). A. Renyi Institute of Mathematics, Hungarian Academy of Sciences, Hungary (jointly with M. Beermann)

Expected Sizes of Poisson-Delaunay Mosaics and Their Discrete Morse Functions. Adv. Appl. Probab. 49, 745-767 (2017) (jointly with H. Edelsbrunner, A. Nikitenko)

SL(n) invariant valuations on polytopes. Discrete Comput. Geom. 57, 571-581 (2017) (jointly with M. Ludwig)

Random points in halfspheres. Random Structures & Algor. 50, 3-22 (2017),  (jointly with I. B\'ar\'any, D. Hug, und R. Schneider)

Limit theory for the Gilbert graph. Adv. Appl. Math. 88, 26-61 (2017) (jointly with M. Schulte und C. Thäle)

Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry. Editors: Peccati, G., Reitzner, M., Bocconi & Springer Series 7; Bocconi University Press, Springer, Milan (2016)

Introduction to Stochastic Geometry. In: Peccati, G. and Reitzner, M. (eds.): Stochastic Analysis for Poisson Point Processes. p. 145-184 (2016). Bocconi & Springer Series 7; Bocconi University Press, Springer, Milan (jointly with D. Hug

U-statistics in stochastic geometry. In: Peccati, G. and Reitzner, M. (eds.): Stochastic Analysis for Poisson Point Processes. p. 229-253 (2016). Bocconi & Springer Series 7; Bocconi University Press, Springer, Milan (jointly with R. Lachieze-Rey)

On the monotonicity of the moments of volumes of random simplices. Mathematika 62, 949–958 (2016) (jointly with B. Reichenwallner)

Beyond the Efron-Buchta identities: distributional results for Poisson polytopes. Discrete Comput. Geom.  53, 226-244 (2015),  (jointly with M. Beermann)

Poisson polyhedra in high dimensions. Adv. Math. 281, 1-39 (2015) (jointly with J. Hörrmann, D. Hug und C. Thäle)

Poisson point processes: Large deviation inequalities for the convex distance. Electron. Commun. Probab. 18, No. 96, 1-7 (2013)

Central limit theorems for U-statistics of Poisson point processes. Ann. Prob. 41, No. 6, 3879-3909 (2013), (jointly with M. Schulte).

The monotonicity of f-vectors of random polytopes. Electron. Commun. Probab. 18, No. 23, 1-8 (2013) (jointly with O. Devillers, M. Glisse , X. Goaoc, G. Moroz)

Many empty triangles have a common edge. Discrete Comp. Geom. 50, 244-252 (2013), (jointly with I. Barany, J.-F. Marckert).

Set Reconstruction by Voronoi cells. Adv. Appl. Probab. 44, 938-953 (2012) (jointly with E. Spodarev, D. Zaporozhets).

On the variance of random polytopes. Adv. Math. 225, 1986-2001 (2010) (jointly with I. Barany).

A classification of SL(n) invariant valuations. Ann. of Math. (2) 172, 1219-1267 (2010) (jointly with M. Ludwig).

Poisson Polytopes. Ann. Prob. 38, 1507-1531 (2010) (jointly with I. Barany).

Random polytopes. In: Molchanov, I. and Kendall, W. (eds.): New perspectives in stochastic geometry. p. 45-76 (2010). Oxford University Press, Oxford.

Mean width of inscribed random polytopes in a reasonable smooth convex body. J. Multivariate Anal. 100, 2287-2295 (2009), (jointly with K. Böröczky jr., F. Fodor, V. Vigh).

Poisson-Voronoi Approximation. Ann. Appl. Probab. 19, 719-736 (2009), (jointly with M. Heveling).

Elementary moves on triangulations. Discrete Comput. Geom. 35, 527-536 (2006) (jointly with M.Ludwig).

Central limit theorems for random polytopes. Probab. Theory Relat. Fields 133, 483-507 (2005). (Thanks to J. Pardon who pointed out an error in my proof, see Central limit theorems for uniform model random polygons, p.6).

The combinatorial structure of random polytopes. Adv. Math. 191, 178-208 (2005).

Gaussian polytopes: variances and limit theorems. Adv. Appl. Probab. 37, 297-320 (2005) (jointly with D.Hug).

The limit shape of the zero cell in a stationary Poisson hyperplane tesselation. Ann. Prob. 32, 1140-1167 (2004), (jointly with D. Hug und R. Schneider).

Asymptotic mean values of Gaussian polytopes. Beitr. Algebra Geom. 45, 531-548 (2004), (jointly with D.Hug und G.O. Munsonius).

Electromagnetic wave propagation and inequalities for moments of chord lengths. Adv. Appl. Probab. 36, 987-995 (2004), (jointly with J. Hansen).

Large Poisson-Voronoi cells and Crofton cells. Adv. Appl. Probab. 36, 667-690 (2004), (jointly with D. Hug und R. Schneider).

Efficient indoor radio channel modeling based on Integral Geometry. IEEE Transactions on Antennas and Propagation 52, 2456-2463 (2004), (jointly with J. Hansen).

Approximation of smooth convex bodies by random circumscribed polytopes. Ann. Appl. Probab. 14, 239-273 (2004) (jointly with K. Böröczky)

Stochastical approximation of smooth convex bodies. Mathematika 51, 11-29 (2004).

Random polytopes and the Efron-Stein jackknife inequality. Ann. Prob. 31, 2136-2166 (2003).

Random polytopes are nearly best-approximating. Rend. Circ. Mat. Palermo Suppl. 70, 263-278 (2002).

Random points on the boundary of smooth convex bodies. Trans. Amer. Math. Soc. 354, 2243-2278 (2002).

The floating body and the equiaffine inner parallel curves of a convex body. Geom. Dedicata 84, 151-167 (2001).

The convex hull of random points in a tetrahedron: Solution of Blaschke's problem and more general results. J. Reine Angew. Math. 536, 1-29 (2001) (jointly with C. Buchta).

Inequalities for convex hulls of random points. Monatsh. Math. 131, 71-78 (2000).

On Gram-Charlier expansion in risk theory. Working Paper of the Lab. of Act. Math., Univ. Copenhagen 161, 1-30 (1999) (jointly with C. Buchta).

A characterization of affine surface area. Adv. Math. 147, 138-172 (1999) (jointly with M. Ludwig).

On a theorem of G. Herglotz about random polygons. Rend. Circ. Mat. Palermo Suppl. 50, 89-102 (1997) (jointly with C. Buchta).

Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points. Probab. Theory Relat. Fields 108, 385-415 (1997) (jointly with C. Buchta).

Optimaler Selbstbehalt in der Kraftfahrzeug-Haftpflichtversicherung. Nicht zur Veröffentlichung bestimmter Forschungsbericht, Wien, 1995, 59 Seiten (jointly with C. Buchta).

Zufällige Polytope im Tetraeder. Dissertation, TU-Wien (1993).