Contact Info
Károly Böröczky
Scientific Advisor - Director of Erdős Center (On Sabbatical)
His research is mostly related to the geometry of the Euclidean, and to less extent, the hyperbolic spaces. These areas include Isoperimetric type inequalities, Geometry of numbers, Stochastic geometry, and Packing and covering. Recent interest is probabilistic inequalities for density functions. He has written a monograph published by the Cambridge University Press.
Main fields of interest are
- Lattice points in large bodies;
- Minkowski type Monge-Ampere equations, Logarithmic Brunn-Minkowski conjecture;
- Toric varieties, applications to singularities;
- Finite packings and coverings;
- Quasi-crystals;
- Gaussian polytopes, Approximation of convex bodies by polytopes;
- Valuations on convex bodies.
Publications
- Abardia-Evéquoz, Judit; Böröczky, Károly J.; Domokos, Mátyás; Kertész, Dávid SL(m,C)-equivariant and translation covariant continuous tensor valuations. J. Funct. Anal. 276 (2019), no. 11, 3325–3362.
- Böröczky, Károly J.; Fodor, Ferenc The Lp dual Minkowski problem for p>1 and q>0. J. Differential Equations 266 (2019), no. 12, 7980–8033.
- Böröczky, Károly J.; Ludwig, Monika Minkowski valuations on lattice polytopes. J. Eur. Math. Soc. (JEMS) 21 (2019), no. 1, 163–197.
- Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong The logarithmic Minkowski problem. J. Amer. Math. Soc. 26 (2013), no. 3, 831–852.
- Böröczky, Károly J. Strongerng for convex bodies. pdf, GAFA, 18 (2008), 657-667. versions of the Orlicz-Petty projection inequality. J. Differential Geom. 95 (2013), no. 2, 215–247.
- Böröczky, Károly J.; Schneider, Rolf A characterization of the duality mapping for convex bodies. Geom. Funct. Anal. 18 (2008), no. 3, 657–667.
- Böröczky, Károly, Jr. Finite packing and covering. Cambridge Tracts in Mathematics, 154.Cambridge University Press, Cambridge, 2004.
- Böröczky, Károly, Jr. Approximation of general smooth convex bodies. Adv. Math. 153 (2000), no. 2, 325–341.
Prizes and Awards
2015
- Rényi Prize: Alfréd Rényi Institute of Mathematics
2005
- János Bolyai Research Fellowship: Magyar Tudományos Akadémia / Hungarian Academy of Sciences
2004
- Erdős Pál Prize: Magyar Tudományos Akadémia
2001
- János Bolyai Research Fellowship: Magyar Tudományos Akadémia / Hungarian Academy of Sciences