Institute of
Discrete Mathematics and Geometry

Michael Drmota

Dean of the Faculty of Mathematics and Geoinformation
Full Professor for Discrete Mathematics

Phone:		+43-1-58801/10450
Fax:		+43-1-58801/10499
Email:		michael.drmota@tuwien.ac.at
Address:		Institut für Diskrete Mathematik und Geometrie, TU Wien Wiedner Hauptstrasse 8–10, A–1040 Wien, Austria Freihaus, Tower A, 5th floor, room DAO5H22

Picture by: Thomas Blazina Fotografie

Short Curriculum Vitae

• 1986: Master's degree (Dipl.-Ing.), TU Wien
• Since 1986: Univ. Assistant, TU Wien
• 1986: Doctor of Technical Sciences, TU Wien
• 1990: Habilitation, TU Wien
• 9/1992: Visiting Professor at University Paris VI
• 1992: Hlawka-Prize of Austrian Academy of Sciences
• 1996: Foerderungspreis of the Austrian Mathematical Society
• 9/1999: Visiting Professor at Université de Versailles
• 2000-2007: Editor in Chief of Internationale Mathematische Nachrichten of the Austrian Mathematical Society
• 2/2001: Visiting Professor at Université de Provence (Marseille)
• Since 2002: Field Editor, since 2006: Managing Section Editor of Discrete Mathematics and Theoretical Computer Science, , section Analysis of Algorithms
• 2004-2012: Head of "Institute of Discrete Mathematics and Geometry"
• Since 2005: Editor of Contributions to Discrete Mathematics.
• 2006-2012: Speaker of the FWF National Research Network Analytic Combinatorics and Probabilistic Number Theory.
• Since 2006: Editor of Uniform Distribution Theory.
• Since 2006: Full Professor for "Discrete Mathematics" (TU Wien).
• 2008-2009: Vice President, 2010-2013 President of the Austrian Mathematical Society.
• Since 2011: Editor of Mathematische Semesterberichte.
• 2013-2015: Dean of the Faculty of Mathematics and Geoinformation (TU Wien)
• Since 2013: Corresponding Member of the Austrian Academy of Sciences .

Projects

• 2013-2016: FWF Project Part Shape Characteristics of Planar Maps and Planar Graphs of the SFB Algorithmic and Enumerative Combinatorics.
• 2006-2012: FWF National Research Network Analytic Combinatorics and Probabilistic Number Theory
• 2000-2005: FWF Project Statistical Properties of Number Systems
• 2000-2003: TU-Wien Research Area Analysis of Algorithms
• 2001-2002: Amadee-Project with Université de Versailles : Probabilistic Analysis of Data Structures
• 1996-1999: FWF Project Multivariate Asymptotic Expansions in Combinatorics

Editorial Duties

• Editor of Online Journal of Analytic Combinatorics
• Editor of Contributions to Discrete Mathematics
• Editor of Discrete Mathematics and Theoretical Computer Science,
• Editor of Uniform Distribution Theory
• Editor of Mathematische Semesterberichte
• Guest Editor of Combinatorics, Probability & Computing #4/5 (2004), special issue for the Eighth Seminar on Analysis of Algorithms , June 23-29, 2002, Strobl, Austria. [pdf]
• Editor of Mathematics and computer science. III. Algorithms, trees, combinatorics and probabilities, Proceedings of the 3nd International Colloquium held at the University of Technology Vienna, September 13--17, 2004. Coedited by Philippe Flajolet, Daniele Gardy, and Bernhard Gittenberger. Trends in Mathematics. Birkhauser Verlag, Basel, 2004.
• Guest Editor of INTEGERS, special issue for Number Theoretic Algorithms and Related Topics, September 27 - October 1, 2004, Strobl, Austria.

Research Interests

• Number Theory
• Combinatorial Enumeration and Analysis of Algorithms
• Stochastic Processes in Combinatorial Structures

Recent Manuscripts

• Scaling Limit of Random k-Trees (with Emma Jin), submitted.
• The discrepancy of generalized Van-der-Corput sequences , submitted.
• Asymmetric Renyi Problem (with A. Magner and W. Szpankowski), submitted.
• An Asymptotic Analysis of Labeled and Unlabeled k-Trees (with Emma Yu Jin), Algorithmica, to appear.
• Stochastic Analysis of the Extra Clustering Model for Animal Grouping (with Michael Fuchs and Yi-Wen Lee), submitted
• The Thue Morse Sequence along Squares is Normal (with Christian Mauduit and Joel Rivat), submitted.
• Pursuing the Giant in Random Graph Processes (with Mihyun Kang and Konstantinos Panagiotou), submitted.
• Systems of Functional Equations and Infinite Dimensional Gaussian Limiting Distributions in Combinatorial Enumeration (with Bernhard Gittenberger and Johannes Morgenbesser), submitted.

Books and Proceedings

• Sequences, Discrepancies, and Applications (with R. Tichy), Lecture Notes in Mathematics 1651, Springer, Berlin, 1997, 503 p. (ISBN: 3-540-62606-9).
• Mathematics and computer science. III. Algorithms, trees, combinatorics and probabilities, Proceedings of the 3nd International Colloquium held at the University of Technology Vienna, September 13--17, 2004. Michael Drmota, Philippe Flajolet, Daniele Gardy and Bernhard Gittenberger eds. Trends in Mathematics. Birkhauser Verlag, Basel, 2004.
• Mathematik für Informatik (with B. Gittenberger, G. Karigl, and A. Panholzer), Heldermann, 2007.
• Random Trees, Springer, Wien-New York, 2009.
• ITSL 2008: Proceedings of the 2008 International Conference on Information Theory and Statistical Learning held in Las Vegas, July 14-17, 2008. Matthias Dehmer, Michael Drmota, and Frank Emmert-Streib eds. CSREA Press, 2008.
• Chapter: Analytic Combinatorics on Random Graphs (with B. Gittenberger), in Analysis of Complex Networks, Matthias Dehmer and Frank Emmert-Streib eds, Wiley-Blackwell, 2009.
• Chapter: Analysis of digital functions and applications (with P. Grabner), in Combinatorics, Automata and Number Theory, Valerie Berthe and Michel Rigo eds, Cambridge University Press, 2010.
• AofA'10: Proceedings of the 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms held in Vienna, June 28 - July 2, 2010. Michael Drmota and Bernhard Gittenberger eds. DMTCS proc. AM

Recent Publications

• Formulae and asymptotics for coefficients of algebraic functions (with Cyril Banderier), Combinatorics, Probability and Computinge 24, Special Issue 01, 1-53, 2015.
• Disproof of a conjecture of Rademacher on partial fractions (with Stefan Gerhold), Proc. AMS Ser. B Volume 1, Pages 121-134 (November 21, 2014) S 2330-1511(2014)00014-6
• The maximum degree of random planar graphs (with Omer Gimenez, Marc Noy, Konstantinos Panagiotou, and Angelika Steger), Proc. London Math. Soc. (2014) doi: 10.1112/plms/pdu024, First published online: June 17, 2014
• An Asymptotic Analysis of Unlabeled k-Trees (with Emma Yu Jin), Proceedings of the 25th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, DMTCS-HAL Proceedings Seriesm, France (Mireille Bousquet-Melou and Michele Soria eds.) DMTCS proc. BA, 2014, 85-96.
• Limit Laws for the Number of Groups formed by Social Animals under the Extra Clustering Model (with Michael Fuchs and Yi-Wen Lee), Proceedings of the 25th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, DMTCS-HAL Proceedings Seriesm, France (Mireille Bousquet-Melou and Michele Soria eds.) DMTCS proc. BA, 2014, 73-84.
• Subsequences of automatic sequences and uniform distribution , Proceedings RICAM Workshop "Uniform Distribution and Quasi-Monte Carlo Methods", in: "Radon Series on Computational and Applied Mathematics" 15 (P. Kritzer, H. Niederreiter, F. Pillichshammer, A. Winterhof eds), DeGruyter, pp. 87--104, 2014.
• Extremal statistics on non-crossing configurations (with Anna de Mier and Marc Noy), Discrete Mathematics 327C, 103-117, 2014.
• A Gaussian limit process for optimal FIND algorithms (with Henning Sulzbach and Ralph Neininger), Electronic Journal of Probability, 19 (3), 1-28, 2014.
• Almost every tree with m edges decomposes K_2m,2m (with Anna Llado), Combinatorics Proability Computing 23 (01), 50-65, 2014.
• Equidistribution of Divisors and Representations by Binary Quadratic Forms (with Mariusz Skalba), Int. J. Number Theory 9 (8), 2011-2018, 2013.
• Coefficients of algebraic functions: formulae and asymptotics (with Cyril Banderier), 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proc. AS, 1065-1076, 2013.
• On a conjecture of Graham and Haeggkvist for random trees, (with Anna Llado), Proceedings of "The Seventh European Conference on Combinatorics, Graph Theory and Applications", CRM Series Volume 16, Springer, 2013, pp 437-441.
• A Master Theorem for Discrete Divide and Conquer Recurrences (with Wojciech Szpankowski), Journal ACM 60 (3), Article 16, 49 p, June 2013.
• Extremal Parameters in Sub-Critical Graph Classes (with Marc Noy), Proceedings Analco 2013, SIAM (Markus Nebel and Wojciech Szpankowki eds.) pp. 1-7.
• A Central Limit Theorem for the Number of Degree-k Vertices in Random Maps (with Konstantinos Panagiotou), Algorithmica 66 (4), 741-761, 2013.
• Embedded trees and the support of the ISE, Europ. J. Combinat. 34, 123-137, 2013.
• Generalized Thue-Morse Sequences of Squares (with Johannes Morgenbesser), Israel J. Math. 190, 157-193, 2012.
• Infinite Systems of Functional Equations and Gaussian Limiting Distributions (with Bernhard Gittenberger and Johannes Morgenbesser), Proceedings AofA 2012, DMTCS proc AQ, 2012, 453-478.
• Mutual Information for a Deletion Channel (with Krishnamurthy Viswanathan and Wojciech Szpankowski), 2012 IEEE International Symposium on Information Theory Proceedings , 2561-2565, 2012.
• On the discrepancy of some generalized Kakutani's sequences of partitions (with Maria Infusino), Uniform Distribution Theory 7, 75-104, 2012.
• Subsequences of automatic sequences indexed by \lfloor n^c \rfloor and correlations (with Jean-Marc Deshoulliers and Johannes Morgenbesser), J. Number Theory, 132, 1837-1866, 2012.
• A precise analysis of Cuckoo hashing (with Reinhard Kutzelnigg), ACM Trans. Algorithms, 8 Issue 2, April 2012.
• A Central Limit Theorem for the Number of Degree-k Vertices in Random Maps (with Konstantinos Panagiotou), Proceedings Analco 2012.
• The Maximum Degree of Random Planar Graphs (with O. Gimenez, Marc Noy, Konstantinos Panagiotou, and Angelika Steger), Proceedings SODA 2012.
• Asymptotic Enumeration of Maps Regardless of Genus (with Roman Nedela), Ars Mathematica Contemporanea 5, No 1, 77-79, 2012.
• The maximum degree of series-parallel graphs (with Omer Gimenez and Marc Noy), Combin. Probab. Comput. 20, no. 4, 529-570, 2011.
• Universal exponents and tail estimates in the enumeration of planar maps (with Marc Noy), Proceedings of Eurocomb 2011, Electronic Notes in Discrete Mathematics 38, 2011, 309-311.
• Asymptotic study of subcritical graph classes (with Eric Fusy, Mihyun Kang, Veronika Kraus, Juanjo Rue), SIAM J. Dicrete Maths. 25, pp. 1615-1651, 2011.
• The expected profile of digital search treese (with Wojciech Szpankowski), J. Combinatorial Theory, Ser. A, 118, 1939-1965, 2011.
• Analsis of block arithmetic coding: discrete divide and conquer recurrences (with W. Szpankowski), Proceedings of 2011 International Symposium on Information Theory, pp 1424-1428, Saint Petersburg, 2011.
• Degree distribution in random planar graphs (with Omer Gimenez and Marc Noy), JCTA 118, 2102-2130, 2011.
• The Sum of Digits Function of Polynomial Sequences (with Christian Mauduit and Joel Rivat), J. London Math. Soc., 84, 81-102, 2011.
• A General Discrete Divide and Conquer Recurrence and Its Applications (with Wojciech Szpankowski), Proceedings SODA 2011, pp. 342-361, San Francisco 2011.
• Weyl sums over integers with digit restrictions (with Christian Mauduit), Journal of Number Theory 130, 2404-2427, 2010.
• The shape of unlabeled rooted random trees (with Bernhard Gittenberger), Europ. J. Combinat. 3, 2028-2063, 2010.
• Tunstall Code, Khodak Variations, and Random Walks (with Yuryi Reznik and Wojciech Szpankowski), IEEE Trans. Inf. Th. 56 (June 2010), 2928-2937.
• Vertices of given degree in series-paralles graphs (with Omer Gimenez and Marc Noy), Random Structures Algorithms 36, 273-314, 2010.
• Combinatorial models for cooperations networks (with Bernhard Gittenberger and Reinhard Kutzelnigg), IWOCA 2009, LNCS 5874, Springer, Berlin, 2009,pp 206-217.
• Embedded trees and the support of the ISE IWOCA 2009, LNCS 5874, Springer, Berlin, 2009,pp 194-205.
• Primes with an Average Sum of Digits (with Christian Mauduit and Joel Rivat), Compositio Math. 145, 271-292, 2009.
• On the Shape of the Fringe of Various Types of Random Trees (with B. Gittenberger, A. Panholzer, H. Prodinger, and M.D. Ward), Mathematical Methods in the Applied Sciences 32, 1207-1245, 2009.
• The height of increasing trees , Annals Combinatorics 12, 373-402, 2009.
• A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree (with A. Iksanov, M. Moehle, and U. Roesler), Random Struc. Algorithms, 34, 319-336, 2009.
• (Un)Expected Behavior of Digital Search Tree Profile (with Wojciech Szpankowski), Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms (Claire Mathieu ed.), 130-138, 2009.
• Block additive functions on the Gaussian integers (with Peter Grabner and Pierre Liardet), Acta Arith. 135, 299--332, 2008.
• The sum of digits of primes in Z[i] (with Joel Rivat and Thomas Stoll), Monatsh. Math. 155, 317--347, 2008.
• On the Construction of (Explicit) Khodak's Code and Its Analysis [pdf] (with Y. Bugeaud and W. Szpankowski), IEEE Trans. Inf. Th. 54, 5073--5086, 2008.
• The degree distribution of thickened trees (with Bernhard Gittenberger and Alois Panholzer), Proceedings of "Mathematics and Computer Science 2008", DMTCS proc AI, 149--162, 2008.
• Degree distribution in random planar graphs (with Omer Gimenez and Marc Noy), Proceedings of "Mathematics and Computer Science 2008", DMTCS proc AI, 163--178, 2008.
• Newman's phenomenon for generalized Thue-Morse sequences [pdf] (with T. Stoll) , Discrete Math. 308, 1191-1208, 2008.
• A Functional Limit Theorem for The Profile of Search Trees (with S. Janson and R. Neininger), Ann. Appl. Prob. 18, 288-333, 2008.
• The Distribution of Patterns in Random Trees [pdf] (with F. Chyzak, T. Klausner, and G. Kok), Comb. Prob. Computing 17, 21-59, 2008.
• On the exit time of a random walk with positive drift (with W. Szpankowski), DMTCS proc AH, 2007, 291-302.
• Asymptotic Results About the Total Branch Length of the Bolthausen-Sznitman Coalescent (with A. Iksanov, M. Moehle, and U. Roesler), Stoch. Proc. Appl. 117, 1404-1421, 2007.
• On a mixed Littlewood conjecture in Diophantine approximation [pdf] (with Y. Bugeaud and B. de Mathan), Acta Arith. 128, 107-124, 2007.

Publications: 1987-2006 (103 papers)

Recent Talks

• Singularities for Systems of Functional Equations IHP Paris, May 3, 2010. (and AG Diskrete Mathematik, TU Wien, May 11, 2010.
• The Binary Search Tree Equation Workshop on Branching Random Walks and Searching in Trees, BIRS Banff, Feb. 1-5, 2010.
• Generalized Thue-Morse Sequences of Squares and Uniform Distribution in Compact Groups Workshop on Dynamical Systems and Uniform Distribution, TU Graz, Jan 28-29, 2010.
• The Maximum Degree of Series Parallel Graphs Random Maps and Graphs on Surfaces, Paris IHP, Nov 2-6, 2009.
• Embedded Trees and the Support of the ISE IWOCA 2009, Hradec nad Moravici, June 30, 2009.
• The Sum of Digits of Primes COMBGRAF, UPC Barcelona, May 21, 2009 (and OeMG-DMV Kongress 2009, Graz, 20.-25.9.2009.
• The degree distribution of random planar graphs One-Day Meeting in Combinatorics, Oxford, March 18, 2009 (and LL-Seminar on Graph Theory, Leoben, April 25, 2009)
• Asymptotics on Random Discrete Object SLC 62, Heilsbronn, Germany, Feb. 23-25, 2009
• (Un)Expected behaviour of digital search tree profile SODA 09, New York, Jan. 4, 2009 (and AofA 09, Frejus, France, June 14-19, 2009).
• Generating functions and central limit theorems FU Berlin, June 23, 2008
• Large random planar graphs CEA-Saclay, June 10, 2008
• Local results on the sum-of-digits function of primes and squares LIAFA, Paris, June 6, 2008
• Recursive Trees 2008 Enrage Topical School on Growth and Shapes, Paris, IHP, Juni 2-6, 2008
• Limiting Distributions in CombinatoricsAfoA 2008, Maresias, Brazil, April 13, 2008
• Digital Expansions, Prime Numbers, and Uniform Distribution modulo 1 TU Graz, October 19, 2007.
• Asymptotic Methods of Enumeration and Applications to Markov Chain Models Queueing theory without limits: transient and asymptotic analysis\\ EURANDOM, Eindhoven (The Netherlands), October 17-19, 2007.
• On the exit time of a random walk with positive drift Analysis of Algorithms 2007, Juan les Pins, June 21, 2007.
• Block additive functions on Gaussian integers Journees de Numeration, TU Graz, April 18, 2007.
• Probabilistic Combinatorics Wissenswertes, TU Wien, March 26, 2007
• Random Trees and Stochastic Processes of Analytic Funktions Mathematisches Kolloquium, Univ. Wien, Jan. 17, 2007 (and CRM Barcelona, Feb. 14, 2007).
• Concentration Properties of Extremal Parameters in Random Discrete Structure, MathInfo 06, Nancy, France, Sept. 18-22, 2006.
• Cuckoo Hashing Revisited AofA 2006, Alden Biesen, Belgien, July 2-8, 2006 (and UPC Barcelona, Feb. 21, 2007)
• Die Mathematik von Quicksort und verwandte Fragestellungen TU Wien, June 2, 2006.
• The Height of Increasing Trees German Open Conference on Probability and Statistics, Frankfurt, Germany, March 13-17, 2006.
• Concentration Properties of Extremal Parameters in Random Trees RSSES/ESI Educational Workshop on Discrete Probability, ESI, Wien, March 13, 2006.
• Die Hoehe von rekursiven Baeumen Kolloquium aus Diskreter Mathematik, TU Graz, December 2, 2005.
• Travelling Waves and the Distribution of the Height of Binary Search Trees OeMG-DMV Kongress Mathematik 2005, Klagenfurt (Austria), September 18-23, 2005.
• Asymptotic Methods of Enumeration and Applications to Markov Chain Models MAM 5, Pisa (Italy), June 21-24, 2005.
• Increasing Tree Families Complex Networks and Random Graphs, Physikzentrum Bad Honnef, July 11-13, 2005.

Students

• Master Thesis
• PhD Thesis

Teaching Activities

Skripten

• RINGVORLESUNG: Mathematische Analyse von Algorithmen: [pdf]
• Skriptum fuer Diskrete Mathematik fuer Geoinformation (ehemals Mathematik 3 f. Vermessungswesen: [ps][pdf]
• Skriptum fuer Diskrete Methoden: [ps][pdf]
• Skriptum fuer Lineare Algebra I f. TM [ps.gz][pdf]
• Skriptum fuer Lineare Algebra II f. TM [ps.gz][pdf]
  Vorlesung LA2: 13.6.2012, Vorlesung LA2: 14.6.2012
• Skriptum fuer Hoehere Mathematik f. Inf. [ps]
• Skriptum fuer Zahlentheorie f. TM [pdf], Uebungen SS2013 [pdf]
• Skriptum fuer Analytische Zahlentheorie [pdf]
• Skriptum fuer Algebraische Zahlentheorie [pdf] [pdf]
• Uebungen "Diskrete Mathematik (f. Informatik) - Discrete Mathematics": [pdf] (2006: [pdf], 2008: [pdf]) 2010: [pdf])
• Uebungen "Analyse von Algorithmen": [Uebungsblatt]