Institut für Diskrete Mathematik

Technische Universität Graz

Steyrergasse 30

8010 Graz, Austria

email: woess[at]TUGraz[dot]at

On November 3, 2020,

I have resigned from AMS membership; read:

Resignation from the American Math. Society

United States: democracy on the verge of failure

- Research interests

- FWF projects

- Books

- Papers

- Conferences

- Coauthors

- Refereeing

- Teaching

- Politics

- True stories

- F.Woess (1915-1995),

- E.Woess (1917-2001)

- Photography by W.W.

Sources: twitter @ukraine (I have never used twitter!)

+ license free face on bottom left

Since May, 2010, we are running a doctoral program (DK = Doktoratskolleg) financed primarily by the Austrian Science Fund (FWF), and also by TU and KFU Graz. This is a joint effort of mathematicians at Technische Universität Graz, Karl Franzens Universität Graz and Montanuniversität Leoben. I am the speaker of this large project. The funding is substantial. The effective work has started in October, 2010. After positive evaluation by 6 referees, the second phase of the DK started at the beginning of 2015. After the successful second prolongation, the third phase has begun in 2019. The preparations, including an almost 300 pages' report+application book, my own 45 minutes' presentation at the "Hearing" in October 2018, etc., had caused an enormous amount of work during 12 months prior to October, 2018. Again, in 2022, the preparation of the final report -- important for obtaining the permit to use the existing funds until mid-2024 -- caused several months of stressful work, no time for my own research. With October 1, 2022, I handed in the speaker function of the DK to my colleague Michael Kerber.

See www.math.tugraz.at/discrete for more details on the DK.

"Passage forbidden for quadrupeds with riding saddle or packsaddle"

The first of these two pictures was taken at the conference

"Geometric Group Theory, Random Walks, and Harmonic Analysis"

in Cortona (Italy), 13-19 June 2004.

You can have a look at the picture gallery of that conference.

The second picture was taken 10 years later, at a different entrance into the town of Cortona, at the conference

"Groups, Graphs, and Random Walks"

2-6 June 2014.

You can also have a look at the picture gallery of this more recent conference.

For 6 years (1982-88) I was Assistant Professor ("Universitätsassistent") at the Institut für Mathematik und Angewandte Geometrie of the Montanuniversität Leoben in Austria.

In 1984/85, I was on leave for a year at the Dipartimento di Matematica "G. Castelnuovo" of the University of Rome_I.

A few years later, in 1988, I moved to Italy permanently. For 6 years (1988-94) I was associate professor at the Dipartimento di Matematica "F. Enriques" of the University of Milan, then for 4 years full professor at the same University and, in the last year, at the Dipartimento di Matematica e Applicazioni of the newly founded Universita` di Milano-Bicocca.

I married in 1988, we have one daughter (born in June 1998). In September 1999 we came back to Austria. From September 1, 1999 until September 30, 2022, I was full professor in Institut für Diskrete Mathematik (formerly at Institut für Mathematische Strukturtheorie) of Technische Universität Graz in Austria. Since October 1, 2022 I am emeritus professor.

From 2000 to 2003, I served as the Secretary ("Schriftführer") of the Austrian Mathematical Society ÖMG.

My Erdös number is 2, thanks to Carsten Thomassen.

You can look at my mathematical genealogy.

You can also have a look at some pictures that I took during my 50th birthday hike in the Styrian alps, to see how nice Styria is. I also have a small photo gallery of Graz pictures for all those who might want to get an idea how the town looks like, and a photo gallery of pictures from the beautiful wine and castle hills South of Graz.

Regarding more ambitious photography in a somewhat different style, see below, Photography by W.W.

On the last day of my trip to Japan in summer 2007, I prepared a small page on my Japanese travel experiences (including a few pictures).

My 55th birthday hike pictures are from the Tyrolean mountains.

And my 60th birthday hike pictures are from the Monti Sibillini on the border between the Italian regions of Umbria and Marche.

At the conference "Boundaries and Ergodic Geometry", Notre Dame (Indiana) 2015, I took some pictures which can be found here.

My 66th birthday hike pictures are again from Mount Habicht (3277m), where I started (from Gschnitz, 1250m) in the darkness and had the sunrise a bit below the summit. In fact, this was 29 days after the birthday, preceded by other hikes.

Curriculum vitae and List of publications (pdf files).

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- Discrete potential theory

- Boundary theory and harmonic functions

- Structure of infinite graphs, groups and formal languages

Here are two older introductory papers (pdf) to the topic of random walks: One by myself, at a very elementary level and in German (from the book "Zur Kunst des formalen Denkens"), and the other, more advanced, by L. Saloff-Coste (from the Notices of the American Mathematical Society).

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You can have a look at the

From October 2006 to March 2011, I was running a second FWF project entitled "Random walks, random configurations, and horocyclic products", project number FWF-P19115-N18. Here is the (initial)

From May 2012 to November 2017, I have been running the next FWF project, number FWF-P24028-N18, entitled "Hyperbolic structures in stochastics, graph theory and topology". (The title is in part due to Agelos Georgakopoulos.) Here is the

Link:

Thereafter, I had obtained a last follow-up project before my retirement in October, 2022. It title was "Walks and Boundaries - a Wide Range", project number FWF-P31889-N35. It has started in spring, 2019 and ended with September, 2023. Here are the

Link:

Besides these projects, there is the Doctoral College (DK) "Discrete Mathematics" starting in 2010, of which I was the speaker until 2022.

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- W. Woess:
*Denumerable Markov Chains - Generating Functions, Boundary Theory, Random Walks on Trees*, EMS Textbooks in Mathematics, European Mathematical Society Publishing House, xviii+351 pages, 2009.

Book reviews: Mathematical Reviews (pdf), Zentralblatt (pdf). Individual feedback (pdf)

Once a book is published, as the author one is bound to find some mistake or misprint every time one opens it. After resisting to open it for quite a while, in April 2010 I found one such mistake: on page 190, the random time "bold epsilon" is not a stopping time. However, this wrong statement is irrelevant for what follows. Another little misprint was pointed out to my by Irving Glick (May, 2010): on page 16, last line, the sum should start with n=1. Eleven years later: page 143, line 6 from bottom: "= y" instead of "= x". Page 144, line 4: it should be "produces k children". Page 149, in the proof of Theorem 5.54: it should be u(m) = 11...12, not 00...01.

In April 2023, Jun Kigami pointed out a mistake in the proof of Proposition 1.43. A corrected version can be found here (pdf).

Regarding the potential theoretic issues of Section 6, I found it desirable to provide some additional remarks on the*Riesz decomposition*for superharmonic functions that are not necessarily bounded below (pdf file). - W. Woess:
*Random Walks on Infinite Graphs and Groups*, Cambridge Tracts in Mathematics 138, Cambridge University Press, 334+xi pages, 2000. Paperback re-edition, 2008.

ERRATA - Four pages of "errata" regarding various misprints and three "true" mistakes. Last updated in January, 2015.

Book reviews: Mathematical Reviews (pdf), Zentralblatt (pdf), Bull. London Math. Soc. (pdf; attention - text starts on bottom of page); Acta Sci. Math. (Szeged) (pdf), Bulletin Amer. Math. Soc. (pdf), Nieuw Archief voor Wiskunde (pdf).

You can find a CORRECTED VERSION (2022) here! - W. Woess:
*Catene di Markov e Teoria del Potenziale nel Discreto*, Quaderni dell' Unione Matematica Italiana**41**, 165+iii pages, 1996.

Book review: Zentralblatt (pdf). - D. Lenz, F. Sobieczky and W. Woess (editors):
*Random Walks, Boundaries and Spectra*, Proceedings (Graz - St. Kathrein, 2009), Progess in Probability, vol 64. Birkhäuser, Basel, 324+xxvi pages, 2011.

- V. A. Kaimanovich with K. Schmidt and W. Woess (editors):
*Random Walks and Geometry*, Proceedings (ESI, Vienna, 2cs-grid-col-d-4001), de Gruyter, Berlin, 532+x pages, 2004. - P. M. A. Grabner, W. Woess (editors):
*Fractals in Graz 2001: Analysis - Dynamics - Geometry - Stochastics*, Proceedings (Graz 2001), Birkhäuser, Basel, 283+iii pages, 2003. - M. A. Picardello, W. Woess (editors):
*Random Walks and Discrete Potential Theory*, Proceedings (Cortona 1997), Symposia Mathematica**XXXIX**, Cambridge University Press, 361+ix pages, 1999.

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June 29 - July 4, 2009, TU Graz

Conference webpage

Scientific committee: Tatiana Nagnibeda, Christophe Pittet, Hamish Short, Wolfgang Woess

Local committee: Ecaterina Sava, Wilfried Huss, Wolfgang Woess

List of selected speakers and participants: Alexander BENDIKOV, Philippe BOUGEROL, Emmanuel BREUILLARD, Donald CARTWRIGHT, Manfred DENKER, Ewa DAMEK, Martin DUNWOODY, Anna ERSCHLER, Vadim KAIMANOVICH, Francois LEDRAPPIER, Volodimyr NEKRASHEVICH, Panos PAPAZOGLOU, James PARKINSON, Massimo PICARDELLO, Tim RILEY, Klaus SCHMIDT, Tim STEGER, Anton THALMAIER, Anatoly VERSHIK

While scientifically successful, the administrative part of this was an absolute nightmare. The money did not arrive in time, and the EU rules which we had to implement were extremely complicated and even contradictory, almost impossible to comply with. In spite of the fact that I tried to prepare it very carefully, a deficit of 1100-1300 Euro was left behind. Reasons were twofold: (1) nobody did tell me at the beginning that I can only declare costs diminuished by VAT, so we had to pay VAT on hotel bills etc., but won't get it back; (2) since the money for the workshop had not arrived in time, it was suggested to me to ask for interim funding from my university, but nobody told me then that the university takes away interests for this loan. Almost all EU projects come along with an overhead from which one can pay such amounts, except for this type of activity (European conferences and training courses).

The whole story has been turning me from an "EU-Paulus" into an "EU-Saulus". Apparently, EU burocracy is like an alien that we are unaware of, breeding in our stomach. When the stomach explodes and the alien emerges, it is not the slimy monster of the movies, but has the appearance of a clerk from some Kafka novel. (Well, I'm still a strong supporter of EU as a union beyond just economic issues - but not as a buerocratic monster!)

May 27 - 28, 2010, TU Graz

Local & scientific committee: Ecaterina Sava, Wilfried Huss, Wolfgang Woess

Main speakers: Jozef BECK, Michael DRMOTA, Steve LALLEY, Stephan WAGNER

April 4-15, 2011, TU Graz

Courses by Geoffrey GRIMMETT, Jeff STEIF, Anders KARLSSON, Michael BJÖRKLUND"

Local & scientific committee: Ecaterina Sava, Wolfgang Woess

Funding by FWF, TU Graz, ESF, ÖMG

July 9-11, 2012, TU Graz

Talks by Steve Lalley (Chicago), Francois Ledrappier (Paris) and others.

Local & scientific committee: Ecaterina Sava, Wolfgang Woess

Funding by FWF, TU Graz, ESF

September 15-18th, Bildungshaus Mariatrost, Graz

Keynote speakers: Myhyun KANG (Graz), Jan KRATOCHWIL (Prague)

Local & scientific committee: Wilfried Huss, Norbert Seifter, Wolfgang Woess

Funding by FWF, TU Graz, MU Leoben, ÖMG

June 30 + July 1, 2016, TU Graz

Invited talks by Mathias Beiglböck (Vienna) and Rudolf Grübel (Hannover).

Local & scientific committee: Ecaterina Sava-Huss, Wolfgang Woess

Funding by TU Graz

September 25-28, 2016, JUFA Judenburg

Keynote speakers: Chris GODSIL (Waterloo), Aleksander MALNIC (Lljubljana), Rögnvaldur Möller (Reykjavik), Vladimir TROFIMOV (Jekaterinburg),

Local & scientific committee: N.N., Wolfgang Woess

Funding by FWF, ÖMG, MU Leoben, town of Judenburg

February 22-24, 2017, Rome

Invited speakers: Alexander Bufetov (Moscow / Marseille), Michel Coornaert (Strasbourg), Rostislav Grigorchuk (College Station), Vadim Kaimanovich (Ottawa), Tatiana Nagnibeda (Geneva), Klaus Schmidt (Vienna), Stanislav Smirnov (Geneva), Alain Valette (Neuchatel)

Organising committee: Daniele D'Angeli, Alfredo Donno, Fabio Scarabotti, Filippo Tolli, Wolfgang Woess

Funding by: Dipartimento S.B.A.I. - Sapienza Università di Roma

Dipartimento di Matematica e Fisica - Università Roma Tre

- Discrete and Continuous

February 17-19, 2020, Perugia

Invited speakers: Nicola Arcozzi (Univ. Bologna, Italy), Marek Bozejko (Wroclaw University, Poland), Joel M Cohen (University of Maryland, USA), Flavia Colonna (George Mason University, USA), Jacques Faraut (Université Pierre et Marie Curie - Paris 6, France), Simon G. Gindikin (Rutgers University, USA), Alessandra Iozzi (ETH Zürich, Switzerland), Vadim A Kaimanovich (Univ. Ottawa, Canada), Gabriella Kuhn (Università di Milano - Bicocca, Italy), Beatrice Pelloni (Heriott Watt Univ., Scotland), Florin Radulescu (Università di Roma - Tor Vergata, Italy), Fulvio Ricci (Scuola Normale Superiore di Pisa, Italy), Peter Sjögren (University of Gothenburg, Sweden)

Organising committee: Enrico Casadio-Tarabusi, Fausto DiBiase, Mauo Pagliacci, Wolfgang Woess

This conference could indeed take place, a few days before the public outbreak of the Covid19-crisis.

June 15-18, 2020, Paris

Invited speakers: Laurent Bartholdi, Itai Benjamini, Jérémie Brieussel, Marc Burger, Alex Eskin (to be confirmed), Joshua Frisch, Alex Furman, Agelos Georgakopoulos, Sebastien Gouëzel, Rostislav Grigorchuk, Yair Hartman, Kate Juschenko, Olga Kharlampovich, François Ledrappier, Jean Mairesse, Nicolas Monod, Tatiana Nagnibeda, Volodymir Nekrashevych, Yuval Peres, Laurent Saloff-Coste, Omer Tamuz, Ryokichi Tanaka, Giulio Tiozzo, Anatoly Vershik, Tianyi Zheng

Organising committee: Sami Abbes, Sara Brofferio, Anna Erschler, Wolfgang Woess

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Sara Brofferio

Alexander Bendikov

Donald I. Cartwright

Tullio Ceccherini-Silberstein

Wojciech Cygan

Peter Gerl

Saverio Giulini

Peter J. Grabner

Chris D. Godsil

Alexander Grigor'yan

Wilfried Huss

Thomas Hirschler

Wilfried Imrich

Vadim A. Kaimanovich

Anders Karlsson

Judith Kloas

Franz Lehner

Bojan Mohar

Anna Muranova

Tatiana Nagnibeda

Markus Neuhauser

Ronald Ortner

James Parkinson

Marc Peigné

Massimo A. Picardello

Christophe Pittet

Laurent Saloff-Coste

Maura Salvatori

Norbert Sauer

Ecaternia Sava

Norbert Seifter

Paolo M. Soardi

Mitch Taibleson

Carsten Thomassen

Mark E. Watkins

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Throughout the years, I have been a referee for the following journals, resp. conferences or publishers (incomplete list):

Abhandlungen des Mathematischen Seminars der Universität Hamburg;

Advances in Applied Mathematics;

Advances in Mathematics;

Annales Blaise Pascal;

Annales de l'Ecole Normale Superieure;

Annales de l'Institut Fourier (Grenoble);

Annales de l'Institut Poincaré-B;

Annali di Matematica Pura ed Applicata;

Annals of Probability;

Annals of Mathematics;

Archiv der Mathematik;

Bollettino dell'Unione Matematica Italiana;

Bulletin de Sciences Math\'ematiques;

Bulletin of the London Mathematical Society;

Cambridge University Press;

Circuits, Systems, and Signal Processing;

Combinatorics, Probability, and Computing;

Computing;

Commentarii Mathematici Helvetici;

Contemporary Mathematics;

Discrete and Computational Geometry;

Discrete Mathematics;

Discussiones Mathematicae;

Electronic Comunications in Probability;

Electronic Journal of Probability;

Glasgow Mathematical Journal;

ICALP;

Illinois Journal of Mathematics;

International Journal of Algebra and Computation;

International Journal of Mathematics and Mathematical Sciences;

International Mathematical Research Notes;

Inventiones Mathematicae;

Israel Journal of Mathematics;

Journal of Algebraic Combinatorics;

Journal of Combinatorial Theory-B;

Journal of Functional Analysis;

Journal of Graph Theory;

Journal of Group Theory;

Journal of Lie Theory;

Journal of Mathematical Analysis and Applications;

Journal of Statistical Physics;

Journal of the European Mathematical Society;

Journal of the American Mathematical Society;

Journal of the London Mathematical Society;

Journal of Theoretical Probability;

Linear and Multilinear Algebra;

Mathematische Annalen;

Mathematische Nachrichten;

Mathematische Zeitschrift;

Monatshefte für Mathematik;

Nagoya Mathematical Journal;

Pacific Journal of Mathematics;

Potential Analysis;

Probability Theory and Related Fields;

Proceedings of the London Mathematical Society;

Random Structures and Algorithms;

Springer Lecture Notes in Mathematics;

STACS;

Transactions of the American Mathematical Society.

From 1990 to 1999 I have served as an Associate Editor of the journal ``Circuits, Systems and Signal Processing'' (Birkhäuser).

In 2007, I have acted as a referee in the evaluation of the Mathematical Insitute of the Slovak Academy of Sciences.

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The original text (in particular the one regarding the so-called "sanctions") is now really out of date, so I removed it at last. As a matter of fact, while probably most Austrian colleagues considered this a peculiar thing to put on my webpage, I had quite a bit of positive feedback from abroad.

Subsequently, Austria has disappeared from most international news, and there have been only few news flashes reporting that after only two and a half years, and a full year before the end of its term, the government had collapsed in autumn 2002 because of a major crisis within the Freedom Party. Since 2003, the same coalition was back to power again, but with the Freedom Party down to 10% instead of the previous 27%. Since 2006, after the Freedom Party has disassembled in two pieces, they had been no more represented in the government, and we were back to the "big coalition" between Social and Christian Democrats, even though these two parties appear to hate each other profoundly.

However, in the meantime, the Freedom Party under its new leader had gained votes, and contrary to 2000, it is nowadays "normal" that the right wing is successful on the basis of agressive populism in most democratic countries. Since 2017, we had again the coalition between the Christian Democrats and the Freedom Party. People seemed to be happy for a while: the coalition partners do not quarrel. That coalition broke down after the 'Ibiza scandal' of the leader of the Freedom Party became public, we now have a coalition between the Green party and the Christian Democrats, who themselves re now involved in more than one scandal of corruption and amorality. At the same time, Freedom party under an even more radical leader is gaining again. My conclusion is a pessimistic view on the "wisdom" of the sovereign, i.e., the voter: no matter whether there is corruption, illiberal democracy and so on - if the surface appears quiet and peaceful then the majority is happy. They are just happy not to hear about all those things which in a critcal and free environment would become visible.

I repeat: I'm not at all convinced that I'll be able to conclude my days without witnessing some new political repressions, of course with different appearance than in the 1930s and 40s. November 2022: the degree of evilness of the following personalities is of course quite variable.

- Bolsonaro - Kickl - Salvini - LePen (daughter)

The list comprises persons who (1) came or may come to power through a more or less democratic procedure (this is why Franco, Salazar, Pinochet are not in the list), and (2) are more or less close to our cultural (hemi)sphere (this is why many others, like e.g. Mugabe, Duarte, Maduro are not comprised).

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Elisabeth Woess (1917-2001)

He was also gifted in painting (mostly water color). He left about 850 pictures, 99% are landscapes.

I have organized a show of some of them in Summer, 2002.

There was another show in Summer, 2006 (originally planned for 2005).

You can have a look at some of his paintings: those from the exhibition in 2006, and others: part1, part2, part3, part4, all four from two booklets with reproductions from the 1990ies, and Greece 1979.

You can read an accompanying text (in German), and find the announcement of the abovementioned first exhibition in 2002.

My mother, Elisabeth Woess (1917-2001) was also a university professor, at the Institute of Botanics of Vienna University. You can see a few late photographs of her and read an obituary (pdf, in German) that appeared in Verh. Zool.-Bot. Ges. Österreich 138 (2001) 275-278. A posthumuous publication has appeared in Plant Systematics and Evolution 258 (2006) 27-37. It has a small background story: my mother had continued her research work until a week before she passed a way at the age of 84. This was supposed to become a joint work with a Professor in Florida of Hungarian origin who years before had sent her specimen of an antarctic algae to be studied and classified. In the last year of her life she often expressed sadness about the fact that she had finished her part of this work, but her colleague would not complete it. (Indeed, he had retired, too, and had no more laboratory access.) I found the manuscript and drawings in the material that she left behind, and managed to convince the director of the Botanical Insitute in Vienna to take care of its publication. It was carefully revised and re-edited. See in particular the Comments and Acknowledgements at the end of the paper.

Geschichte der Rechts- und Staatsswissenschaftlichen Fakultät Wien 1918-38

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I have now started to create a separate page with my work in this type of photography: Fotoseite Wolfgang Woess.

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Link new homepage of the Institute of Discrete Mathematics (still under construction).

Link to the old homepage of Institut für Mathematik C.

Last modified on April 1, 2024.

Impressum:

Für den Inhalt verantwortlich: Wolfgang Woess

Institut für Diskrete Mathematik

TU Graz, Steyrergasse 30, A-8010 Graz