Goethe-Universität — Prof. Dr. Jochen Blath

Stochastik

Willkommen auf meiner Homepage / welcome to my homepage!

I am a mathematics professor (W3) at Goethe University Frankfurt. Before that, I had research and teaching positions at TU Berlin, Oxford University, and TU Kaiserslautern.

As a probabilist I am interested in the mathematically rigorous understanding of the dynamics of stochastic individual based systems, for example arising in population biology and evolution, and their scaling limits on multiple scales.

A feature that has attracted my special attention in recent years are the population-level consequences of dormancy, that is, the ability of an individual to switch into a reversible (and protected) state of vanishing metabolic activity. Dormancy comes in many guises (quiescence, persistence, latency, hibernation, cryptobiosis,...) and is ubiquitous for example in microbial communities. It typically offers protection from external stress (fluctuating environments, antibiotic treatment, intra/inter-species competition, predation, etc.), but at the same time maintenance of a dormancy trait is also costly, which gives rise to complex trade-offs. Dormancy also has important evolutionary and ecologcial implications across multiple scales, affecting patterns of population genetic, species, and metacommunity diversity.

The related abstract type switching mechanisms can be seen as a new paradigm in interacting particle systems, with often profound mathematical consequences (loss of Markov property, introduction of memory and delay, new universal scaling behaviour). One future goal is to use mathematical insight gained from abstract interacting systems to improve the understandig of the evolutionary, ecological and pathogenic implications of dormancy in the life sciences.

Other mathematical areas of interest include coalescent theory (in particular multiple merger coalescents arising from sweepstakes reproduction, including the derivation of statistical inference methods), measure-valued diffusions (e.g. generalized Fleming-Viot processes and the symbiotic branching model), superprocesses (super-Brownian motion and its relatives), duality for Markov processes (e.g. via look-down constructions), interacting particle systems (e.g. contact process and relatives) and risk theory (e.g. principle of a single big jump).

Some Info:

Stellv. Senator der GU Frankfurt und Mitglied des erweiterten GU Senats, since 2025
Affiliated PI of the C3S - Center for Critical Computational Studies, GU Frankfurt, since 2024
Member of the Assembly of the Rhein-Main Universities (RMU Assembly), since 2023
Editorial board, Annals of Applied Probability, 2019 - 2024
Co-organizer, Rhein Main Kolloquium Stochastik, since 2022
Math+ Exzellenzcluster (EXC-2046/1 Berlin), PI of project EF4-7 (jointly with Prof. Wilke Berenguer),
Berlin Mathematical School (BMS), member of admissions committee (2013 - 2021), member of BMS committee (2018-2021)
Co-speaker, DFG RTG 1845 "Stochastic analysis with applications in biology, finance and physics" (2011-2016)
Member of collaborative research units (selection): DFG IRTG Berlin-Oxford, DFG RTG 1845, DFG IRTG Berlin-Zurich, DFG SPP 1590, Matheon, ECMath
Managing Director, Institut für Mathematik, TU Berlin (2011-2013)
Chair of the organizing committee, 33rd Conference for Stochastic Processes and Their Applications (SPA Berlin 2009)
Member of Senior Common Room, St Hugh's College, Oxford University, 2004 - 2005

Lehrveranstaltungen / Courses

WiSe 2026/2027

Vorlesung ,,Höhere Stochastik'' / ,,Advanced Stochastics'' (4+2 SWS) (LSF)

Aktuelle Informationen zur Veranstaltung (Übungen, Hausaufgabenblätter etc.) finden Sie nach und nach auf der Moodle/studium digitale Seite. Die organisatorischen Details zur Vorlesung besprechen wir auch zum ersten Vorlesungstermin.

Vorlesung "Stochastische Modelle der Populationsgenetik ((4+2 SWS) (LSF)
Aktuelle Informationen zur Veranstaltung (Übungen, Hausaufgabenblätter etc.) finden Sie nach und nach auf der Moodle/studium digitale Seite. Die organisatorischen Details zur Vorlesung besprechen wir auch zum ersten Vorlesungstermin

Oberseminar "Stochastische Prozesse und ihre Anwendungen" (LSF)

Anleitung zum wissenschaftlichen Arbeiten für Bachelor- und Masterkandidaten sowie Doktoranden (Termine nach Vereinbarung)

Weitere regelmäßige Veranstaltungen:

Rhein-Main Kolloquium Stochastik (Informationen hier)

Stochastik-Kolloquium (Informationen hier)

SoSe 2026

Vorlesung ,,Elementare Stochastik'' (4+2 SWS) (LSF)
Aktuelle Informationen zur Veranstaltung (Übungen, Hausaufgabenblätter etc.) finden Sie nach und nach auf der Moodle/studium digitale Seite. Die organisatorischen Details zur Vorlesung besprechen wir auch zum ersten Vorlesungstermin.

Gemeinsames Seminar der Rhein-Main-Universiäten (RMU): "Stochastische Modelle der Evolutionsbiologie'', gemeinsam mit der JGU Mainz (Prof. Matthias Birkner) (2 SWS). (LSF)
Das Seminar richtet sich an Bachelor- und Master-Studierende der Mathematik mit Vertiefungsbereich Stochastik, die mindestens die Elementare Stochastik sowie eine weitere 4-stündige Stochastikvorlesung gehört haben (also Stochastische Prozesse I oder Höhere Stochastik). Kenntnisse der Spezialvorlesung ,,Stochastische Modelle der Populationsgenetik'' sind von Vorteil, aber keine Voraussetzung.

Interessierte melden sich bitte bis 20.02.2026, 12:00 direkt bei mir oder bei Heike Suckfüll. Termin für die Vorbesprechung in Mainz ist der 27.02.2026.

Wir treffen uns um 14:00 c.t. an der JGU Mainz in Raum 05-426 im Institut für Mathematik, Staudingerweg 9, 55128 Mainz. Anreiseinformationen finden Sie hier:

https://www.staff.uni-mainz.de/birkner/SMEB26/

Das Seminar wird als Blockveranstaltung abwechselnd in Frankfurt und Mainz stattfinden.

Oberseminar "Stochastische Prozesse und ihre Anwendungen" (LSF)

Anleitung zum wissenschaftlichen Arbeiten für Bachelor- und Masterkandidaten sowie Doktoranden (Termine nach Vereinbarung)

Weitere regelmäßige Veranstaltungen:

Rhein-Main Kolloquium Stochastik (Informationen hier)

Stochastik-Kolloquium (Informationen hier)

WiSe 2025/2026

Forschungssemester

Forschungsseminar Stochastik, Haus Bergkranz, Riezlern

Publikationen / Publications

Books:

Stochastische Modelle der Versicherungsmathematik, Springer - Birkhäuser MaKo Reihe, (2025)
Blath, J.; Ortgiese, M.; Scheutzow, M.
DOI: https://doi.org/10.1007/978-3-031-88115-2
Surveys in Stochastic Processes, Proceedings of the 33rd SPA conference in Berlin 2009, European Mathematical Society Series of Congress Reports, EMS Press, (2011)
Blath, J.; Imkeller, P.; Rœlly, S. (eds.)
DOI: https://doi.org/10.4171/072
Trends in Stochastic Analysis, London Mathematical Society Lecture Note Series 353, Cambridge University Press, (2009) Blath, J.; Mörters, P.; Scheutzow, M. (eds.)

Articles and Preprints:

The interplay of selection and dormancy in a Moran model can lead to coexistence of types, preprint: arXiv:2602.24106, (2026),
with B. Le Duigou and A. Tóbiás
Emergence of microbial host dormancy during a persistent virus epicemic, accepted by Journal of Mathematical Biology, (2026)
with A. Tóbiás.
DOI: https://doi.org/10.48550/arXiv.2504.04943
How the interplay of dormancy and selection affects the wave of advance of an advantageous gene, Stoch Proc Appl 181, (2025)
with M. Hammer, D. Jacobi and F. Nie
DOI: https://doi.org/10.48550/arXiv.2106.08655
A stochastic population model for the impact of cancer cell dormancy on therapy success, Journal of Theoretical Biology 597, (2025)
with A. Kraut, T. Paul and A. Tóbiás.
DOI: https://doi.org/10.1016/j.jtbi.2024.111995
Dormancy in stochastic population models, DMV Jahresbericht 126, (2024)
with N. Kurt, M. Slowik and M. Wilke Berenguer.
DOI: https://doi.org/10.1365/s13291-024-00289-z
The impact of dormancy on evolutionary branching, Theoretical Pop Biology 156, 66-76, (2024)
with T. Paul, A. Tóbiás and M. Wilke Berenguer
DOI: https://doi.org/10.48550/arXiv.2209.01792
The contact process with switching, MathematicS In Action 12 (1), 135-154, (2023)
with F. Hermann and M. Reitmeier
DOI: https://doi.org/10.48550/arXiv.2205.07275
On/off super-Brownian Motion: Characterization, construction and long-term behaviour, preprint (2023)
with D. Jacobi
DOI: https://doi.org/10.48550/arXiv.2307.10968
A stochastic adaptive dynamics model for bacterial populations with mutation, dormancy and transfer, ALEA Lat Am J Probab Math Stat 20, 313-357, (2023)
with T. Paul, A. Tóbiás.
DOI: https://doi.org/10.30757/ALEA.v20-12
Virus dynamics in the presence of contact-mediated host-dormancy, ESAIM: Probability and Statistics 27, 174-220, (2023)
with A. Tòbias
DOI: https://doi.org/10.1051/ps/2022022
The stochastic Fisher-KPP equation with seed bank and on/off branching Brownian motion, Stoch PDE: Anal Comp, (2022)
with M. Hammer, F. Nie
DOI: https://doi.org/10.48550/arXiv.2005.01650
Principles of seed banks and the complexity emerging from dormancy, Nature Communications 12, 4807, (2021)
with J. T. Lennon, F. den Hollander, M. Wilke Berenguer
DOI: https://doi.org/10.1038/s41467-021-24733-1
The interplay of dormancy and transfer in bacterial populations: Invasion, fixation and coexistence regimes, Theor Pop Biology 139,18-49 (2021)
with A. Tóbiás
DOI: https://doi.org/10.1016/j.tpb.2021.05.001
A branching process model for dormancy and seed banks in randomly fluctuating environments, J Math Biology 85(17), (2021)
with F. Hermann, M. Slowik
DOI: https://doi.org/10.48550/arXiv.2007.06393
Invasion and fixation of microbial dormancy traits under competitive pressure, Stoch Proc Appl 130(12), (2020)
with A. Tóbiás
DOI: https://doi.org/10.48550/arXiv.1910.13156
The symbiotic branching model: Duality and Interfaces, in: Probabilistic Structures in Evolution (E. Baake and A. Wakolbinger, eds.), EMS Press, Berlin, 311-336, (2021)
with M. Ortgiese
DOI: https://doi.org/10.48550/arXiv.2002.02825
Genealogies and inference for populations with highly skewed offspring distributions, in: Probabilistic Structures in Evolution (E. Baake and A. Wakolbinger, eds.), EMS Press, Berlin, 151-178, (2021)
with M. Birkner
DOI: https://doi.org/10.48550/arXiv.1912.07977
Population genetic models of dormancy, in: Probabilistic Structures in Evolution (E. Baake and A. Wakolbinger, eds.), EMS Press, Berlin, 247-266, (2021)
with N. Kurt
DOI: https://doi.org/10.48550/arXiv.2012.00810
Separation of time-scales for the seed bank diffusion and its jump-diffusion limit, J Math Biology 82(53), (2021)
with E. Buzzoni, A. Gonzalez-Casanova, M. Wilke-Berenguer
DOI: https://doi.org/10.48550/arXiv.1903.11795
Statistical tools for seed bank detection, Theor Pop Biology 132, 1-15, (2020)
with E. Buzzoni, J. Koskela, M. Wilke-Berenguer
DOI: https://doi.org/10.48550/arXiv.1907.13549
The seed bank coalescent with simultaneous switching, Electron J Probability 25, 1-21, (2020)
with N. Kurt, A. Gonzalez-Casanova, M. Wilke-Berenguer
DOI: https://doi.org/10.48550/arXiv.1812.03783
Structural properties of the seed bank and the two-island diffusion, J Math Biology 79(1), 369-392, (2019)
with E. Buzzoni, A. Gonzalez-Casanova, M. Wilke-Berenguer
DOI: https://doi.org/10.48550/arXiv.1710.08164
The site-frequency spectrum associated with Xi-coalescents, Theor Pop Biology 10, 36-50, (2016)
with M. Cronjaeger, B. Eldon, M. Hammer
DOI: https://doi.org/10.1016/j.tpb.2016.04.002
The scaling limit of the interface of the continuous-space symbiotic branching model, Annals of Probability 44(2), 807-866, (2016)
with M. Hammer, M. Ortgiese
DOI: https://doi.org/10.48550/arXiv.1312.2870
A new coalescent for seed-bank models, Annals of Applied Probability 26(2), 857-891, (2016)
with A. Gonzalez-Casanova, N. Kurt, M. Wilke-Berenguer
DOI: https://doi.org/10.48550/arXiv.1411.4747
Genetic variability under the seed bank coalescent, Genetics 200, 921-934, (2015)
with B. Eldon, A. Gonzalez-Casanova, N. Kurt, M. Wilke-Berenguer
DOI: https://doi.org/10.1101/017244
Can the site-frequency spectrum distinguish exponential population growth from multiple-merger coalescents?, Genetics 199, 841-856, (2015)
with M. Birkner, B. Eldon, F. Freund
DOI: https://doi.org/10.1534/genetics.114.173807
Genealogy of a Wright Fisher model with strong seed-bank component, Birkhäuser Progress in Probability 69, 81-100, (2015)
with A. Gonzalez Casanova, B. Eldon, N. Kurt
DOI: https://doi.org/10.48550/arXiv.1403.2925
A new class of large claim size distribution: Definition, properties, and ruin theory, Bernoulli 21, 2457-2483, (2015)
with S. Beck, M. Scheutzow
DOI: https://doi.org/10.48550/arXiv.1307.6149
The largest strongly connected component in Wakeley et al's cyclical pedigree model, Theor Pop Biology 98, 28-37, (2014)
with S. Kadow, M. Ortgiese
DOI: https://doi.org/10.48550/arXiv.1405.7276
Strong seedbank effects in bacterial evolution, J Theoretical Biology 356, 62-70, (2014)
with A. González-Casanova, E. Aguirre-von-Wobeser, G. Espín, L. Servín-González, N. Kurt, D. Spanò, G. Soberón-Chávez
DOI: https://doi.org/10.1016/j.jtbi.2014.04.009
(G, \mu)-quadratic stochastic operators, J Difference Equations and Applications 20 (8), 1258-1267, (2014)
with U. Jamilov, M. Scheutzow
DOI: https://doi.org/10.48550/arXiv.1307.1265
Statistical properties of the site-frequency spectrum associated with Lambda-coalescents, Genetics 195, 1037-1053, (2013)
with M. Birkner, B. Eldon
DOI: https://doi.org/10.48550/arXiv.1305.6043
On the ancestral process of long-range seedbank models, J Applied Probability 50 (3), 741-759, (2013)
with A. Gonzalez Casanova, N. Kurt, D. Spano
DOI: https://doi.org/10.1239/jap/1378401233
An ancestral recombination graph for diploid populations with skewed offspring distribution, Genetics 193, 255-290, (2013)
with M. Birkner, B. Eldon
DOI: https://doi.org/10.48550/arXiv.1203.4950
Analysis of DNA sequence variation within marine species using Beta-coalescents, Theor Pop Biology 87, 15-24, (2013)
with M. Steinruecken, M. Birkner
DOI: https://doi.org/10.1016/j.tpb.2013.01.007
Lebensversicherungsmathematik, Kapitel 8.2 im Springer Taschenbuch der Mathematik, Springer Spektrum, 3. Aufl., 997-1005, (2012)
DOI: https://doi.org/10.1007/978-3-8348-2359-5
Schadenversicherungsmathematik, Kapitel 8.3 im Springer Taschenbuch der Mathematik, Springer Spektrum, 3. Aufl., 1005-1015, (2012)
DOI: https://doi.org/10.1007/978-3-8348-2359-5
Survival and Extinction of Caring Double-Branching Annihilating Random Walk, Electron Comm Probability 16, 271-282, (2011)
with N. Kurt
DOI: https://doi.org/10.1214/ECP.v16-1631
On the moments and the interface of the symbiotic branching model, Annals of Probability 39, 252-290, (2011)
with L. Döring, A. Etheridge
DOI: https://doi.org/10.1214/10-AOP543
Importance Sampling for Lambda Coalescents in the infinitely many sites model, Theor Pop Biology 79, 155-173, (2011)
with M. Steinruecken, M. Birkner
DOI: https://doi.org/10.1016/j.tpb.2011.01.005
Rescaled stable generalised Fleming-Viot processes: Flickering random measures, Electron J Probab. 15, 2418-2437, (2009)
with M. Birkner
DOI: https://doi.org/10.1214/EJP.v14-712
Measure-valued Processes, Self-Similarity, and Flickering Random Measures, Birkhäuser Progress in Probability 61, 175-196, (2009)
DOI: https://doi.org/10.1007/978-3-0346-0030-9_6
A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks, ALEA Lat Am J Probab Math Stat. 6, 25-61, (2009)
with M. Birkner, M. Möhle, M. Steinrücken, J. Tams
Measure-valued diffusions, general coalescents and population genetic inference, Trends in Stochastic Analysis LMS 353, Cambridge University Press, 329-363, (2009)
with M. Birkner
DOI: https://doi.org/10.1017/CBO9781139107020.015
Propagation of singularities in the semi-fractional Brownian sheet, Stoch Proc Appl 118, 1264-1277, (2008)
with A. Martin
DOI: https://doi.org/10.1016/j.spa.2007.06.010
Computing likelihoods for coalescents with multiple collisions in the infinitely-many-sites model, J Math Biology 57, 435-465, (2008)
with M. Birkner
DOI: https://doi.org/10.1007/s00285-008-0170-6
Inference for Lambda-coalescents, Weierstrass Institut - WIAS Preprint 1211, 38 pages, (2007)
with M. Birkner
DOI: https://doi.org/10.20347/WIAS.PREPRINT.1211
Coexistence in locally regulated competing populations and survival of branching annihilating random walk, Annals of Applied Probability 17, 1474-1507, (2007), extended version available here.
with A. Etheridge, M. Meredith
DOI: https://doi.org/10.1214/105051607000000267
Thick points of super-Brownian motion. Probab Theory Related Fields 131, 604-630, (2005)
with P. Moerters
DOI: https://doi.org/10.1007/s00440-004-0387-2
Alpha-stable branching and Beta-coalescents. Electron J Probab. 10, 303-325, (2005)
with M. Birkner, M. Capaldo, A. Etheridge, M. Möhle, J. Schweinsberg, A. Wakolbinger
DOI: https://doi.org/10.1214/EJP.v10-241

Dormancy

Conferences on Dormancy

Mindmaps on Dormancy

Projekte (Auswahl) / Projects (selection)

MATH+ Berlin Mathematics Research Center (DFG excellence cluster EXC-2046/1)

Project EF 4-7 "The impact of dormancy on the evolutionary, ecological and pathogenic properties of microbial populations ", PI jointly with Prof. Dr. Maite Wilke Berenguer (HU Berlin), 1 PhD-student (since 2021)

DFG funded projects:

DFG BL 1105/5-1. "The role of dormancy in population genetics", project within DFG SPP 1590, 1 post-doc for 3 years.
DFG BL 1105/4-1, "Interacting stochastic partial differential equations, combinatorial stochastic processes and duality in spatial population dynamics", project within DFG SPP 1590, 1 post-doc for 2 years.
DFG BL 1105/3-2, "Genealogies and inference for populations with highly skewed offspring distributions under further evolutionary forces", project within DFG SPP 1590, 1 post-doc for 3 years.
DFG BL 1105/3-1, "Genealogies and inference for populations with highly skewed offspring distributions under further evolutionary forces", project within DFG SPP 1590, 1 post-doc for 3 years.
DFG BL 1105/2-1, "Stochastic PDEs, combinatorial stochastic processes and duality", 1 post-doc for 1 year.
DFG BL 1105/1-1, internationcal Conference "SPA - 33rd Conference on Stochastic Processes and Their Applications" (2009), conference funding.

Participation in DFG collaborative grants (selection):

DFG IRTG 2544 Berlin - Oxford, supervisor for the PhD project of Dave Jacobi (since 2020)
Stellv. Sprecher, DFG RTG 1845 "Stochastic analysis with applications in biology, finance and physics" (2011-2016)
DFG RTG 1845, supervisor for PhD project of Dr Adrián González Casanova (now at UNAM Mexico City)
DFG IRTG 1339 Berlin - Zurich, supervisor for the PhD project of Dr Matthias Steinrücken (now at U Chicago)
DFG SPP 1590 Probabilistic Structures in Evolution
BMS Berlin Mathematical School, member of BMS committee (governing body of BMS, 2018-2022)
BMS Berlin Mathematical School, member of admissions committee (2011-2022), member of faculty (2009-2022)

Aktuelle Vorträge / Recent talks

06/2026 invited session talk, IMS meeting, Salzburg, Austriia
03/2026 (cancelled) invited lecture, IIT Bombay, Mumbai, India
11/2025 Plenary double lecture, 53rd Stochastics meeting Lunteren 2025, Lunteren, NL
07/2025 Oberseminar Stochastik, TU Darmstadt
06/2025 Stochastik Kolloquium, TU Braunschweig
05/2025 Conference on Cancer dormancy and therapy resistance, Istituto Superiore di Sanità (ISS), Rome, I
09/2024 Bonn - Mainz Probability Summerschool in Umbria, I
07/2024 Physikalischer Verein Frankfurt am Main, Themenreihe Naturwissenschaft und Technik
05/2024 4th Italian meeting on probability and statistics, Sapienza University, Rome, I
05/2024 Conference on “Probability and Evolutionary Biology", CIRM Luminy, F
03/2024 Conference on "Evolution in structured populations: recent progress and new challenges", Statistics Department, Oxford University, UK (cancelled due to illness)
11/2023 CMMS Center for multiscale modeling / FIAS, Frankfurt
09/2023 Séminaire Probabilités et Statistique, Institut Élie Cartan, Université de Lorraine, Nancy, F
09/2023: Talk on "Probabilistic structures emerging from dormancy", workshop "Stochastic models in Life Sciences", Eurandom, Eindhoven, NL
07/2023: "Die Mathematik der Dormanz", Antrittsvorlesung (Inaugural Lecture), Goethe-Universität Frankfurt
03/2023: Talk on "Probabilistic structures emerging from dormancy", CRM - ISM Montreal probability seminar, Montréal, Canada
12/2022: Talk on "Dualities in population dynamics and evolution: Recent progress and open problems.", workshop "Stochastic duality", Eurandom, Eindhoven, NL
11/2022: Berlin Probability Colloquium / IRTG 2544 "The effects of dormancy in populationgenetics, evolution and ecology"
11/2022: Alumni-Treffen am IfM, GU Frankfurt "Stochastische Modelle der Populationsgenetik"
07/2022: Talk on "The effects of dormancy in population genetics and population dynamics", mini-symposium on dormancy at "Mathematical Modeling in Evolution and Ecology" MMEE Conference 2022, University of Reading, UK
05/2022: Minicourse (4 Lectures) on "The effects of dormancy in population genetics and population dynamics", Junior Trimester on stochastic modelling in the life science, Hausdorff Research Institute for Mathematics (HIM), Bonn
03/2022: Talk on "Probabilistic patterns emerging from dormancy: Results and perspectives", MFO workshop 2210 on "Population dynamics and Statistical physics in Synergy", Mathematisches Forschungsinstitut Oberwolfach (MFO).

Research Seminars / Forschungsseminare

"SPIELE" - Stochastic Processes in EvoLution and Ecology

RM 10, Raum 711 groß