January 18 - April 16, 2027
Mentors: Marie Doumic (Inria and Ecole polytechnique), Eugenia Franco (Bonn), J. J. L. Velázquez (Bonn)
Description: The development of mathematical models describing biological phenomena has been an active research field during the last decades. Significant progress in experimental biology provides a large amount of precise quantitative information on many biological systems. This poses the challenge of understanding these processes using well established mathematical and physical models. A particularly difficult task is the development of mathematical tools allowing to analyze systems out of equilibrium. In addition, in many biological problems the study of inverse problems and the methods of control theory are playing an increasingly important role.
During this Junior Trimester Program we will bring together researchers working in classical branches of mathematical biology, as for instance structure population models, renewal equations and reaction-diffusion systems, as well as scientists interested in biological systems in which the lack of equilibrium plays a crucial role in their behavior, or experts in inverse problems with biological applications. Structure population models and reaction-diffusion equations had played a crucial role in areas like population dynamics, epidemiology and understanding pattern formation. There are still a large number of problems in biology in which these classical tools can be useful. At the same time tools of statistical physics and inverse problem theory have an enormous number of potential applications in biology.
The program will offer a series of events focused on these topics and host researchers at all levels on topics related with the one proposed in the trimester.
The second application round is now open until June 28, 2026 (CEST).
Global Mobility Fellowships
Our Global Mobility Fellowships offer fully-funded and fully-organized visits to the Trimester Programs of the Hausdorff Research Institute for Mathematics and participation spots for the Special Topic Schools of the Hausdorff School for Mathematics for selected researchers and PhD students from countries of the Global South. With this program we aim to reduce economic and practical barriers to participation in some of the core initiatives of HCM and to welcome researchers from around the world to our programs and events!
Click here for further information.
In case of questions, please contact Magdalena Balcerak Jackson, Emma Seggewiss or Kanami Ueda.
Please click on each event to see the list of participants. You will be redirected to the page of Indico.
Some participants have registered anonymously, the others are only visible to the other participants.
- Dual Trimester Program
- School: Differential Equations in Mathematical Biology: Analysis, Stochasticity, and Modelling (January 18 - 22, 2027)
- Workshop: Recent trends in PDEs for mathematical biology: dynamics, stability and patterns (February 15 - 19, 2027)
- Workshop: Mathematical biology across scales: from interacting particle models to PDEs via kinetic theory (March 15 - 19, 2027)
- Workshop: Stochastic and deterministic perspectives on reaction and interaction networks (April 12 - 16, 2027)
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TBA
January 18 - 22, 2027
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: TBA
Description: Biological systems are inherently multiscale and their mathemati
cal treatment requires complementary perspectives attracting researchers from
different scientific fields. From intracellular reaction networks to interacting
populations and ecological communities, their dynamics are shaped by complex
interactions, stochastic effects, and spatial structure. Capturing these features
calls for a diverse mathematical toolbox ranging from stochastic processes and
reaction networks to kinetic theory and nonlinear partial differential equations.
This research school brings together various perspectives and techniques in
mathematical biology. The lectures will introduce recent analytical and proba
bilistic methods for studying biological systems across scales, emphasizing the
interplay between deterministic and stochastic descriptions.
The aim of the school is to provide participants with a coherent view of mod
ern mathematical techniques in mathematical biology, highlighting how PDE
analysis, and stochastic techniques interact in the study of non-equilibrium bi
ological systems. Particular attention will be paid to methodological bridges
between frameworks and to emerging analytical challenges.
The school is intended to serve as a comprehensive introduction to the pro
gram and to facilitate the interaction between different research communities.
In case of questions concerning services and administration, please contact Emma Seggewiss or Kanami Ueda.
February 15 - 19, 2027
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: TBA
Description: Biological systems are inherently complex, with a wide variety of
interactions among their components that give rise to dynamic, self-organized
behaviors spanning multiple levels of organization. Mathematical models based
on the use of Partial Differential Equations have proven to be powerful tools
to help understand collective dynamics and interactions, providing a rigorous
mathematical framework for modeling the evolution of biological systems. Such
models offer insights into fundamental questions concerning the mechanisms
driving the observed behaviors, including the conditions for the emergence and
persistence of patterns, the robustness of biological structures under perturba
tions, and the long-time behavior of complex systems.
This workshop will focus on recent developments in the use of PDEs for mod
eling biological systems, highlighting theoretical advances, methodological in
novations, and applications. Such applicatios will range from developmental
biology and collective cell migration to ecology, illustrating the broad relevance
of PDE models across life sciences.
Over the course of five days, the workshop will provide participants with op
portunities to present recent results, exchange ideas, discuss methodological
innovations, and explore future directions in the use of PDEs for understanding
living systems. It will foster interdisciplinary dialogue among researchers from
different areas of expertise, bridging theory and applications, thus providing a
comprehensive perspective on the role of PDEs in mathematical biology.
Please note that the workshops are exclusively for trimester program participants; therefore, it is not possible to apply only for the workshops.
In case of questions concerning services and administration, please contact Emma Seggewiss or Kanami Ueda.
March 15 - 19, 2027
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: TBA
Description: Biological systems are inherently multiscale: complex collective be
haviours emerge from the interactions of many individual agents. Depending on
the modelling framework, agents may be described solely by mechanical vari
ables such as position and velocity, or may additionally carry internal states.
Mathematical models of such systems therefore naturally span several levels
of description, ranging from stochastic interacting particle models of McKean
type and individual-based models to kinetic equations and macroscopic partial
differential equations.
This workshop focuses on the mathematical links between these modelling
scales, with emphasis on kinetic theory and stochastic scaling limits — powerful
tools to connect microscopic agent dynamics to continuum PDE descriptions.
Applications include but are not limited to structured population dynamics,
collective animal behaviour, neuronal networks, and coagulation–fragmentation
processes.
A central objective of the workshop is to bring together researchers working on analytical, numerical and stochastic perspectives. By fostering dialogue
between these communities, we aim to promote a deeper understanding of the
connections between probabilistic particle systems, kinetic theory, and macro
scopic PDE models. In particular, we will explore both classical and recent
analytical, probabilistic, and numerical methods, including scaling limits, er
godicity and hypocoercivity methods.
Please note that the workshops are exclusively for trimester program participants; therefore, it is not possible to apply only for the workshops.
In case of questions concerning services and administration, please contact Emma Seggewiss or Kanami Ueda.
April 12 - 16, 2027
Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: TBA
Description: Reaction (or interaction) networks provide a unifying framework
for modeling systems of interacting entities across a wide range of disciplines.
When specified in concrete applications, the nature of the entities and their in
teractions varies. In chemistry, they describe chemical species and the reactions
among them. In epidemiology, they represent compartmental classes and the
transitions between them. In ecology, they encode trophic relations within food
webs or other competitive relations. In economics, they model goods that are
transformed through industrial activities.
From this broad range of applications and relevance follows a wide vari
ety of mathematical tools. Deterministic approaches are grounded in algebraic
geometry and dynamical systems theory, and they address the existence and sta
bility of equilibria, as well as non-equilibrium dynamics. Stochastic approaches
include particle-based and agent-based models that capture randomness, finite
population effects and emergent behaviour; they address long-time behaviour,
metastability and large-deviation principles. Key questions concern the connec
tion between interaction rules and qualitative behaviour across stochastic and
deterministic descriptions.
The workshop aims at bringing together these complementary mathematical
perspectives, connected by a common interest in systems of interacting entities
regulated by a network structure. A main goal is to profit from different ap
proaches to similar problems and to discover at the same time new directions
and applications, with the goal of fostering dialogue between stochastic and
deterministic viewpoints.
Please note that the workshops are exclusively for trimester program participants; therefore, it is not possible to apply only for the workshops.
In case of questions concerning services and administration, please contact Emma Seggewiss or Kanami Ueda.
5 minute walk from Bonn central train station to HIM
Leave the station through the back exit into the street called Quantiusstrasse. Cross at the zebra crossing and turn left. Walk to the corner: the cross-street is the Poppelsdorfer Allee. Cross (careful of traffic from your left) and walk to the right up the Poppelsdorfer Allee, towards the Poppelsdorfer Castle in the distance. At the next intersection, continue straight on up the avenue. HIM is building No. 45 on the left side of Poppelsdorfer Allee behind the wrought iron gate.
The airport shuttle drops you in front of the central train station. Cross at the traffic light nearest you and take the escalator down to the underground passage. Go straight to the end of the passageway until you reach the street (Quantiusstrasse) and follow the directions above.
If you are coming to a Workshop or School, go straight to Poppelsdorfer Allee 45 and sign-in.
If you are coming for a (Junior) Trimester Program, come first to the HIM Administration at Poppelsdorfer Allee 82, diagonally across the street from the Institute proper.