Prof. Dr. Anja Sturm
Professorin für Angewandte Stochastik
Geschäftsführende Direktorin des Instituts für Mathematische Stochastik
I am a Professor for Stochastics and its Applications at the University of Göttingen.
From 2004 to 2009 I was an Assistant Professor at the Department of Mathematical Sciences at
the University of Delaware, USA. I received my DPhil from Oxford University in 2002, where I
was supported by a Rhodes Scholarship and an EPSRC award. I
started my undergraduate work at the University of Tübingen, Germany,
in Mathematics and Physics. I then received a Master of Science in Applied
Mathematics from the University of Washington. Before joining the
University of Delaware, I was a postdoctoral fellow at the
Weierstrass Institute of Applied Mathematics and Stochastics
in Berlin and at the University of British Columbia, Vancouver, as well as
a Junior Professor of Applied Probability at the Technical University Berlin.
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My research interests lie in Probability theory and its applications.
The main focus of my work has been on probability models and stochastic processes
that describe the evolution of interacting particle systems and population
models forward and backward in time. Many of these models have implications
for the applied sciences, especially for Biology and Physics. My particular interest has
been on models in population genetics and ecology. Here, realistic mathematical
models of the underlying processes that govern which genes are passed on
from one generation to the next are of ever increasing importance as they are
prerequisite to the correct quantitative analysis and interpretation of the
unprecedented quantities of genetic data available today.
Apart from studying stochastic models that are of relevance to biological application, in particular in Genetics, I am interested in applying similar models and probabilistic tools to Financial Mathematics and expect to direct my research efforts towards this area in the near future.
My own recent research has been centered on suitably chosen models of populations (of individuals or genes) that realistically incorporate the influence of two factors which have a significant impact on genetic data: firstly, spatial substructure of the population
manifesting itself through local reproduction and interaction as well as locally varying
environments; secondly, variations in reproductive success as they may arise due to inherent randomness or a selective advantage or disadvantage stemming from the genetic type of an individual, its location, or its surrounding environment (of other competing individuals). Recently, I have received funding from the National Science Foundation to continue to develop the mathematical theory on various aspects of such spatial models with varying offspring laws.
Backward in time the focus is on analyzing the genealogical tree of a small sample from a population and their diffusion limits (as the overall population size is large). These models of genealogies are also known as coalescent processes because the ancestral lines forming the genealogical tree of the sample coalesce as we follow them into the past. Such coalescent processes connected to populations models with singular offspring distributions -corresponding to potentially large individual families- have attracted much recent attention as several deep connections to different classes of stochastic processes have been discovered and exploited - albeit in a non-spatial setting. On the other hand, spatial settings arising from models with population subdivision and migration (and small offspring variances) have been studied for some time. In my work, one aim will be to bring these two directions of research together by studying the genealogies of spatial population models with larger offspring variances.
For applications, the goal is to describe the distribution of genetic variability one should expect to see
in the sample given these characteristic influences. Comparison with data then allows for inference of the population's history. On the level of individuals this answers to the question "Where did we come from?", on the level of genes it also sheds light onto the importance and function of particular parts of our genetic code.
Forward in time one of the central questions being addressed is to determine parameter regimes for
long-term survival without explosion of the population size and -if multiple types of particles are present initially- of long-term coexistence of various or all types. Stochastic particle models that may exhibit such phenomena are generally spatial models with an interaction mechanism between particles that gives small populations (of a particular type) an advantage. Unlike these particle systems with self-regulation those with independent reproduction of all individuals, which are mathematically simpler and have been well studied, do not have this property and are known to either go extinct or explode. The ultimate goal is to determine whether there are phase transitions in the parameter space that separate survival of the populations from extinction and coexistence from dominance of single types. This allows to conclude
which mechanisms and forces lead to a stable population with lasting diversity.
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"Stochastische Modelle in der Populationsgenetik".
Book chapter in "Facettenreiche Mathematik: Einblicke in die moderne mathematische Forschung"
(K. Wendland and A. Werner, Editors) Vieweg Teubner (2011).
DPhil thesis: On spatially structured population
processes and relations to stochastic partial differential equations,
Oxford University, 2002.
Master thesis: On mechanisms to synchronize neuronal activity,
University of Washington, Seattle, 1998.
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In the winter semester 2014/15 I am teaching the following courses:
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Past teaching at the University of Göttingen included
Stochastic processes I (Einführung)
Seminar on Stochastic Processes (Branching processes)
Seminar on Financial Mathematics (with Prof. Schuhmacher)
Oberseminar on Stochastic Processes (Tree-valued processes)
From 2004 to 2009 I have taught courses at the University of Delaware including Theory of Probability, Martingales, Brownian motion, and stochastic calculus, Introduction to stochastic processes, Probability Theory and Applications, Mathematical Statistics, and Ordinary differential equations.
Prior to 2004 I have taught Introductory Probability at the University of British Columbia and a graduate level course on population processes- referring to branching processes, superprocesses and coalescent processes- at the Technical University Berlin. I have also been a teaching assistant and tutor at Oxford University for the following courses: Basic Probability, Applied Probability, Stochastic Processes, Statistics, Differential Equations, Discrete Mathematics and Linear Programming.
Stochastic processes I (Einführung), Stochastic processes II (Vertiefung), Stochastic processes III (Spezialisierung), Stochastic processes IV (Aspekte)
Basic probability (Grundlagen der Stochastik)
Measure and probability theory (Mass - und Wahrscheinlichkeitstheorie)
Stochastisches Praktikum I
Statistics for Geologists (Statistik für Geologen)
Seminars on Stochastic processes
(Coagulation- and fragmentation processes, Levy processes, random graphs, percolation, stochastic differential equations, large deviations, Poisson processes, DNA sequence evolution, random walk in random environment, modelling gene genalogies)
"The most important questions of life are, for the most part, really only problems of probability."
(Pierre Simon de Laplace, Theorie Analytique des Probabilites)
"How dare we speak of the laws of chance? Is not chance the antithesis of all law?"
(Joseph Bertrand, Calcul des probabilites)
"The theory of probability as a mathematical discipline can and should be developed from axioms in exactly the same way as geometry and algebra."
(Andrei Kolmogorov, Foundations of the Theory of Probability)
"Mathematicians are like a certain type of Frenchman: when you talk to them they
translate it into their own language and then it soon turns into something
entirely different. " [Die Mathematiker sind eine Art Franzosen: Redet man zu
ihnen, so uebersetzen sie es in ihre Sprache, und dann ist es alsobald ganz
(Johann Wolfgang von Goethe, Maxim 1279)
More probability quotes
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