© Berlin Mathematical School
The Berlin Mathematical School (BMS) is the graduate school of the Cluster of Excellence MATH+ and a joint endeavor of the mathematics departments at the universities in Berlin: Freie Universität (FU), Humboldt-Universität (HU) and Technische Universität (TU). MATH+ and the BMS are funded by the DFG (German Research Foundation) as part of the "Excellence Strategy".
The BMS integrates the rich Berlin mathematics research environment and broad expertise in mathematics at the three Berlin universities into an excellent environment for graduate studies in one single mathematics graduate school. It is designed to combine many of the traditional strengths of the German PhD training system with new structures modeled on successful graduate schools at US universities which BMS's initiators had themselves experienced as doctoral students and postdoctoral fellows. The program of studies at BMS is taught in English and leads from a Bachelor's degree to an oral Qualifying Exam directly to a doctoral degree in four to five years. More than 200 PhD students from around 50 countries are currently working towards their PhDs at the BMS.
The BMS PhD program consists of two phases: In three to four semesters Phase I leads from a Bachelor's degree level to an oral Qualifying Exam. The course program for Phase I covers both a broad mathematical background and the specialization required for high-level research. Phase II (four to six semesters) is dedicated to thesis research, preferably within one of the focused training programs provided by Research Training Groups (RTGs), International Max Planck Research Schools (IMPRSs), the Collaborative Research Centers (CRCs), and the Weierstraß Institute for Applied Analysis and Stochastics (WIAS), or the Konrad-Zuse-Institute (ZIB). The BMS integrates mathematics RTGs, CRCs, and IMPRSs as certified units that provide the research environment and supervision for Phase II students. For entering straight into Phase II, applicants are expected to have a Master's degree or equivalent, or must pass the BMS qualifying exams and meet the regular admission requirements of the Berlin universities' Ph.D. programs.
The BMS offers a wide range of supervision to its students and creates outstanding conditions for study, such as the working environment at the three universities, supervision, and mentoring. Each of the three universities has a BMS area with its own lounge as a gathering point for BMS students. The One-Stop Office advises students on matters ranging from the BMS application process to visa, housing, and child-care, all the way to applying for post-doc positions. BMS professors look after students individually as mentors/advisors, helping each to find the best way through the manifold opportunities of the Berlin mathematics landscape. Women in particular find special encouragement on their mathematics career path. Currently more than 30% of BMS students are women.
Financial support is available in Phase I and Phase II through merit-based scholarships. Applications for funding need to be submitted together with the application for admission. At the moment approximately 50% of the Phase I and 25% of the Phase II students receive BMS funding. However, all PhD students in the BMS are financially supported for the duration of their studies. Other possible sources include MATH+ projects, the RTGs, CRCs, and IMPRSs, TA or RA positions at the universities or research institutes.
Phase I with scholarship: 1 December 2019
Phase I without scholarship: 1 April 2020
Phase II (Master's degree finished by 31 March 2020): 1 December 2019
Phase II (Master's degree finished by 30 September 2020): 1 April 2020
The subject of the Berlin Mathematical School is Mathematics, which encompasses many fields that are traditionally termed either "pure" or "applied" mathematics.
The BMS prefers, however, not to make that distinction; instead, the teaching areas covered by the BMS are grouped into seven parts, each of which covers a quite broad, but coherent, part of mathematics. The core offering of the BMS Phase I study program consists of 17 one-semester basic courses, at least two for each of the eight teaching areas. These courses are modern introductions to research in the respective areas, stressing interdisciplinary and trans-disciplinary connections and applications, modern trends and current questions. Their purpose is to provide solid foundations in the field, geared towards ambitious students who after the BMS Phase I will head towards mathematics PhD research work.
The geometry groups at the three Berlin universities cover a wide range of current research topics in the fields of differential geometry, geometric analysis, and mathematical physics. Cooperation among the Berlin mathematicians working in these fields has a long tradition.
This research area comprises algebraic geometry, arithmetic geometry, and number theory. For many decades, all the three mentioned fields have occupied a distinguished position at the very heart of mathematics. Moreover, the mutual interaction between the three fields has strongly stimulated the research in this area. Driving forces in the research of algebraic geometry are the minimal model program for higher dimensional algebraic varieties, breakthroughs in moduli theory, and Hodge theory. At the borderline between algebraic and arithmetic geometry are the theory of motives. In arithmetic geometry, arithmetic intersection theory culminating in arithmetic Riemann-Roch-type theorems and its applications to diophantine problems are at the core of present research, along with the study of rational points over various fields, and of properties of fundamental groups. In algebraic number theory, the research is primarily fostered by the p-adic Langlands program, whereas analytic number theory has been fundamentally influenced by the groundbreaking results on measure rigidity in ergodic theory.
The Berlin-Potsdam stochastics community consists of researchers at HU, TU, U Potsdam, and WIAS. It is globally visible and highly active at forefronts of many key areas of modern Stochastics with applications in various fields. It participates in and shapes several national and international research networks of various sizes. Brisk exchange occurs in several regular research seminars on subdomains like Finance and SPDEs, and on applications in Biology and Physics. Frequent organisations of high-class scientific events like workshops, congresses and schools of various sizes regularly invite many of the world experts to the Berlin-Potsdam area.
Discrete mathematics has its origins at the intersection of mathematics and computer science, but in recent decades, it has been established as an independent field of study. Its models, methods, tools, and algorithms are at the core of key application fields such as transportation, logistics, telecommunications, bioinformatics, and image processing, to mention just a few.
Modern methods of discrete mathematics are remarkably diverse and flexible: Their spectrum includes algorithmic, randomized, probabilistic, approximative, geometric, topological, algebraic, and optimization methods. The combination and interaction of such tools has enormously increased the power and the range of combinatorial reasoning in recent years, especially for applications in computer science, optimization, and operations research.
Berlin researchers in geometry have been very active in investigating the interplay of the two fields of differential geometry (studying smooth curves and surfaces like the solutions to many variational problems) and discrete geometry (studying polyhedral surfaces, like the typical representations used in computers). In particular, problems in mathematical visualization and geometry processing require novel discretization techniques in geometry.
Numerical mathematics is concerned with the development and analysis of efficient algorithms for the solution of mathematical problems such as those arising in natural sciences and engineering, and has thus always played an important role in applications. The larger field of scientific computing has emerged from the mutual interplay of numerical mathematicians and external users. Aiming at the simulation and optimization of real-life processes, scientific computing combines numerical mathematics with mathematical modeling and advanced computations.
Applied analysis links mathematics and scientific computing to engineering and natural sciences. Modeling in the applied sciences typically leads to systems of nonlinear ordinary or partial differential equations or variational problems. The nonlinearities reflect complex phenomena which result in oscillations, concentrations, or singularities in the mathematical model. Most problems involve the interaction of processes on different time and length scales, leading to so-called multiscale systems. Resolution on all scales is usually impossible, which requires deriving hierarchies of models to describe the problem on the various scales.
Berlin applied analysis is highly visible internationally, with the most important areas being represented by leading scientists.
The 21th century is coined the age of data due to the massive amounts of data collected on a daily basis, not only in social networks, but foremost also in science such as life sciences. The ever increasing diversity of such data ranging from images over data on manifolds to immensely complex high-dimensional data has to be matched by sophisticated methodologies for their acquisition, analysis, storage, and transmission. This poses an intriguing challenge to mathematics as a whole, since not only is it evidently of key importance for such methods to have a substantial mathematical foundation, but also often only a mathematical approach allows the development of appropriate approaches. In addition, data-based methods such as deep neural networks have lately shown tremendous success in even outperforming mathematical methods based on traditional modeling such as in the area of inverse problems or for numerical analysis of partial differential equations.
The novel area of mathematics of data science draws from various areas of traditional mathematics such as applied harmonic analysis, functional analysis, numerical linear algebra, optimization, and statistics. It also intersects with the area of machine learning, customarily assigned to computer science. Another intriguing feature of this area is the interplay between the development of deep mathematical theories and a truly interdisciplinary and even transdisciplinary component.
The BMS offers an English PhD program. Its purpose is to provide a broad and deep graduate education whose structure is compatible with international standards and thus attracts excellent students from around the world. It is designed to combine the traditional strengths of the German graduate education with the format of successful US graduate schools.
The BMS study program has two phases. Students with a Bachelor's degree start with Phase I. Admission to Phase II is either upon successful completion of Phase I or with a Master's degree or equivalent.
The purpose of the three-semester Phase I study program is to provide all BMS students with an excellent and broad mathematics graduate education, and thus with a secure basis for their own thesis research work. The program of this phase consists of basic courses giving a broad view of mathematics, and first advanced courses including seminar courses, which provide in-depth background in various areas of specialization and thus prepare students for their future thesis research.
The core offering of the BMS Phase I study program consists of two or three basic courses for each of the eight areas. The requirement for admission to the Qualifying Exam is the successful completion of five basic courses, including courses from at least three different BMS areas, and two advanced courses: one lecture course of four hours per week (or two of two hours per week) and one seminar.
The coursework is typically completed within the first three semesters, leaving time in the fourth semester for a possible master's thesis and the BMS Qualifying Exam. The Qualifying Exam will be oral and conducted by at least two examiners from the BMS faculty. Two-thirds of the BMS Qualifying Exam is devoted to the student's intended area of research. This could cover eight semester-hours of coursework, for instance one Basic Course and one Advanced Course, but usually goes somewhat beyond standard coursework. In the case that the student is working on or has completed a master's thesis, this part of the Qualifying Exam usually covers the contents of that thesis, and can even take the form of a thesis defense. The final third of the BMS Qualifying Exam is devoted to an unrelated topic, typically the contents of a BMS Basic Course. Since the BMS Areas overlap to some extent, to ensure the desired breadth it is necessary but not sufficient that this course be from a different BMS Area. Passing the Qualifying Exam will assert that the student has reached a sufficient level of general and specialized training to begin high-level research in the chosen area of mathematics.
The Phase II study program, the research phase, has a maximum duration of six semesters. During this phase, students work on their specific thesis projects. Many of them will be integrated into one of the Berlin RTGs, CRCs or IMPRSs or into MATH+ projects. In addition, students in the research phase are offered further advanced courses and special lecture series, some of them organized by MATH+, the RTGs, CRCs and IMPRSs. Phase II students will also be given the opportunity to gain teaching experience as tutors for basic courses in Phase I. The final examinations will be carried out according to the regulations of the university that confers the PhD degree.
To design and monitor the study program, each student will have a member of the BMS faculty as a mentor. The mentor will be independent of the thesis supervisor. The thesis supervisor will provide support in all aspects relating to the dissertation, including advice on choosing the right conferences and publishing articles. The separate mentor gives the student advice and feedback, and can help resolve problems and provides non-scientific advice.
On every second Friday during semester time, the Friday colloquia of MATH+ represent a common meeting point for Berlin mathematics: a colloquium with broad emanation that permits an overview of large-scale connections and insights. The conversation is about "mathematics as a whole," and mathematical breakthroughs are discussed. So far, two Field medalists presented their work. At the lunches prior to the "Sonia Kovalevskaya Colloquia" female students have a chance to discuss the career paths of successful women in mathematics.
In addition, the BMS offers annual Summer Schools, which rotate among the participating universities and have a different focus each year.
For admission to our program in 2020, applications will be accepted via our online portal from 15 September to 1 December 2019 and from 1 March to 1 April 2020.
The first round application deadline of 1 December 2019 is for
The second round application deadline of 1 April 2020 is for
Please use our online submission form to apply for the BMS program. Note that in order to access the application form, you have to first register: This is a very simple procedure - see the login form on the main page www.math-berlin.de.
Students wishing to enter Phase I of the BMS are expected to have a bachelor degree or equivalent. For students who are further advanced, part of the Phase I course requirements may be waived. For entering Phase II, students are expected to have a master or an equivalent degree, or to pass the BMS Qualifying Exam. It is not necessary that you have completed your degree by the time you submit your application. You need to have a degree by the time you want to start at BMS! For example, you are pursuing a master degree that will be completed in May. When you submit your application to the BMS in December, you already need to apply for Phase II! If you will have finished your Bachelor degree by October, you are welcome to apply for Phase I even though you currently hold no degree.
The academic calendar at the BMS is in accordance with its three supporting universities (FU, HU, TU):
Applications submitted by 1 December 2019 will be decided in March 2020. You will receive an e-mail notification about the admission decision by the end of March. Some of the applicants will be invited to attend the BMS Days on 17 and 18 February 2020.
Materials required to apply:
German applicants are allowed to submit their application in German! If your native language is German, your "Abitur" or "Matura" grade of at least "befriedigend" in English will serve as proof of English proficiency. If you cannot submit a copy of your "Abitur" or "Matura" or it does not show a grade for English you will have to submit a result of another English language test.
Phase I (three to four semesters) leads students from the Bachelor's degree to the Qualifying Exam. Students need to achieve an average grade of at least "good" on the German grading scale in their Phase I courses to be allowed to take the Qualifying Exam. Students must pass the Qualifying Exam with at least a grade of "good" to be allowed into Phase II. Successfully passing the Phase I confirms that the student achieved a satisfactory level on which the dissertation can be built. Students are now ready to undertake independent research. Students who are either not admitted to take the Qualifying Exam or received grade of less than "good" are given the chance to do a master. The allocation of scholarships for Phase II is based on the student's performance in Phase I and in the Qualifying Exam. Having had a Phase I scholarship does no guarantee a Phase II scholarship!
Berlin Mathematical School (BMS)
Nadja Wisniewski, Managing Director
Raum MA 221
Google media is disabled