RTG Activities

The following activities will be offered as part of the RTG. Our calendar webpage contains information about when each of these activities is offered and how to participate in them.

First-year seminars for undergraduate students

We plan to develop several first-year seminars for undergraduate students with themes in dynamical systems and probability; example seminars we will offer are "Patterns in nature" and "Probability via examples". Offering such classes enables us to identify early on those students with an interest in the mathematical sciences. It also allows us to encourage these students and to take a personal interest in their development during their time at Brown. By offering applied mathematics seminars in the first year, we also highlight the presence of applied mathematics at Brown.

Introductory and advanced graduate-level courses

Our curriculum currently covers dynamical systems, PDEs, and stochastic processes in separate courses. To help students make the connections between these areas, we will develop a new graduate-level course on "Deterministic and random dynamical systems" for second-year students that covers both deterministic and stochastic aspects of differential equations. This course seeks to lay the foundations of discrete and continuous deterministic and stochastic dynamical systems in a single integrated course. The idea, in each instance, is to have the analysis of a class of deterministic dynamical systems followed by the study of a corresponding stochastic counterpart in a way that elucidates the relationship between these systems.

Building on this introductory course, we will offer new topics courses that integrate dynamical systems, PDEs, stochastics, and their applications. These courses will be taught in alternating years for more advanced graduate trainees. Sample topics courses, which will be taught by faculty or by one of the postdoctoral fellows associated with the program, are "Modelling with differential equations", "Stochastic networks", and "Models of domain coarsening and growth".

Summer working groups for undergraduates, graduate trainees, and postdoctoral fellows

Each summer, we will organize working groups that consist of undergraduate students, graduate trainees, postdoctoral fellows, and faculty. Over a period of 4-8 weeks, these groups will focus through a combination of lectures, computer labs, and hands-on projects on an applied or theoretical topic that involves dynamics and stochastics. The format will be very flexible, and will allow for a wide range of experiences. Student projects may vary considerably, from reading survey papers, to exploratory computer simulations, to working on special cases and examples, to exploring different models in applications. At the end of the summer, graduate and undergraduate participants will write up a project report and give an oral presentation on their discoveries. Postdoctoral fellows and advanced graduate students will be involved by mentoring undergraduate students and first-year graduate trainees, helping with computer labs, and delivering short lectures that give background information and additional details relevant to the topic of the working group.

AMDUG

The Applied Mathematics Departmental Undergraduate Group (AMDUG) is organized by undergraduate applied mathematics concentrators. Its aim is to build a community of undergraduates who are interested in applied mathematics, form relationships between students and faculty, and invite lectures by faculty or outside speakers. We plan to support the AMDUG in a more substantial way to allow the students to invite more outside speakers, for instance from Harvey Mudd, Williams College, and colleges in New England, and to broaden the scope of their activities. We will also screen one or two movies per semester on noteworthy mathematicians (for example, "Julia Robinson and Hilbert's Tenth Problem" or "I Want to Be a Mathematician: A Conversation with Paul Halmos"), invite speakers who can popularize mathematics, organize excursions such as a trip to a baseball game preceded by a video of Henry Pollack's lecture on "Some Mathematics of Baseball", and collect a repository of popular books on mathematics and its applications.

Internships with industry

Summer internships provide our graduate trainees with valuable experience and personal contacts in companies. Several researchers at INRIA, IBM's Watson Research Labs, and Alcatel-Lucent's Bell Labs have expressed an interest in supervising students from our program and to consider them for internships in topics such as revenue management and applications of random matrix theory to the design of wireless systems. We expect additional summer internship opportunities to emerge from ongoing collaborations of several of the PIs with researchers in industrial labs (such as Microsoft and Schlumberger) in the New England area.

Mentoring and professional development

and any other topics that participants find useful. The format will be very informal with an open discussion among the participants.

Research conferences for graduate students and postdocs

Each fall, we will organize a 3-4 day research conference geared primarily to graduate students and postdoctoral fellows. In addition to prominent outside speakers, we will invite advanced graduate students and postdoctoral fellows from other institutions who work on topics related to the workshop theme. These junior participants as well as our graduate trainees and postdoctoral fellows will be encouraged to give oral or poster presentations at the workshop: besides enhancing their communication and presentation skills, this will allow them to introduce themselves and their work to other researchers. Inviting junior participants from other institutions allows the group to network and establish contacts with other peers who work in the same field.

Research conferences for undergraduate students

To showcase the environment at Brown, we will hold a recruitment conference every summer for college juniors who will apply to graduate school in mathematics the following fall. These 2-3 day meetings will feature one or two distinguished speakers, two lecture series given by graduate students or postdoctoral fellows, and a poster session. Social events and a film screening on mathematics-related movies, such as "Wolfgang Doeblin: A Mathematician Rediscovered", will complement the program and help establish personal contacts. Our goal is to convey some of the elegant theoretical concepts in dynamical systems and probability, as well as to describe some exciting applications in these fields that have both benefited from and propelled the development of the theory. The talks will be carefully designed so as to be accessible to an audience with only basic mathematical knowledge.