New team-taught course offered spring 2014: “Differential geometry in classical and quantum mechanics”

1) Introduction and Motivation

We would like to call attention to a new class offered this winter/spring 2014 quarter, being taught jointly by Prof. Daniel Ruberman in Mathematics and Prof. Albion Lawrence in Physics.  This is being listed jointly as Physics 202a (Quantum Field Theory) and Math 221b (Topics in Topology).  It is being team-taught under the auspices of the Brandeis Geometry and Dynamics IGERT program.

This course aims to introduce basic notions of fiber bundles and connections on them, and their application to basic physical examples in classical and quantum mechanics: especially the mechanics of deformable bodies, and Berry’s phase.  The target audience is mathematics and physics students, and mathematically inclined students in physical chemistry, neuroscience, computer science, and economics.  The essential principles here find applications to chemical and neural oscillators and control theory; there have even been suggestions that it is a useful language for describing currency trading.

The mathematics covered here typically appears in advanced courses on quantum and statistical field theory.  However, it has much broader applicability, and the instructors felt that studying more elementary physics examples better highlighted the essential mathematics and lead to a broader perspective that would better prepare students to find new and creative uses for the mathematics.  Furthermore, they allow us to teach a broader audience, as the essential physics background is straightforward and can be explained without the student needing two years of graduate-level physics courses.

This course is essentially a graduate course, but it is certainly appropriate for senior undergraduates with a solid mathematical background (math and physics majors especially).  The modern mathematical language of manifolds and vector bundles will be introduced and used throughout, but with reference to physical and geometric notions.  This will provide physics students with an appropriate vocabulary for further study, while mathematics students can try to grasp the intuition behind the formalism.  Note that the course satisfies one of the IGERT course requirements; however, we strongly encourage non-IGERT students to enroll.

The course is scheduled to take place Mondays and Wednesdays from 2-3:20pm. [Read more…]

Gessel named Berenson Professor of Mathematics

According to BrandeisNOW, Ira Gessel has been named the fourth Theodore W. and Evelyn G. Berenson Professor of Mathematics. A 2013 fellow of the American Mathematical Society, Gessel does research in the area of combinatorics, the science of counting finite structures.

“It is a great honor to be awarded the Berenson Chair,” Gessel says. “The mathematics department has been a wonderful place to teach and do research, and I look forward to continuing my work here for years to come.”

Quantum Field Theory: An Interdisciplinary Study Group

William Hicks, a grad student in Physics, writes:

    This semester, graduate students from a wide range of departments will be coming together to study quantum field theory (QFT) as part of the interdisciplinary IGERT program. QFT is a subject whose mathematical underpinnings crop up in a wide range of seemingly unrelated fields, and the study group hopes to take advantage of the varied backgrounds of its members. Mathematicians in the group can help provide mathematical rigor, while physicists can help supply the physical intuition for many of the otherwise abstruse corners of the subject.  Students from other disciplines will be able to broaden the discussion by showing how some of the techniques discussed also show up in their fields.

The study group will meet from noon to 1:00 every Wednesday in Goldsmith 226. All are welcome!

Harald Helfgott ’98 and the Odd Goldbach Conjecture

The Computer Science Dept blog passed on the report from the New Scientist that Harald Halfgott ’98 (Math/Co Sci), now working at the École Normale Supérieure in Paris, has proved the odd (weak) Goldbach conjecture, which states that every odd number above 5 is the sum of three primes. For the paper “Major Arcs for Goldbach’s Problem”, see http://arxiv.org/abs/1305.2897

see also: http://blogs.scientificamerican.com/roots-of-unity/2013/05/15/goldbach-variations/

Brandeis mathematicians in inaugural class of AMS fellows

Department members and emeritus professors named as AMS fellows.

The Math department website notes that Professors Ruth Charney, Ira Gessel, and Kiyoshi Igusa, along with emeritus professors Edgar Brown, David Buchsbaum, Harold Levine, Richard Palais, and Gerald Schwarz, have been named to the inaugural group of Fellows of the American Mathematical Society.  According to the description on the AMS website, the “Fellows of the American Mathematical Society program recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics.” The first class was announced earlier this month. Among Brandeis alumni in this first batch of fellows, we noted Karen Uhlenbeck (PhD ’68), Jill Mesirov (PhD ’74), Ralph Cohen (PhD ’78), and Ulrike Tillmann ‘85.

Gessel awarded Simons Fellowship

Professor of Mathematics Ira Gessel has been awarded a prestigious Simons Fellowship in Mathematics.  He is part of the initial class of awardees for this fellowship, which will support research activities during his sabbatical leave in the spring of 2013.  Other recipients included Math alumni János Kollár (PhD ’84), now at Princeton, and Irena Peeva (PhD ’95), now at Cornell.

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