Mathematics Department - Colloquium - Spring 2017

Colloquium - Spring 2017



Mathematics Department Colloquia take place on Friday afternoons from 4:00-5:00PM in the Hill Center, Room 705, on Busch Campus. Also, due to recent construction on Route 18, most on-line maps and driving instructions are out of date. Here are updated driving directions. If you need information on public transportation , you may want to check the New Jersey Transit page for information on fares and schedules for the Northeast Corridor Line. Taxis are available at the New Brunswick train station (fare about $7) and can take you to and from the Hill Center (Victory Cabs, (732) 545-6666). The Rutgers Campus Bus System provides free inter-campus transportation, with the A and H buses taking passengers between Busch Campus and College Avenue, with the A providing a faster ride from College Avenue and the H providing a faster ride from the Hill Center : please visit their website for bus schedules and maps, including real-time tracking of campus buses.

Unfortunately, colloquium cancellations do occur from time to time. Please feel free to call our department (732)-445-3921 before embarking on your journey.

Colloquium participants and hosts may wish to also consult the Rutgers University academic calendar, as well as its calendars of religious holidays and of weather emergencies and university closings.

Organizer(s)

Vladimir Retakh

Archive

Website

http://www.math.rutgers.edu/~az202/colloquium



Upcoming Talks


Friday, March 3rd

Tim Austin, Courant Institute

"Ergodic theory and the geometry of high-dimensional metric spaces"

Time: 4:00 PM
Location: Hill 705
Abstract: The most basic examples of shift-systems with positive entropy are the Bernoulli shifts, under which the coordinates are independent. In the special case of Bernoulli shifts, it was shown by Ornstein that entropy is actually a complete invariant. In order to prove this, Ornstein developed a concrete necessary and sufficient condition for a general shift-system to be isomorphic to a Bernoulli shift. We also know that Bernoulli shifts often appear as images of other, more complex systems under equivariant maps: by a theorem of Sinai, this is true whenever the necessary inequality between their entropies is satisfied.

The proofs of these more advanced results requires a delicate investigation of the finite-dimensional marginals of the shift-system, regarded as a sequence of discrete probability spaces endowed with their Hamming metrics. It turns out that other ergodic theoretic consequences are related to open problems on the possible structure of such discrete `metric probability spaces'. After sketching the history of this area, I will describe some of these connections.

This talk will require a knowledge of basic real analysis and some measure theory, and some simple probability theory will be helpful. I will not assume anything from dynamics or ergodic theory.


Friday, March 10th

Jean Bricmont , Univ. Catholique de Louvain

"TBA"

Time: 4:00 PM
Location: Hill 705


Friday, March 24th

Lauren Williams, Berkeley

"TBA"

Time: 4:00 PM
Location: Hill 705


Friday, March 31st

Mohammed Abouzaid, Columbia University

"TBA"

Time: 4:00 PM
Location: Hill 705


Friday, April 7th

Denis Auroux, Berkeley

"TBA"

Time: 4:00 PM
Location: Hill 705


Friday, April 14th

Francois Treves, Rutgers University

"TBA"

Time: 4:00 PM
Location: Hill 705


Friday, April 28th

Tobias Colding, MIT

"TBA"

Time: 4:00 PM
Location: Hill 705





Past Talks


Friday, February 24th

Richard Schwartz, Brown University

"5 points on the sphere "

Time: 4:00 PM
Location: Hill 705
Abstract: Thomson's problem, which goes back to 1904, asks how N points will arrange themselves on the sphere so as to minimize their electrostatic potential. A more general problem asks what happens for other power law potentials. In spite of quite a bit of experimental evidence accumulated over the past century, and some spectacular results for values of N associated with highly symmetric polyhedra, there have been few rigorous results for the modest case N=5. In my talk I will explain my recent proof that, for N=5, the triangular bi-pyramid is the minimizer with respect to all power laws up to a constant S=15.04808..., and then the minimizer changes to a pyramid with square base. My talk will have some nice computer animations.


Friday, February 17th

Lenhard Ng , Duke University

"Studying knots through symplectic geometry and cotangent bundles "

Time: 4:00 PM
Location: Hill 705
Abstract: Symplectic geometry has recently emerged as a key tool in the study of low-dimensional topology. One approach, championed by Arnol'd, is to examine the topology of a smooth manifold through the symplectic geometry of its cotangent bundle, building on the familiar concept of phase space from classical mechanics. I'll focus on one particular application of this approach that yields strong invariants of knots. I'll discuss a mysterious connection between these knot invariants and string theory, as well as a recent result (joint with Tobias Ekholm and Vivek Shende) that the invariants completely determine the underlying knot.


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