Monday 1
|
|
Tuesday 2
|
4:10 pm, room 1425. Departmental Welcome. Professor Tsinakis will share his thoughts about the direction of the department this year, and Professor Crooke will introduce new faculty and graduate students. Refreshments will be served.
|
Wednesday 3
|
4:10 pm, room 1310.
Topology
& Group Theory Seminar. Gunnar Carlsson, Stanford University. Representations and K-theory of fields.
Over the last ten years, a great deal of progress has been made in the study of the algebraic K-theory of fields. Notably, due to
work of Voevodsky and others, we have a proof of the Bloch-Kato and Milnor conjectures which describes an E_2-term of a spectral sequence
which converges to the algebraic K-theory of a field F in terms of the cohomology groups of the absolute Galois group. In this talk, I will
present a different approach which (conjecturally) identifies the algebraic K-theory spectrum in terms of a spectrum constructed out of
the complex representation theory of the absolute Galois group of the field. I will also discuss some cases where the conjecture has been
proved, and strategies toward a proof in all cases.
|
Thursday 4
|
4:10-5 pm, room 5211. Colloquium. Gunnar Carlsson, Stanford University. Topology and Data. Investigators in all areas of science are aware that data of various kinds are being produced at a rate which appears to be swamping our capacity to analyze it. In this talk, we will present some methods based on topological thinking which permit the qualitative analysis of data in a number of situations, and in addition provide a methodology for extending ideas from statistics into the study of "structural" invariants. I will talk about the theory of these methods, as well as about some examples. Tea at 3:30 pm in SC 1425.
|
Friday 5
|
4:10-5:00 pm, room 1307. Partial Differential Equations Seminar. Misha Perepelitsa, Vanderbilt University. Dynamics of a density discontinuity in compressible viscous flows. We will discuss the evolution of the interface of a density discontinuity in the model of Navier-Stokes equations for compressible flows. All time existence of weak, near equilibrium solutions will be established, when the interface is in non-singular contact with the boundary of the flow domain. A singular contact problem will be considered on a model system of equations for which we show instantaneous change of some geometrical properties of the interface.
|
