IU/PU/IUPUI Joint Topology Seminar

December 5, 2015
IUPUI
Indianapolis, IN, USA

The 4th meeting of the IU/PU/IUPUI Joint Topology Seminar will be held at IUPUI in Indianapolis, Indiana on Saturday December 5, 2015. Talks will begin at 10am and end at 12:30pm, followed by lunch.

Registration

If you plan to attend, please email Dan Ramras (dramras at iupui.edu), and indicate if you will need a parking pass and if you plan to come to lunch. We can provide parking passes, which allow you to park in the lots in front of the LD building. (Most parking spots on the IUPUI campus require a permit, even on weekends.)  Note that IU and Purdue parking permits are valid at IUPUI.  More details are below.

Confirmed Speakers

Charmaine Sia, Indiana University: Structures on forms of K-theory
Marco Varisco, University at Albany, SUNY: Algebraic K-theory of group rings via the Farrell-Jones assembly map and the cyclotomic trace

Schedule:

10am: Charmaine Sia

11:30am: Marco Varisco

Abstracts:

Charmaine Sia, Structures on forms of K-theory

Abstract: In the early 1970's, Morava studied forms of K-theory and observed that they have interesting number theoretic connections. Until very recently, forms of K-theory have not been studied in greater depth and integrated into the theory of tmf. I establish some expected structured ring spectra results on forms of K-theory. Forms of objects are usually classified by Galois cohomology. Based on the structured ring spectra results established, I give a criterion for distinguishing homotopy equivalence classes of forms of K-theory via a computation in the second homotopy group of the spectrum.


Marco Varisco, Algebraic K-theory of group rings via the Farrell-Jones assembly map and the cyclotomic trace

Abstract: Whitehead groups, and more generally higher algebraic K-theory groups of group rings, play an important role in the study of high-dimensional manifolds. The Farrell-Jones Conjecture provides conceptual and computational tools for understanding these groups. I will present joint work with Wolfgang Lück, Holger Reich, and John Rognes [arXiv:1504.03674], in which we prove that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds for cyclotomic fields. This generalizes (and reproves) a seminal result of Bökstedt, Hsiang, and Madsen. In many cases the number theoretic conjectures are true, so we obtain rational injectivity results about assembly maps, in particular for Whitehead groups, under finiteness assumptions on the group only. The proof uses the cyclotomic trace map to topological cyclic homology, Bökstedt-Hsiang-Madsen’s functor C, and new general isomorphism and injectivity results about the assembly maps for topological Hochschild homology and C.

Directions

Talks will be held on the IUPUI campus in downtown Indianapolis, in the basement of the LD building, room LD 026. Note that the LD building and the SL building are joined; LD rooms are on the southern side (further from Michigan St.).

Parking Information

IU permits are valid in certain IUPUI surface lots.  Detailed information is available here.  There are two lots in front of the LD/SL building. Those with an IU A or C permit can park in either lot, and those with an IU E permit can park in the southern lot. Purdue permits are also honored at IUPUI. If you will need a parking pass, please email Dan Ramras (dramras at iupui.edu).

Campus Map

Organizers

Dan Ramras (dramras at iupui dot edu)
Mike Mandell (mmandell at indiana dot edu)
David Gepner (dgepner at purdue dot edu)

Please contact us with questions.

Past meetings:

April 25, 2015

January 31, 2015

November 8, 2014


Email: dramras at iupui dot edu