Brave New Rings seminar 2007

Future seminars:

Friday October 19th at 10.15 - 12.00 in room B63
CLARK BARWICK:
D-crystals, II
(This seminar may be moved to December.)

Past seminars:

Friday January 19th at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-categories for fun and profit, X
Wednesday January 24th at 14.15 - 16.00 in room B91
CLARK BARWICK:
Infinity-categories for fun and profit, XI
Wednesday February 14th at 14.15 - 16.00 in room B91
CLARK BARWICK:
Homotopical algebraic geometry, III
Wednesday February 21st at 14.15 - 16.00 in room B91
CLARK BARWICK:
Homotopical algebraic geometry, IV
Friday February 23rd at 10.15 - 12.00 in room B63
CLARK BARWICK:
Infinity-categories for fun and profit, XII
Wednesday February 28th at 14.15 - 16.00 in room B91
CLARK BARWICK:
Homotopical algebraic geometry, V
Friday March 2nd at 10.15 - 12.00 in room B63
JOHN ROGNES:
Topological logarithmic structures, II
Wednesday March 7th at 14.15 - 16.00 in room B91
CLARK BARWICK:
Homotopical algebraic geometry, VI
Friday March 23rd at 10.15 - 12.00 in room B63
PHILIPP REINHARD (Glasgow):
Cellular simplicial algebras, II
Wednesday March 28th at 14.15 - 16.00 in room B91
ANDY BAKER (Glasgow/Oslo):
More on André-Quillen homology and minimal atomic S-algebras
I will discuss further facts about TAQ and how to do calculations to check whether various S-algebras are minimal atomic.
Friday April 13th at 10.15 - 12.00 in room B63
CLARK BARWICK:
Homotopical algebraic geometry, VII
Tuesday April 17th at 14.15 - 16.00 in room B63
CLARK BARWICK:
Homotopical algebraic geometry, VIII
Friday April 27th at 10.15 - 12.00 in room B63
CLARK BARWICK:
K-theory of infinity-categories, I
Friday May 4th at 14.15 - 15.15 in room B63
ANDY BAKER:
Power operations and non-extensions of S-algebras
Wednesday May 9th at 14.15 - 16.00 in room B91
JOHN ROGNES:
Topological logarithmic structures, IV
Friday May 11th at 10.15 - 12.00 in room B63
CLARK BARWICK:
K-theory of infinity-categories, II
Wednesday May 16th at 14.15 - 16.00 in room B91
JOHN ROGNES:
Topological cyclic homology, I
A basic introduction to Bökstedt's model for topological Hochschild homology (THH) of a symmetric ring spectrum, its cyclic fixed points, the Frobenius and restriction maps, and topological cyclic homology (TC).
Friday May 18th at 10.15 - 12.00 in room B63
JOHN ROGNES:
Topological cyclic homology, II
We discuss the norm-restriction sequence for cyclic fixed points of THH for Gamma-rings.
Friday August 31st at 10.15 - 12.00 in room B71
CLARK BARWICK:
Grothendieck-Verdier duality, I
Tuesday September 4th at 14.15 - 16.00 in room B63
CLARK BARWICK:
Grothendieck-Verdier duality, II
Wednesday September 5th at 14.15 - 16.00 in room B62
SVERRE LUNØE-NIELSEN:
Homotopy of the Tate construction
We will discuss a procedure to compute the homotopy groups of the homotopy inverse limit of bounded below spectra of finite type. Given such a limit system of spectra Y -> ... -> Y_n -> Y_n+1, there is a version of the Adams spectral sequence due to Caruso-May-Priddy that calculates the p-adic homotopy of Y based on the direct limit of the cohomology groups H^* (Y_n; F_p) as n tend to minus infinity.
Our main examples of such towers come from the Tate construction on X, where X is a G-spectrum. This Tate construction can expressed as a homotopy inverse limit, and there is a (co-)homological Tate spectral sequence converging, under certain hypotheses, to the limiting cohomology groups above.
Our interest in the Tate construction stems from its relation to the study of the natural map X^G -> X^hG comparing fixed points and homotopy fixed points of the G-spectrum X. Hopefully the talk will include some motivating background of the problem, putting it into context.
Friday September 7th at 10.15 - 12.00 in room B71
CLARK BARWICK:
D-crystals, I
Wednesday September 12th at 14.15 - 16.00 in room B62
SVERRE LUNØE-NIELSEN:
The topological Singer construction, I
Friday September 14th at 10.15 - 12.00 in room B62
JOHN ROGNES:
Topological logarithmic structures, repeat, I
Wednesday September 19th at 14.15 - 16.00 in room B62
SVERRE LUNØE-NIELSEN:
The topological Singer construction, II
Friday September 21st at 10.15 - 12.00 in room B62
JOHN ROGNES:
Topological logarithmic structures, repeat, II
Wednesday September 26th at 14.15 - 16.00 in room B62
BOB BRUNER:
The Segal conjecture for cyclic groups
(Following D.C. Ravenel.)
Friday October 5th at 10.15 - 12.00 in room B62
MARCEL BÖKSTEDT:
Higher cyclic reduced/extended powers
(Following I. Ottosen.)
Tuesday October 9th at 14.15 - 16.00 in room B63
MARCEL BÖKSTEDT:
Higher cyclic reduced/extended powers, II
Wednesday October 10th at 14.15 - 16.00 in room B62
SVERRE LUNØE-NIELSEN:
C_p-fixed points of THH(F_p) and THH(Z)
We will study the canonical map THH(B)^C -> THH(B)^hC for the cyclic group C = C_p of order p and B = HF_p, HZ. The result, already known by work of Hesselholt-Madsen and Bökstedt-Madsen, is that fixed points and homotopy fixed points are p-adically equivalent on connective covers, in homotopy with (suitably chosen) finite coefficients.
Our proof of this fact will be carried out by using homological methods, including a precise description of the continuous cohomology of the C_p-Tate construction on THH(B), for the S-algebras B in question.
For the field of p elements, we show that the continuous cohomology of THH(F_p)^tC_p is isomorphic, as a left A-module, to the module gotten from R₊(F_p) by inducing the latter up to a left A-module over the sub algebra A₀. A similarly statement is true for B = HZ.
Our main technical tool is the map of spectra Psi: R₊(B) -> THH(B)^tC_p. We will describe the homological Tate spectral sequences involved and the map of spectral sequences induced by Psi.
Friday October 12th at 10.15 - 12.00 in room B62
SVERRE LUNØE-NIELSEN:
C_p-fixed points of THH(F_p) and THH(Z), II

Past years:

fall 2006

YFF home page:

Brave New Rings

John Rognes / October 5th 2007