pAdic Geometry and Homotopy Theory
Conference at Hotel Alexandra, Loen, Norway, August 2nd8th 2009
The Research Council of Norway funds a research program on Brave New Rings
in the period 2005  2009. In this framework, there will
be a Conference on pAdic Geometry and Homotopy Theory at Hotel Alexandra
at Loen in the Nordfjord region of western Norway.
The aim of the conference is to develop the current interplay
between arithmetic algebraic geometry and stable homotopy theory.
Using structured ring spectra one can form topological structure sheaves
for moduli stacks of elliptic curves or other abelian varieties, whose
ring spectra of global sections define powerful new homology theories.
Using sheaves of infinitycategories one can form topological crystalline
cohomology, with associated de RhamWitt complexes closely related to
topological cyclic homology and padic algebraic Ktheory. For complete
local rings of mixed characteristic, or for structured ring spectra of
mixed chromatic types, there are log (= logarithmic) geometric extensions
of these theories, leading to de RhamWitt complexes with log poles,
log topological cyclic homology and log Ktheory. The hope is that both
algebraic geometers and homotopy theorists will have something to learn
from the modern developments in these adjacent fields.
Here is a list of titles and
abstracts. Talks marked (L) are in Loensal 3 on the first floor,
while talks marked (F) are in Fjordsal 1+2 on the ground floor.
Lecture notes for some of the talks are available below.
Program:
Sunday August 2nd
 WF158 arrival

Widerøe flight WF158 OsloSandane, departure OSL 11:55, arrival
SDN 12:58.
Fjord1 chartered bus SandaneLoen, boarding from 13:00, arrival ca 14:30.
 WF153 arrival

Widerøe flight WF153 OsloSandane, departure OSL 16:10, arrival
SDN 17:13.
Fjord1 chartered bus SandaneLoen, boarding from 17:15, arrival ca 18:45.
 19:00  21:00

Dinner buffet in Restaurant Charlotte 19:00  21:00.
Drinks are bought separately.
Monday August 3rd
 07:00  10:00

Breakfast.
 10:00  11:00 (L)

JeanMarc Fontaine (Orsay): "padic cohomologies and comparison theorems"
(lecture notes)
 11:30  12:30 (L)

Arthur Ogus (Berkeley): "Logarithmic geometry"
(lecture notes)
 13:00  14:00

Lunch in Restaurant Charlotte.
 15:00  16:00 (L)

Christian Schlichtkrull (Bergen): "Symmetric spectra and diagram spaces"
(lecture notes)
 16:30  17:00

Coffee/tea break in Loensal salon.
 17:00  18:00 (L)

Steffen Sagave (Münster): "Graded log symmetric ring spectra"
(lecture notes)
 19:00  21:00

Dinner in Restaurant Charlotte.
Tuesday August 4th
 07:00  10:00

Breakfast.
 10:00  11:00 (L)

Luc Illusie (Orsay): "Review of de RhamWitt theory"
(lecture notes)
 11:30  12:30 (L)

Kiran Kedlaya (MIT): "Rigid cohomology and its coefficients"
(lecture notes)
 13:00  14:00

Lunch in Restaurant Charlotte.
 15:00  16:00 (F)

Teena Gerhardt (Indiana): "Fixed points of THH and the de RhamWitt complex"
 16:30  17:00

Coffee/tea break in Loensal salon.
 17:00  18:00 (L)

Christian Ausoni (Bonn): "Algebraic Ktheory of the fraction field
of topological Ktheory"
(lecture notes)
 19:00  21:00

Dinner in Restaurant Charlotte.
Wednesday August 5th
 07:00  09:30

Breakfast.
Niels Henrik Abel's birthday.
 09:30  10:30 (L)

Amnon Besser (Ben Gurion): "Syntomic regulators and special values
of padic Lfunctions"
(lecture notes)
 10:30  11:00

Coffee/tea break in Loensal salon.
 11:00  12:00 (F)

Wiesława Niziol (Utah): "padic comparison morphism via Ktheory"
 12:00  13:00

Lunch in Restaurant Charlotte.
 Conference excursion

Meet outside hotel at 13:05.
Bus departure to Sande, MS Kjendal boat at
13:30 across Loenvatnet.
Bus and easy walk to Kjenndalsbreen glacier arm. Return from
Kjenndalsanden at 16:30, reaching hotel ca 17:30.
 Alternative hike

Meet outside hotel at 13:05. Minibus transport to Oppheim. Mountain hike
to Lofjellet (1379 meters, six hours, "magnificent view over Loen and
Olden valley").
 Other alternatives


Mountain hike to Årheimsfjellet (three hours easy walk, "good
mountain track with beautiful views").

Mountain hike to Auflemåsen (four to five hours, "breathtaking
views from the summit").
 19:00  21:00

Dinner in Restaurant Charlotte.
Thursday August 6th
 07:00  10:00

Breakfast.
 10:00  11:00 (F)

Tyler Lawson (Minnesota): "Topological automorphic forms"
 11:30  12:30 (F)

Clark Barwick (Harvard): "Equivariant derived algebraic geometry
and crystalline realizations of Ktheory, I"
(lecture notes)
 13:00  14:00

Lunch in Restaurant Charlotte.
 15:00  16:00 (F)

John Rognes (Oslo): "Logarithmic THH and TC"
(lecture notes)
 16:30  17:00

Coffee/tea break in Loensal salon.
 17:00  18:00 (F)

Wiesława Niziol (Utah): "Logarithmic Ktheory"
 19:00  21:00

Dinner in Restaurant Charlotte.
Friday August 7th
 07:00  10:00

Breakfast.
 10:00  11:00 (L)

Markus Szymik (Bochum): "Brave new rings from K3 surfaces"
(lecture notes)
 11:30  12:30 (F)

Clark Barwick (Harvard): "Equivariant derived algebraic geometry
and crystalline realizations of Ktheory, II"
(lecture notes)
 13:00  14:00

Lunch in Restaurant Charlotte.
 15:00  16:00

Mike Hill (Virginia): "On the slice filtration and the Kervaire
invariant one problem"
(lecture notes)
 16:30  17:00

Coffee/tea break in Loensal salon.
 17:00  18:00 (F)

Jack Morava (Johns Hopkins): "A theory of base motives"
(lecture notes)
 19:00  21:00

Dinner in Restaurant Charlotte.
Saturday August 8th
 07:30  09:45

Breakfast.
Please settle hotel bills before departure.
 WF165 departure

Fjord1 chartered bus departure from hotel Saturday at 09:45, for
Widerøe flight WF165 SandaneOslo, departure SDN 12:00, arrival
OSL 12:57.
 Alternative ending

Climb to, or towards, the summit of Skåla
at 1848 meters above sea level. Allow five hours for ascent and three
hours for descent. Good physical condition and proper hiking shoes
required.
Please check the weather
forecast before walking in the mountains.
 19:00  21:00

Dinner in Restaurant Charlotte 19:00  21:00.
Sunday August 9th
 07:30  10:00

Breakfast.
Please settle hotel bills before departure.
 WF159 departure

Fjord1 chartered bus departure from hotel Sunday at 11:00, for
Widerøe flight WF159 SandaneOslo, departure SDN 13:13, arrival
OSL 14:10.
Participants:
 Vigleik Angeltveit (Chicago)
 Christian Ausoni (Bonn)
 Andy Baker (Glasgow)
 Clark Barwick (Harvard)
 Julie Bergner (UC Riverside)
 Amnon Besser (Ben Gurion)
 Stanisław Betley (Warsaw)
 Andrew Blumberg (Stanford)
 Morten Brun (Bergen)
 Bob Bruner (Wayne State)
 Scott Carnahan (MIT)
 Christopher Davis (MIT)
 Bjørn Dundas (Bergen)
 Halvard Fausk (Oslo)
 JeanMarc Fontaine (Orsay)
 John Francis (Northwestern)
 David Gepner (UI Chicago)
 Teena Gerhardt (Indiana)
 Idar Hansen (Trondheim)
 Yonatan Harpaz
 John E. Harper (Lausanne)
 Mike Hill (Virginia)
 Luc Illusie (Orsay)
 Kiran Kedlaya (MIT)
 Thomas Kragh (Oslo)
 Tore A. Kro (Sarpsborg)
 Tyler Lawson (Minnesota)
 Helge Maakestad
 Mike Mandell (Indiana)
 Jack Morava (Johns Hopkins)
 Wiesława Niziol (Utah)
 Jumpei Nogami (UI Chicago)
 Arthur Ogus (Berkeley)
 Kyle Ormsby (Michigan)
 Paul Arne Østvær (Oslo)
 Geoffrey Powell (Paris)
 Birgit Richter (Hamburg)
 John Rognes (Oslo)
 Constanze Roitzheim (Glasgow)
 Sergey Rybakov (Moscow)
 Steffen Sagave (Münster)
 Andrew Salch (Johns Hopkins)
 Rekha Santhanam (Johns Hopkins)
 Tomer Schlank
 Christian Schlichtkrull (Bergen)
 Noam Solomon (Ben Gurion)
 Neil Strickland (Sheffield)
 Olga Stroilova (MIT)
 Markus Szymik (Bochum)
 Barry J. Walker (Northwestern)
 Tim Wouters (Leuven)
John Rognes / August 21st 2009