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Conference and Summer School in Algebraic Topology in honor of Huynh Mui's 60th birthday.
Vietnam National University, Hanoi, August, 2004
School: August 9--14
Conference: August 16--20
Summer School Courses:
John Hubbuck: Invariant theory and the Steenrod algebraHaynes Miller: The theory of p-compact groups
Stewart Priddy: Stable splittings of classifying spaces of finite groups
Speakers at the Conference:
Tilman Bauer, MuensterCarlos Broto, Barcelona
Jesper Grodal, Chicago
Le Minh Ha, Lille
Hans-Werner Henn, Strasbourg
Kenshi Ishiguro, Fukuoka
Masaki Kameko, Toyama
Nick Kuhn, Virginia
John Martino, Western Michigan
Mamoru Mimura, Okayama
Pham Anh Minh, Hue
Dietrich Notbohm, Leicester
Tran Ngoc Nam, Hanoi
Mara Neusel, Texas Tech
John Palmieri, Seattle
Geoffrey Powell, Paris XIII
Peter Symonds, Manchester
Michishige Tezuka, Ryukyu
Antonio Viruel, Malaga
Frank Williams, Las Cruces
Nobuaki Yagita, Ibaraki
Schedule of the Summer School
Monday August 9, 20048:00-8:30: Participant Registration
8:30-8:45: Opening Ceremony
Opening Speech by Prof. Tran Van Nhung, Vice-Minister of Education and Training
8:45-9:40: Course 1 by John Hubbuck: Invariant theory and the Steenrod algebra,
9:40-10:00: Tea break,
10:00-10:55: Course 2 by Haynes Miller: The theory of p-compact groups,
10:55-11:15: Tea break,
11:15-12:10: Course 3 by Stewart Priddy: Stable splittings of classifying spaces of finite groups.
Tuesday August 10 -- Saturday August 14, 2004
8:30-9:25: Course 1 by John Hubbuck: Invariant theory and the Steenrod algebra,
9:25-9:45: Tea break,
9:45-10:40: Course 2 by Haynes Miller: The theory of p-compact groups,
10:40-11:00: Tea break,
11:00-11:55: Course 3 by Stewart Priddy:
Stable splittings of classifying spaces of finite groups.
and
Thursday August 12, 2004
15:00-15:50: Question and Answer section: the 3 lecturers answer questions from the audiences.
15:50-16:10: Tea break
16:10-17:00: Question and Answer section (continued)
Schedule of the Confernce
Monday August 16 Morning8:00-8:30: Participant Registration
8:30-9:00: Opening Ceremony
(a) Opening Speech by Prof. Dao Trong Thi, Director of the VNU
(b) Presentations on Huynh Mui's work by one of the scientific committee member and by other colleagues
(c) Huynh Mui's reply and impression
9:00-9:45: Talk 1
9:45-10:05: Tea break
10:05-10:50: Talk 2
10:50-11:05: Tea break
11:05-11:50: Talk 3
Tuesday August 17- Friday August 20 Morning
8:30-9:15: Talk 1
9:15-9:30: Tea break
9:30-10:15: Talk 2
10:15-10:35: Tea break
10:35-11:20: Talk 3
Monday August 16-Tuesday August 17 Afternoon
14:30-15:15: Talk 1
15:15-15:30: Tea break
15:30-16:15: Talk 2
16:15-16:35: Tea break
16:35-17:20: Talk 3
Wednesday August 18 Afternoon
There might be an Excursion.
Wednesday August 18 Evening
19:00: Banquet offered by the VNU.
Thursday August 19 Afternoon
15:00-15:30: Problem Section
15:30-16:00: Tea break
16:00-16:30: Problem Section (continued)
Schedule of the conference
Monday morning: Kuhn, Kameko, WilliamsMonday afternoon: Henn, Tezuka, Viruel
Tuesday morning: Palmieri, Nam, Neusel
Tuesday afternoon: Symonds, Ishiguro, Powell
Wednesday morning: Minh, Mimura, Martino
Wednesday afternoon: Excursion
Wednesday evening: Banquet
Thursday morning: Broto, Ha, Bauer
Thursday afternoon: Problem section
Friday morning: Yagita, Notbohm, Grodal
Scientific Organizing Committee:
Nguyen H. V. Hung, Vietnam National University, nhvhung@vnu.edu.vnJohn Hubbuck, University of Aberdeen, j.hubbuck@maths.abdn.ac.uk
Haynes Miller, Massachusetts Institute of Technology, hrm@math.mit.edu
Goro Nishida, Kyoto University, nishida@kusm.kyoto-u.ac.jp
Stewart Priddy, Northwestern University, priddy@math.northwestern.edu
Lionel Schwartz, University of Paris XIII, schwartz@math.univ-paris13.fr
Executive Committee:
Nguyen H. V. Hung, Chair (Vietnam National Univ., Hanoi)Nguyen Gia Dinh (Univ of Hue, Hue)
Nguyen Viet Dong (Vietnam National Univ., Hochiminh City)
Nguyen Viet Dung (Institute of Math., Hanoi)
Pham Viet Hung (Vietnam National Univ., Hanoi)
Vu The Khoi (Institute of Math., Hanoi)
Nguyen Van Mau (Vietnam National Univ., Hanoi)
Nguyen Huynh Phan (Quangbinh Pedagogical College, Quangbinh)
Phan Huy Phu (Thang Long Univ., Hanoi)
Lionel Schwartz (Univ. de Paris 13, Paris)
Nguyen Sum (Quinhon Pedagogical Univ., Quinhon)
Phan Doan Thoai (Hanoi Pedagogical Univ., Hanoi)
Abstracts of Talks
Carles Broto"Cohomology of exotic finite Chevalley p-local finite groups"
Abstract: (joint work with J. Moeller) To a p-compact group X and unstable Adams operation of exponent q, we attach a p-local finite group X(q) that we call of Chevalley type. We will describe some aspects of the theory with special attention to the new exotic p-local finite groups obtained in this way. In particular, we will describe how cohomology rings and invariant theory are used in order to identify the classifying space of X(q) with the homotopy fixed points of the action of the unstable Adams operation on the classifying space of X.
Jesper Grodal
"Root systems for p-compact groups"
Abstract: (joint work with Kasper Andersen) The classification of p-compact groups, p odd, as proved by Andersen-myself-Moller-Viruel, states that there is a 1-1 correspondence between connected p-compact groups and finite reflection groups over the p-adic integers. For p=2 the conjectural statement replaces reflection groups by "root data". In this talk I'll explain the concept of a root datum for a p-compact group and describe how automorphisms of the root datum relate to automorphisms of the maximal torus normalizer and the p-compact group.
Kenshi Ishiguro
"Classifying spaces of compact Lie groups that are p-compact for a set of prime numbers"
Abstract: We consider a problem on the conditions of a compact Lie group $G$ that its loop space of the $p$--completed classifying space be a $p$--compact group for a set of primes. In particular, we discuss the classifying spaces $BG$ that are $p$--compact for all primes when the groups are certain subgroups of simple Lie groups. We also discuss invariant rings and some properties of $B\Gamma_2$ and $BG_2$ at $p=3$ where $\Gamma_2$ is a quotient group of a subgroup of the exceptional Lie group $G_2$. An isomorphism of cohomology rings need not imply the equivalence of the two representations.
Le Minh Ha
"Robinson bicomplex revisited"
Gamma homology, constructed by Robinson and Whitehouse, is a version of homology theory for commutative (S)-algebras. For any Gamma module $F$, Robinson constructed a functorial bicomplex $\Xi(F)$ whose homology is the stable homotopy of $F$. We show how to simplify, and at the same time, generalize this construction to obtain similar bicomplex for each stage in the Goodwillie tower of $F$. As an application, we attack a problem about Lambda algebra.
Hans-Werner Henn
"The cohomology of the second Morava stabilizer group at $p=2$ - revisited"
Abstract: This talk discusses joint work with Goerss, Mahowald and Rezk. The mod-2 cohomology of the second Morava stabilizer group $\SS_2$ at $p=2$ has been calculated in the late 1970's by Ravenel by Hopf algebra methods as well as by evaluating the spectral sequence of a suitable group extension. We revisit his calculation and compare it with an approach which depends on an approximation via the cohomology of centralizers of elementary abelian subgroups. Both approaches lead to the construction of finite ''resolutions'' of the trivial module by permutation modules. The interest of such ''resolutions'' is that they are the source for constructing homotopy theoretic finite ''resolutions'' of the $K(2)$-local sphere. These homotopy theoretic resolutions are made from certain homotopy fixed point spectra which are closely related to the $K(2)$-localization of the spectrum $TMF$.
Masaki Kameko
"Mui's invariants and Milnor's operations"
Abstract: In this talk, I will give a description of rings of invariants of finite general linear groups acting on polynomial tensor exterior algebras over a finite field using Milnor's operations Q_0, Q_1, ... instead of determinants and give a proof of Mui's theorem.
Nick Kuhn
"The cohomology of G as an Out(G)-module, from the unstable point of view"
Abstract: Let G be a finite group, F a characteristic p field, and e a nonzero idempotent in the group ring F[Out(G)]. A decade ago, Martino and Priddy asked whether the Krull dimension of eH^*(G;F) is always equal to the evident upper bound: the p-rank of G. I will discuss recent work on this problem that makes use of the nilpotent filtration of unstable A-modules.
John Martino
"Homotopy equivalence of posets of subgroups of compact Lie groups"
Abstract. (joint work with A. Libman and S. Priddy) We examine the homotopy types of the nerves of several posets of subgroups of a compact Lie group. In the process we use a version of Quillen's Theorem A for topological posets. We also relate our work to that of J. S{\l}omi\'{n}ska.
Mamoru Mimura
"Stiefel-Whitney classes and representations of the exceptional Lie group E_8"
Abstract: We give a strategy how to show the collapsing of the Rothenberg-Steenrod spectral sequence converging to H*(BE_8;Z/2), by using the adjoint representation of E_8.
Pham Anh Minh
"Any nilpotency degree occurs in mod-$p$ cohomology of $p$-groups"
Abstract. Let $p$ be an odd prime number and let $n$ be an arbitrary = positive number. We prove that there exists a $p$-group $G$ whose = mod-$p$ cohomology ring has a nilpotent element $x\in H^2(G)$ satisfying = $x^n\ne 0, x^{n+p-1}=0$. As a corollary, we exhibit a $p$-group whose = mod-$p$ cohomology ring contains an element of nilpotency degree $n+1$."
Mara Neusel
"Inseparable Extensions over the Steenrod Algebra"
Abstract: We will look at inseparable extensions of fields (and more generally algebras) over the Steenrod algebra. In particular, we consider purely inseparable extensions H \hra F[V] and H \hra F[V]^G We apply our results to invariant theory of finite groups.
Dietrich Notbohm
"Simplicial complexes, Stanley Reisner Algebras and topological interpretations"
Abstract: To each simplicial complex one can associated the (graded) face ring or Stanley-Reisner algebra, which also appear as the cohomolgy of particular spaces. We will use homology decomposition techniques to prove (global) homotopy uniqueness results for particular families as well as reprove results of Reisner and Stanley which characterized Cohen-Macaulay and Gorenstein properties of the face rings in terms of the combinatorics of the associated simplicial complexes.
This is partly joint work with Nigel Ray.
John Palmieri
"The cocomplete Lambda algebra"
Abstract: There is an algebra endomorphism of the Lambda algebra which sends lambda_n to lambda_{2n+1}. This map induces Sq^0 on the Adams E_2 term for the sphere. In this talk, we use this map to study the Adams E_2 term.
Geoffrey Powell
"Endomorphisms of the cohomology of Eilenberg-MacLane spaces"
Abstract: The complete stable splitting of the Eilenberg-MacLane space of an elementary abelian p-group is approached by calculating the complete decomposition of its mod-p cohomology as a module over the Steenrod algebra. The problem is reduced to the calculation of the endomorphism ring of the cohomology in the category of unstable modules; the theory of localization away from the nilpotent unstable modules is exploited to perform this calculation.
Peter Symonds
"Permutation complexes for profinite groups"
Abstract: We discuss various results about permutation modules and complexes of permutation modules for profinite groups and describe how these can be used to construct examples of interest in homotopy theory.
Antonio Viruel
"All $p$-local finite groups of rank two for odd prime $p$"
(joint work with Antonio D{\'\i}az and Albert Ruiz) We give a classification of the rank two $p$-local finite groups for odd prime p. This study requires the analysis of the possible saturated fusion systems in terms of the outer automorphism group and the proper radical subgroups. Also, for each case in the classification, either we give a finite group with the corresponding fusion system or we check that it corresponds to an exotic p-local finite group, getting some new examples of these for $p = 3$.
Frank Williams
"Presentations of Algebras of Invariants over the Steenrod Algebra"
(Joint with David Pengelley)
Nobuaki Yagita
"Stable splitting and cohomology of p-local finite groups associated to the extraspecial p-group order p^3 and exponent p"
Abstract: In this talk, we study the stable splitting and cohomology of groups whose p-Sylow subgroups are isomorphic to the extraspecial p group of order p^3 and exponent p. In particular, by using the result by Ruiz and Viruel, we show the splitting for classifying spaces of all such finite groups for the case p=3. The splittings are represented by some graph for seeing them easily.
Trích từ trang web của Masschusettes Institute of Technology (MIT) - Department of Mathematics : http://www-math.mit.edu/~hrm/vietnam.html
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