Rocky Mountain Algebraic Combinatorics Seminar

Linear actions of $\mathbb{Z}/p \times \mathbb{Z}/p$ on $S^n \times S^n$

Jim Fowler
The Ohio State University

In 1925, Hopf first stated the spherical space form asking for which groups act freely on Sn. Some fifty years later, Madsen, Thomas, and Wall proved in 1978 that certain necessary conditions (discovered by Smith in 1944 and Milnor in 1957) were in fact sufficient. Easy generalizations of this question, like determining which groups G can act freely on Sn ×Sn, are still open. Even for a fixed group, there is the question of classifying the possible actions. The situation of linear actions of \mathbbZ/p ×\mathbbZ/p on Sn ×Sn can partly be understood by relating them to the easier case of \mathbbZ/p actions on Sn, that is, to lens spaces.

This is a preliminary report on joint work with Courtney Thatcher. The talk, being partly an overview of the broader problem, promises to be broadly accessible.


Maximal subgroup growth of some groups

Andrew Kelley
Binghamton University

Let mn(G) denote the number of maximal subgroups of a finitely generated group G of index n. How do the algebraic/structural properties of G control the growth rate of mn(G)? Others have researched the broad picture and described what it means for mn(G) to be bounded above by a polynomial in n. However, there are only a few groups whose degree of growth is known. If we restrict to particularly nice classes of groups however, then asymptotic formulas (or bounds) can be given. We will focus on metabelian groups, especially those that are abelian by cyclic. Beyond this, current progress on virtually abelian groups and Baumslag-Solitar groups may also be mentioned.


Weber 223
4–6 pm
Friday, December 2, 2016
(Refreshments in Weber 117, 3:30–4 pm)
Colorado State University

This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly. Anyone interested is welcome to join us at a local restaurant for dinner after the talks.

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Previous Seminars:

November 11, 2016
Joseph Gersch, Joshua Maglione
October 28, 2016
John MacLaren Walsh, Henry Adams
October 14, 2016
JM Landsberg, James B. Wilson
September 30, 2016
Alexander Hulpke, Oscar Levin
September 16, 2016
Delaram Kahrobaei, Amit Patel
June 23, 2016
Jason Cantarella, Michal Adamaszek
April 29, 2016
Nick Loehr, Jason Williford
April 15, 2016
Alexander Hulpke, Klaus Lux
April 1, 2016
Eamonn O'Brien, Izabella Stuhl
February 19, 2015
James Wilson, Anton Betten
December 4, 2015
Maria Monks Gillespie, Dane Flannery
November 13, 2015
Richard Green, Tim Penttila
October 23, 2015
Christina Boucher, Sylvia Hobart
October 9, 2015
Josh Maglione, Ghodratollah Aalipour
September 25, 2015
Ross McConnell, Henry Adams
September 11, 2015
James B. Wilson, Tim Penttila
May 8, 2015
Amanda Schaeffer Fry, Peter Brooksbank
April 24, 2015
Heide Gluesing-Luerssen, Phil DeOrsey
March 6, 2015
Felice Manganiello, Eric Moorhouse
February 20, 2015
Anton Dzhamay, Anton Betten
February 6, 2015
Alexander Hulpke, Morgan Rodgers
December 5, 2014
Stefaan De Winter, Gretchen Matthews
November 14, 2014
Greg Coxson, Tom Dorsey
October 31, 2014
Octavio Paez Osuna, Sylvia Hobart
October 10, 2014
Takunari Miyazaki, Eric Moorhouse
September 26, 2014
Elissa Ross, Anton Betten
September 12, 2014
Petr Vojtěchovský, Alexander Hulpke
May 9, 2014
Philip DeOrsey, Tim Penttila
April 25, 2014
William J Martin, Jason Williford
April 11, 2014
Victor Pambuccian, George Shakan
March 7, 2014
Nathan Lindzey, Jens Harlander
February 21, 2014
Ross McConnell, Anton Betten
November 22, 2013
Justin Hughes, Josh Maglione

Department of Mathematics
Fort Collins, Colorado 80523