Rocky Mountain Algebraic Combinatorics Seminar

Automorphisms of small p-groups

Josh Maglione
Colorado State University

One of the basic, and still unanswered, questions concerning p-groups is whether or not the automorphism group of a p-group is also a p-group. Within the last few years, we have developed algorithms to improve the task of computing automorphisms of p-groups. We were asked to use these algorithms to expand the known data concerning this question about automorphism groups, but along the way, we encountered an uncompromising class of groups. We constructed an algorithm to efficiently compute automorphisms for these groups, which naturally fits into work with P.A. Brooksbank and J.B. Wilson on groups of genus 2. In addition, we also find that many small p-groups have an automorphism whose order is not a power of p.


A weighted version of matrix-tree theorem and its application to simplicial complexes.

Ghodratollah Aalipour
University of Colorado, Denver

The well-known Kirchhoff matrix-tree theorem counts the number of spanning trees of a graph in terms of its non-zero Laplacian eigenvalues. By assigning a weight to each edge of the graph, the new weighted Laplacian matrix contributes well to find the corresponding vertex-degree generating function for the number of spanning trees of the graph. This powerful technique has been extended to simplicial and cellular complexes by Duval, Klivans and Martin. In this talk, we present a slight improvement of their generalized matrix-tree theorem. As an application, we obtain the weighted count for spanning trees in several families of simplicial and cellular complexes. This is joint work with Art Duval and Jeremy L. Martin.


Weber 223
4–6 pm
Friday, October 9, 2015
(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:

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