Rocky Mountain Algebraic Combinatorics Seminar

Mathematics of 3D Printing

Alexander Hulpke
Colorado State University

3D printing is a new manufacturing technology that produces an object from scratch without having to remove undesired surrounding material. Since it specifies objects by their coordinates it is eminently suitable for constructing mathematical models. I will describe scope and limitations of the technology for this purpose and give ample examples.


A new family of Cameron--Liebler line classes

Morgan Rodgers
Los Medanos College

Cameron-Liebler line classes are sets of lines in PG(3, q) having many nice combinatorial properties; they were originally studied as generalizations of symmetric tactical decompositions of PG(3, q), as well as of orbits of subgroups of PΓL(4,q) having equally many orbits on points and lines. Under the Klein correspondence, Cameron?Liebler line classes of PG(3, q) correspond to tight sets in the hyperbolic quadric Q+(5, q).

Many new examples of Cameron?Liebler line classes found by computer search were described in recent work, here we detail results proving the existence of a new infinite family of examples in PG(3, q) having parameter \fracq2−12 for all q ≡ 5 or 9\mod12. When q ≡ 9\mod12, these examples occur as line classes in symmetric tactical decompositions of PG(3, q) having four classes on points and lines. In this situation we have q = 32e positive integer e. The nature of these decompositions allows us to also prove the existence of sets of type (\frac12(32e−3e),\frac12(32e+3e))


Weber 223
4–6 pm
Friday, February 6, 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:

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