Rocky Mountain Algebraic Combinatorics Seminar

Algorithmic Group Theory, Computational Complexity, Application to Information Security

Delaram Kahrobaei

I will give an overview of some algorithmic group theoretic problems with their computational complexity as well as how they have been proposed for applications in information security. The talk will discuss both theory and application behind these problems. The talk will be accessible to general audience mathematicians/computer scientists.


Semicontinuity of Persistence Diagrams

Amit Patel
Colorado State University

Let f: M → R be a Morse function. An r-sublevel set of f is the set of all points x in M such that f(x) is at most r. The Morse function f therefore filters M by sublevel sets. The d-th persistence diagram of this filtration is a summary of how the d-th dimensional homology groups of the sublevel sets vary with increasing r. Very importantly, the persistence diagram is stable to continuous perturbations of the function f. This makes the persistence diagram an interesting tool to study the topology of data as data is inherently noisy.

Until very recently, the persistence diagram only made sense in the setting of vector spaces. That is, the homology groups must be computed using coefficients in a field. In this talk, I will present a vast generalization of the persistence diagram which implies a persistence diagram for homology groups computed over the integers. This opens the way to study persistent torsion in data.


Weber 223
4–6 pm
Friday, September 16, 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:

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