Speaker: El
iot Fried (Okinawa Institute of Science and Technology)\n

\n

\n

Title: Kaleidocycles and Möbius bands\n

\n

\n

Abstract: Many of Escher’s works have become
mainstays of popular culture. Famous examples include his kaleidocycles\,
each consisting of six identical regular tetrahedra and being capable of u
ndergoing a cyclic everting motion that brings different tesselations of t
he tetrahedra into view. Esher also provided memorable interpretations of
Möbius bands. We will consider kaleidocycles made from seven or more ident
ical twisted tetrahedra\, or disphenoids\, and expose a deep\, and to our
knowledge\, previously unnoticed connection between kaleidocycles and the
3π-twist Möbius band.

\n END:VEVENT BEGIN:VEVENT UID:17lu9kfmove4992vvh0kspu0k5@google.com DTSTAMP:20180421T134741Z CATEGORIES;LANGUAGE=en-US:Colloquia and seminars CONTACT: DESCRIPTION: Elliot Ossanna\, Master’s presentation\, Monday\, April 30\ , 2018\, 10:30 am\, Keller 403 Title: Fractal Nature of Generalized Binomial Triangles modulo p\n\n Abstract: A well-known property of Pascal’s Triangle is that reducing entries modulo a prime yields a fractal\, Sierpinski’s Triangle-like pattern. We generalize this to tria ngles generated by strong divisibility Lucas Sequences\, and concl ude that the generated fractal is uniquely determined by the prime modulus \, not the underlying generating sequence. DTSTART;TZID=Pacific/Honolulu:20180430T103000 DTEND;TZID=Pacific/Honolulu:20180430T110000 SEQUENCE:0 SUMMARY:Elliot Ossanna\, Master’s presentation URL:http://math.hawaii.edu/wordpress/event/elliot-ossanna-masters-presentat ion/ X-ALT-DESC;FMTTYPE=text/html:\\n\\n\\n \\n\\n

\n

Abstract: A well-known property of Pascal’s Triangle is that reducing e ntries modulo a prime yields

a fractal\, Sierpinski’s Triang le-like pattern. We generalize this to triangles generated by strong divis ibility

Lucas Sequences\, and conclude that the generated fr actal is uniquely determined by the prime modulus\,

not the underlying generating sequence.\n END:VEVENT BEGIN:VEVENT UID:2indhmkcbrhj9tlbellgfdsod4@google.com DTSTAMP:20180421T134741Z CATEGORIES;LANGUAGE=en-US:Colloquia and seminars CONTACT: DESCRIPTION:Keller Hall 403Dissertation draft (department only)Alejandro Gu illen\, PhD defense\, Tuesday\, May 1\, 2018\, 12 noon\, Title: On the Generalized Word Problem for Finitely Presented Lattices” Abst ract: The generalized word problem for a lattice L in a variety V asks if\ , given a finite subset Y of L and an element d in L\, there is an algorithm to determine if d is in the subalgebra of L generated by Y. Freese and Nation showed that the generalized word problem for finitel y presented lattices is solvable. This algorithm\, though effectiv e\, is potentially exponential. We present a polynomial time algor ithm for the generalized word problem for free lattices\, but expl ain the complications which can arise when trying to adapt this algorithm to the generalized word problem for finitely presented lattices. T hough some of the results for free lattices are shown to transfer over for finitely presented lattices\, we give a potential syntactic algor ithm for the generalized word problem for finitely presented latti ces. Finally\, we give a new proof that the generalized word probl em for finitely presented lattices is solvable\, relying on the pa rtial completion\, PC(P)\, of a partially defined lattice P. DTSTART;TZID=Pacific/Honolulu:20180501T120000 DTEND;TZID=Pacific/Honolulu:20180501T140000 SEQUENCE:0 SUMMARY:Alejandro Guillen’s PhD defense URL:http://math.hawaii.edu/wordpress/event/alejandro-guillens-phd-defense/ X-ALT-DESC;FMTTYPE=text/html:\\n\\n\\n \\n\\n \\n\\n \\n\\n

\n END:VEVENT BEGIN:VEVENT UID:17lu9kfmove4992vvh0kspu0k5@google.com DTSTAMP:20180421T134741Z CATEGORIES;LANGUAGE=en-US:Colloquia and seminars CONTACT: DESCRIPTION: Elliot Ossanna\, Master’s presentation\, Monday\, April 30\ , 2018\, 10:30 am\, Keller 403 Title: Fractal Nature of Generalized Binomial Triangles modulo p\n\n Abstract: A well-known property of Pascal’s Triangle is that reducing entries modulo a prime yields a fractal\, Sierpinski’s Triangle-like pattern. We generalize this to tria ngles generated by strong divisibility Lucas Sequences\, and concl ude that the generated fractal is uniquely determined by the prime modulus \, not the underlying generating sequence. DTSTART;TZID=Pacific/Honolulu:20180430T103000 DTEND;TZID=Pacific/Honolulu:20180430T110000 SEQUENCE:0 SUMMARY:Elliot Ossanna\, Master’s presentation URL:http://math.hawaii.edu/wordpress/event/elliot-ossanna-masters-presentat ion/ X-ALT-DESC;FMTTYPE=text/html:\\n\\n\\n

Ell
iot Ossanna\, Master’s presentation\, Monday\, April 30\, 2018\, 10:30 am\
, Keller 403

*Tit
le*: Fractal Nature of Generalized Binomial Triangles modulo p~~\n~~

\n

Abstract: A well-known property of Pascal’s Triangle is that reducing e ntries modulo a prime yields

a fractal\, Sierpinski’s Triang le-like pattern. We generalize this to triangles generated by strong divis ibility

Lucas Sequences\, and conclude that the generated fr actal is uniquely determined by the prime modulus\,

not the underlying generating sequence.\n END:VEVENT BEGIN:VEVENT UID:2indhmkcbrhj9tlbellgfdsod4@google.com DTSTAMP:20180421T134741Z CATEGORIES;LANGUAGE=en-US:Colloquia and seminars CONTACT: DESCRIPTION:Keller Hall 403Dissertation draft (department only)Alejandro Gu illen\, PhD defense\, Tuesday\, May 1\, 2018\, 12 noon\, Title: On the Generalized Word Problem for Finitely Presented Lattices” Abst ract: The generalized word problem for a lattice L in a variety V asks if\ , given a finite subset Y of L and an element d in L\, there is an algorithm to determine if d is in the subalgebra of L generated by Y. Freese and Nation showed that the generalized word problem for finitel y presented lattices is solvable. This algorithm\, though effectiv e\, is potentially exponential. We present a polynomial time algor ithm for the generalized word problem for free lattices\, but expl ain the complications which can arise when trying to adapt this algorithm to the generalized word problem for finitely presented lattices. T hough some of the results for free lattices are shown to transfer over for finitely presented lattices\, we give a potential syntactic algor ithm for the generalized word problem for finitely presented latti ces. Finally\, we give a new proof that the generalized word probl em for finitely presented lattices is solvable\, relying on the pa rtial completion\, PC(P)\, of a partially defined lattice P. DTSTART;TZID=Pacific/Honolulu:20180501T120000 DTEND;TZID=Pacific/Honolulu:20180501T140000 SEQUENCE:0 SUMMARY:Alejandro Guillen’s PhD defense URL:http://math.hawaii.edu/wordpress/event/alejandro-guillens-phd-defense/ X-ALT-DESC;FMTTYPE=text/html:\\n\\n\\n

Keller
Hall 403

Dissertation draft (department only)

A
lejandro Guillen\, PhD defense\, Tuesday\, May 1\, 2018
\, 12 noon\,

*Title
*: On the Generalized Word Problem for Finitely Presented Lattic
es”

*Abstract*: The gene
ralized word problem for a lattice L in a variety V asks if\, given a fini
te

subset Y of L and an element d in L\, there i
s an algorithm to determine if d is in the subalgebra

of L generated by Y. Freese and Nation showed that the generalized
word problem for finitely

presented lattices is
solvable. This algorithm\, though effective\, is potentially exponential.
We

present a polynomial time algorithm for the
generalized word problem for free lattices\, but

explain the complications which can arise when trying to adapt this alg
orithm to the generalized

word problem for fini
tely presented lattices. Though some of the results for free lattices are

shown to transfer over for finitely presented l
attices\, we give a potential syntactic algorithm

for the generalized word problem for finitely presented lattices. Final
ly\, we give a new proof

that the generalized w
ord problem for finitely presented lattices is solvable\, relying on the <
/span>

partial completion\, PC(P)\, of a partially defi
ned lattice P.

Kyle Da
iley\, Master’s presentation\,
Friday\, May 4\, 2018\, 1:00\, Keller 404

*Title*: Rahman Polynomials and Lie Algeb
ra Representations

*Abstract*<
span>: In this paper\, we examine a close connection between a certain cl
ass of orthogonal polynomials and Lie algebra repr
esentations. We use a specific inner product to observe how
polynomials arise within the structure of representations of
special linear algebras. We also

use this inne
r product to give proofs of properties of the polynomials\, such as orthog
onality

and recurrence relations. Our paper is
guided by previous results on the topic\, in this paper

we outline a new approach to achieve these results\, as well as
the difference between our

approach and previou
s papers on the topic.

Title: Nonaut onomous Dynamics

\nChristian Pötzsche

\nAlpen-Adria Universität
Klagenfurt\, Austria

\nchristian.poetzsche@aau.at

http://www u.uni-klu.ac.at/cpoetzsc/Christian_Potzsche/english.html

\nThe theor y of dynamical systems has seen a remarkable progress over the last 100 ye ars\, beginning with the contributions of Poincaré and Lyapunov to a conte mporary detailed understanding of the attractor for various infinite-dimen sional systems. This success is partly due to the restriction to autonomou s systems. However\, many real-world problems are actually nonautonomous. That is\, they involve time-dependent parameters\, controls\, modulation a nd various other effects. Special cases include periodically or almost per iodically forced systems\, but in principle the time dependence can be arb itrary. As a consequence\, many of the now well-established concepts\, met hods and results for autonomous systems are no longer applicable and requi re appropriate extensions.

\nWe discuss several basic ingredients fr om the theory of nonautonomous dynamical systems. Among them are (pullback ) convergence\, the dichotomy spectrum (to indicate stability) and approac hes to understand nonautonomous bifurcations.

\n END:VEVENT END:VCALENDAR