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DTSTART;TZID=America/Los_Angeles:20190307T120000
DTEND;TZID=America/Los_Angeles:20190307T133000
DTSTAMP:20260417T230702
CREATED:20190205T180911Z
LAST-MODIFIED:20190205T180911Z
UID:1194-1551960000-1551965400@colleges.claremont.edu
SUMMARY:Non-existence of epimorphisms between certain genus two handlebody-knot groups (Ryo Nikkuni\, Tokyo Woman's Christian University)
DESCRIPTION:For two genus $g$ handlebody-knots $H_{1}$ and $H_{2}$\, we denote $H_{1} \geq H_{2}$ if there exists an epimorphism from the fundamental group of the handlebody-knot complement of $H_{1}$ onto the one of $H_{2}$. In the case of $g = 1$\, this order is a partial order on the set of prime knots and has been determined up to $11$ crossings by Kitano-Suzuki and Horie-Kitano-Matsumoto-Suzuki. In this talk\, we consider the case of $g = 2$ and exhibit a lot of ordered pairs of irreducible genus $2$ handlebody-knots in the Ishii-Kishimoto-Moriuchi-Suzuki table up to $6$ crossings\, each of which does not admit this order. This is a joint work with Y. Ozawa and M. Suzuki.
URL:https://colleges.claremont.edu/ccms/event/non-existence-of-epimorphisms-between-certain-genus-two-handlebody-knot-groups-ryo-nikkuni-tokyo-womans-christian-university/
CATEGORIES:Topology Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190228T120000
DTEND;TZID=America/Los_Angeles:20190228T133000
DTSTAMP:20260417T230702
CREATED:20190127T185703Z
LAST-MODIFIED:20190220T150331Z
UID:1171-1551355200-1551360600@colleges.claremont.edu
SUMMARY:Applying Quantum Representations of Mapping Class Groups (Wade Bloomquist\, UCSB)
DESCRIPTION:One foundational pillar of low dimensional topology is the connection between link invariants and 3-manifold invariants.  One generalization of this has been given by Reshetikhin and Turaev to a surgery theory for colored ribbon graphs.  Then to complete the analogy rather than 3-manifold invariants we now have a 2+1 dimensional topology quantum field theory (TQFT).  For this talk we will only be focusing on one corner of a TQFT\, in particular the representations of mapping class groups which are afforded (called quantum representations).  We will first go through a brief construction of these representations\, focusing on how colored ribbon graphs give rise to a basis.  Then we will dive into some applications of these representations both in recovering classical topology and in a proposal for a topological quantum computing protocol.  A strong effort will be made to keep things relatively self contained with as many pictures as possible.
URL:https://colleges.claremont.edu/ccms/event/applying-quantum-representations-of-mapping-class-groups-wade-bloomquist-ucsb/
LOCATION:Roberts North 104\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Topology Seminar
ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190221T120000
DTEND;TZID=America/Los_Angeles:20190221T133000
DTSTAMP:20260417T230702
CREATED:20190123T234443Z
LAST-MODIFIED:20190123T234443Z
UID:1163-1550750400-1550755800@colleges.claremont.edu
SUMMARY:A nonorientable version of the Milnor Conjecture (Cornelia A. Van Cott\, USF)
DESCRIPTION:In 1968\, Milnor famously conjectured that the smooth 4-genus of the torus knot T(p\,q) is given by (p-1)(q-1)/2. This conjecture was first verified by Kronheimer and Mrowka in 1993 and has received several other proofs since then. In this talk\, we discuss a nonorientable analogue of this conjecture\, first formulated by Josh Batson. We prove the conjecture for infinite families of of torus knots\, using tools from knot Floer homology. We also connect the problem to the world of continued fractions\, which gives an alternative perspective on the problem. This is joint work with Stanislav Jabuka.
URL:https://colleges.claremont.edu/ccms/event/a-nonorientable-version-of-the-milnor-conjecture-cornelia-a-van-cott-usf/
LOCATION:Roberts North 104\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Topology Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190131T123000
DTEND;TZID=America/Los_Angeles:20190131T133000
DTSTAMP:20260417T230702
CREATED:20190127T185244Z
LAST-MODIFIED:20190127T185524Z
UID:1168-1548937800-1548941400@colleges.claremont.edu
SUMMARY:The Roger-Yang Arc Algebra (Helen Wong\, CMC)
DESCRIPTION:  \nBased on geometric considerations\, J. Roger and T. Yang in 2014 defined a version of the Kauffman bracket skein algebra for punctured surfaces that includes arcs going from puncture to puncture. We’ll provide a brief survey of known results about this arc algebra. In particular\, I’d like to mention a recent algebraic result whose proof uses  “generalized” corner coordinates to describe arcs on a triangulated surface. This is joint work with Han-bom Moon. \n 
URL:https://colleges.claremont.edu/ccms/event/the-roger-yang-arc-algebra/
LOCATION:Roberts North 104\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Topology Seminar
ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190124T120000
DTEND;TZID=America/Los_Angeles:20190124T133000
DTSTAMP:20260417T230702
CREATED:20190113T145840Z
LAST-MODIFIED:20190115T051329Z
UID:1066-1548331200-1548336600@colleges.claremont.edu
SUMMARY:Simplicial Complexes\, Configuration Spaces\, and "Chromatic" Invariants (Andrew Cooper\, NC State)
DESCRIPTION:Given a space $X$\, the configuration space $F(X\,n)$ is the space of possible ways to place $n$ points on $X$\, so that no two occupy the same position. But what if we allow some of the points to coincide? \nThe natural way to encode the allowed coincidences is as a simplicial complex $S$. I will describe how the configuration space $M(S\,X)$ obtained in this way gives rise to polynomial and homological invariants of $S$\, how those invariants are related to the cohomology ring $H^*(X)$\, and what this has to do with the topology of spaces of maps into $X$. \nI will also mention some potential applications of this structure to problems arising from international relations and economics. \nThis is joint work with Vin de Silva\, Radmila Sazdanovic\, and Robert J Carroll
URL:https://colleges.claremont.edu/ccms/event/topology-seminar-1-24-2019-andrew-cooper-nc-state/
LOCATION:Roberts North 104\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Topology Seminar
ORGANIZER;CN="Sam Nelson":MAILTO:snelson@cmc.edu
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