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- Homogeneous Metrics on Spheres — Department of Mathematics and Computer Science

Navigation SLU Home Arts Sciences Home Apply Now Prospective Students Info Homogeneous Metrics on Spheres filed under Topology Seminar James Munden Saint Louis University What Topology Seminar When Fri Apr 26 2013 from 11 00 AM to 11 50 AM Where Ritter Hall 316 Add event to calendar vCal iCal Abstract Spheres can be expressed as homogeneous spaces in numerous ways In this talk we will give a method of constructing homogenous metrics on the spheres We will show that different descriptions of the spheres as homogeneous spaces give rise to different families of homogeneous metrics and naturally different geometries We will investigate which homogeneous metrics correspond to the metric of constant sectional curvature on the sphere Document Actions iCalendar vCalendar Send this Print this Subscribe to Talklist Sign up here for a weekly email of upcoming department events Email address Your name February 2016 February Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Upcoming Events Geometry Topology Seminar Tue Feb 16 2016 Orbifolds 04 Kimberly Druschel Math CS Club Wed Feb

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/tba (2016-02-12)

Open archived version from archive - Random Projections, the Johnson-Lindenstrauss Lemma and Topological Persistence (continued) — Department of Mathematics and Computer Science

Topology Seminar When Fri Apr 19 2013 from 11 00 AM to 11 50 AM Where Ritter Hall 316 Add event to calendar vCal iCal Document Actions iCalendar vCalendar Send this Print this Subscribe to Talklist Sign up here for a weekly email of upcoming department events Email address Your name February 2016 February Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/random-projections-the-johnson-lindenstrauss-lemma-and-topological-persistence-continued (2016-02-12)

Open archived version from archive - Random projections, the Johnson-Lindenstrauss Lemma, and topological persistence — Department of Mathematics and Computer Science

Info Random projections the Johnson Lindenstrauss Lemma and topological persistence filed under Topology Seminar David Letscher Saint Louis University What Topology Seminar When Fri Apr 12 2013 from 11 00 AM to 11 50 AM Where Ritter Hall 316 Add event to calendar vCal iCal Abstract The Johnson Lindenstrauss lemma says that you can project sets points in a high dimensional space to a much smaller dimension that roughly preserves pairwise distances In fact with some probability a random projection will suffice We prove a similar result holds when considering topological information In particular with some probability random projections to a lower dimension does not significantly change the homology of a union of balls in Euclidean space This leads to a practical probabilistic algorithm for calculating persistent homology for high dimensional spaces Document Actions iCalendar vCalendar Send this Print this Subscribe to Talklist Sign up here for a weekly email of upcoming department events Email address Your name February 2016 February Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Upcoming Events Geometry

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/random-projections-the-johnson-lindenstrauss-lemma-and-topological-persistence (2016-02-12)

Open archived version from archive - An Example of an Automatic Graph of Intermediate Growth — Department of Mathematics and Computer Science

vCal iCal Abstract We give the first example of a 4 regular in finite automatic graph of intermediate growth It is constructed as a Schreier graph of a group generated by 2 state Mealy automaton In the first half of the talk we will review the notion of groups generated by automata and explain why this class of groups is interesting Then we will recall the well established notion of an automatic group which is different from a group generated by automaton The class of automatic groups is important in particular because it admits many computational routines On the other hand many groups are not automatic A wider class of Cayley automatic groups was recently introduced by Kharlampovich Khoussainov and Miasnikov One of the open questions about this class is whether it contains groups of intermediate growth i e groups whose growth functions grow faster than any polynomial and slower than exponential function The example that we construct could potentially serve as a basis for answering this question This work is joint with Alexei Miasnikov Document Actions iCalendar vCalendar Send this Print this Subscribe to Talklist Sign up here for a weekly email of upcoming department events Email address Your

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/topology-seminar-1 (2016-02-12)

Open archived version from archive - Submanifold Projection (Part 2) — Department of Mathematics and Computer Science

from 11 00 AM to 11 50 AM Where Ritter Hall 316 Add event to calendar vCal iCal Abstract The outer automorphism group of the free group Out F n has a deep connection with the mapping class group of a surface That connection has been fruitfully exploited to study various aspects of Out F n including most recently its geometry One of the most useful tools for studying the geometry of the mapping class group has been the subsurface projections of Masur and Minsky In this talk discussing research that is joint with Dmytro Savchuk we will discuss an analogue of subsurface projection for Out F n that we call submanifold projection Our projection is topological in nature using intersections of embedded 2 spheres in a particular 3 manifold We discuss a number of desirable properties of submanifold projection including a Behrstock inequality and a Bounded Geodesic Image theorem Document Actions iCalendar vCalendar Send this Print this Subscribe to Talklist Sign up here for a weekly email of upcoming department events Email address Your name February 2016 February Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/submanifold-projection-part-2 (2016-02-12)

Open archived version from archive - Submanifold Projection — Department of Mathematics and Computer Science

00 AM to 11 50 AM Where Ritter Hall 316 Add event to calendar vCal iCal Abstract The outer automorphism group of the free group Out F n has a deep connection with the mapping class group of a surface That connection has been fruitfully exploited to study various aspects of Out F n including most recently its geometry One of the most useful tools for studying the geometry of the mapping class group has been the subsurface projections of Masur and Minsky In this talk discussing research that is joint with Dmytro Savchuk we will discuss an analogue of subsurface projection for Out F n that we call submanifold projection Our projection is topological in nature using intersections of embedded 2 spheres in a particular 3 manifold We discuss a number of desirable properties of submanifold projection including a Behrstock inequality and a Bounded Geodesic Image theorem Document Actions iCalendar vCalendar Send this Print this Subscribe to Talklist Sign up here for a weekly email of upcoming department events Email address Your name February 2016 February Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/submanifold-projection (2016-02-12)

Open archived version from archive - Some aspects of the large scale geometry of Out(F) — Department of Mathematics and Computer Science

Outreach SLU Navigation SLU Home Arts Sciences Home Apply Now Prospective Students Info Some aspects of the large scale geometry of Out F filed under Topology Seminar Patrick Reynolds University of Utah What Topology Seminar When Fri Feb 01 2013 from 11 00 AM to 11 50 AM Where Ritter Hall 316 Add event to calendar vCal iCal Abstract We will explain some large scale features of outer automorphism groups of free groups all denoted Out F via actions of Out F on certain Gromov hyperbolic spaces There are several such spaces each one we will discuss is a curve complex for Out F and each is useful for understanding certain aspects of the geometry of Out F Document Actions iCalendar vCalendar Send this Print this Subscribe to Talklist Sign up here for a weekly email of upcoming department events Email address Your name February 2016 February Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Upcoming Events Geometry Topology Seminar Tue Feb 16 2016 Orbifolds 04 Kimberly Druschel Math CS Club Wed

Original URL path: http://mathcs.slu.edu/seminars/old-seminars/some-aspects-of-the-large-scale-geometry-of-out-f (2016-02-12)

Open archived version from archive - Vertex Groups of Locally Oriented Orbifolds, Orbifold Cobordism, and a Differential Graded Algebra — Department of Mathematics and Computer Science

fairly well understood invariants and generators are known One step in studying the actual orbifold cobordism ring involves determining which combinations of finite degree n subgroups of SO n can occur in an oriented or locally oriented n dimensional orbifold This was key in calculations up through dimension four I ll give a brief overview of orbifold cobordism with examples and pictures I ll then focus on the above question by providing a first obstruction to a given set of such subgroups occurring in some oriented n orbifold This is the only obstruction in dimensions two through four From this we build a differential d associated with finite degree n subgroups of SO n with n varying and hence obtain a homology I ll show how this homology relates to orbifold cobordism and compute d for many cases including dimensions less than or equal to four and also direct sums and products Additionally if an oriented degree n group G admits an orientation reversing linear automorphism u we construct a semidirect product of G by u 1 in degree n 1 I ll present equations for calculating d of this semidirect product Document Actions iCalendar vCalendar Send this Print this

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/vertex-groups-of-locally-oriented-orbifolds-orbifold-cobordism-and-a-differential-graded-algebra (2016-02-12)

Open archived version from archive