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- The primitive length spectrum of tori and generalized Loewner inequalities. (Preliminary report) — Department of Mathematics and Computer Science

the field of systolic geometry by proving a sharp inequality relating the length of the shortest non contractible closed curve to the area of any Riemannian metric g on the two dimensional torus T 2 Moreover the inequality is sharp because equality holds if and only if T 2 g is an equilateral flat torus Since then Loewner s inequality has been generalized to other surfaces and to higher dimensional manifolds In this talk I will present a different kind of generalization Restricting to Riemannian metrics g on the two dimensional torus T 2 there are families of sharp lower bounds on the area in terms of the length of the shortest non contractible closed curve the length of the second shortest which is not homotopic to a multiple of the fi rst and the third shortest not homotopic to a multiple of the fi rst or second and so on etc The sequence of these lengths is called the primitive length spectrum of T 2 g Along the way one discovers formulas for the terms of the primitive length spectrum of flat tori as functions on the space of flat tori Document Actions iCalendar vCalendar Send this Print this

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/the-primitive-length-spectrum-of-tori-and-generalized-loewner-inequalities.-preliminary-report/?searchterm=None (2016-02-12)

Open archived version from archive - The primitive length spectrum of tori and generalized Loewner inequalities — Department of Mathematics and Computer Science

field of systolic geometry by proving a sharp inequality relating the length of the shortest non contractible closed curve to the area of any Riemannian metric g on the two dimensional torus T 2 Moreover the inequality is sharp because equality holds if and only if T 2 g is an equilateral flat torus Since then Loewner s inequality has been generalized to other surfaces and to higher dimensional manifolds In this talk I will present a different kind of generalization Restricting to Riemannian metrics g on the two dimensional torus T 2 there are families of sharp lower bounds on the area in terms of the length of the shortest non contractible closed curve the length of the second shortest which is not homotopic to a multiple of the first and the third shortest not homotopic to a multiple of the first or second and so on etc The sequence of these lengths is called the primitive length spectrum of T 2 g Along the way one discovers formulas for the terms of the primitive length spectrum of flat tori as functions on the space of flat tori Document Actions iCalendar vCalendar Send this Print this Subscribe to Talklist

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/the-primitive-length-spectrum-of-tori-and-generalized-loewner-inequalities/?searchterm=None (2016-02-12)

Open archived version from archive - Metrical Diophantine Properties for Translation Surfaces — Department of Mathematics and Computer Science

Home Arts Sciences Home Apply Now Prospective Students Info Metrical Diophantine Properties for Translation Surfaces filed under Geometry Topology Seminar Andy Parrish Saint Louis University What Geometry Topology Seminar When Tue Nov 19 2013 from 02 00 PM to 02 50 PM Where Ritter Hall 223 Add event to calendar vCal iCal Abstract In 1926 Khintchine established a result for Diophantine approximation of a vector In 1960 Wolfgang Schmidt refined this result We will approach a much weakened version of Schmidt s result using the tools of hyperbolic dynamics most crucially the pointwise ergodic theorem and Siegel s formula While this is not the first dynamical proof of its type the method demonstrated may be extended to the setting of translation surfaces 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

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/old-seminars/metrical-diophantine-properties-for-translation-surfaces/?searchterm=None (2016-02-12)

Open archived version from archive - The Three Loop Invariant — Department of Mathematics and Computer Science

Loop Invariant filed under Geometry Topology Seminar Heather Dye McKendree University What Geometry Topology Seminar When Tue Mar 25 2014 from 02 00 PM to 02 50 PM Where Ritter Hall 142 Add event to calendar vCal iCal Abstract This talk is based on the paper The Three Loop Isotopy and Framed Isotopy Invariants of Virtual Knots and Links and is joint work with Micah Chrisman Monmouth University We introduce a finite type invariant of virtual knots called the three loop invariant The invariant is a Gauss diagram formula where regions of the diagram are enhanced with the relative index of the arrows We investigate its properties with respect to symmetries and connected sums The invariant is an analog of the Grishanov Vassiliev finite type invariant of degree two 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

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/the-three-loop-invariant/?searchterm=None (2016-02-12)

Open archived version from archive - Free transformations of S1×Sn of prime period — Department of Mathematics and Computer Science

24 2014 from 04 20 PM to 05 10 PM Where 222 Ritter Hall Add event to calendar vCal iCal ABSTRACT Let p be an odd prime and let n be a positive integer I classify 2014 the set of equivariant homeomorphism classes of free C p actions on the product S 1 S n of spheres up to indeterminacy bounded in p The description is expressed in terms of number theory The techniques are various applications of surgery theory and homotopy theory and we perform a careful study of h cobordisms The p 2 case was completed by B Jahren and S Kwasik 2011 The new issues for the odd p case are the presence of nontrivial ideal class groups and a group of equivariant self equivalences with quadratic growth in p The latter is handled by the composition formula for structure groups of A Ranicki 2009 More information about this event 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

Original URL path: http://mathcs.slu.edu/seminars/free-transformations-of-s1xsns-1-times-s-n-of-prime-period/?searchterm=None (2016-02-12)

Open archived version from archive - Necktie knots, formal languages and network security — Department of Mathematics and Computer Science

3149777002 Add event to calendar vCal iCal A chore for some space for personal expression for others the necktie knot used to have very few speci c knots in widespread use In their 1999 paper Fink Mao Designing tie knots by random walks Nature 398 no 6722 1999 31 32 list all possible ways to tie a necktie They limit their enumeration task by focusing on knots that present a flat front just like all the classical tie knots This way they established a list of 85 possible tie knots Tie knots with intricate patterns of the necktie winding into symmetric but no longer at front displays have emerged in the past decade introduced by the movie Matrix Reloaded and recreated hobbyists These tie knots are tied with the narrow end of the tie wrapping it to create patterns on the surface of the tie knot As such these knots are not covered by the listing proposed by Fink Mao With a team of collaborators I have extended the listing by Fink and Mao to cover these new tie knots While doing this we have been able to determine the computational complexity classes of the grammar that describes tie knots The formal language techniques that help us analyze the tie knot grammars are used in contemporary security research a large class of security problems online emerge from different implementations of a communications protocol disagreeing on the actual grammar used We will talk about the connections between the language techniques for tie knots and those that help us analyze security For recent news coverage on this result see the following http www newscientist com article dn25019 matrix villain spawns 177000 ways to knot a tie html http phys org news 2014 02 mathematicians ways html Document Actions iCalendar vCalendar Send this

Original URL path: http://mathcs.slu.edu/seminars/computer-science-seminar/necktie-knots-formal-languages-and-network-security/?searchterm=None (2016-02-12)

Open archived version from archive - Complete Connection on the Causal Boundary of Spherically Symmetric Static Spacetimes, II — Department of Mathematics and Computer Science

When Tue Nov 03 2015 from 02 10 PM to 03 00 PM Where 225 Ritter Hall Contact Name Dr Khan Add event to calendar vCal iCal A continuation of Part I 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

Original URL path: http://mathcs.slu.edu/seminars/topology-seminar/complete-connection-on-the-causal-boundary-of-spherically-symmetric-static-spacetimes-ii/?searchterm=None (2016-02-12)

Open archived version from archive - Finite Subgroups of SO(4) — Department of Mathematics and Computer Science

iCal The finite subgroups of SO 3 are the dihedral groups and the three symmetry groups of Platonic solids the tetrahedron octahedron and icosahedron groups which are in turn the alternating and symmetric groups A 4 S 4 and A 5 The multiplication of quaternions leads nicely to a determination of the finite subgroups of SO 4 the special orthogonal group of dimension four real matrices There are many infinite families of such groups and as for SO 3 some individual groups which relate to symmetries of regular polytopes We will derive this list and look at some of the groups properties and specific examples including symplectic groups and symmetry groups of regular four polytopes and quotients by these groups This is a background talk for talks I ll give early next semester on orbifolds There I ll focus on low dimensional orbifolds particularly those of dimensions four and five vertex group homology in those degrees and orbifold cobordism and invariants This talk is meant to be accessible to all graduate students 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

Original URL path: http://mathcs.slu.edu/seminars/finite-subgroups-of-so-4/?searchterm=None (2016-02-12)

Open archived version from archive