# Seminars and Colloquia

## Topology et al. Seminar

Apr 18

04:20 pm

一道本不卡免费高清Exley Science Center Tower ESC 638

一道本不卡免费高清 MelissaZhang, Boston College Symmetries in topological spaces and homology-type invariants Abstract:Topologistsoften encounter spaces with interesting symmetries. By analyzing the symmetriesof an object through the regularities of its algebraic invariants, we are ableto learn more about the object and its relationship with smaller, less complexobjects. For example, by using the right tools, we can easily see that for atopological space Xequipped with a cyclic action, the rank of thesingular homology of Xis at least that of the fixed point set. In low-dimensional topology, knots and links are ubiquitous and far-reaching intheir associations. One particular interesting algebraic invariant of links isKhovanov homology, a combinatorial homology theory whose graded Eulercharacteristic is the Jones polynomial. In this talk, we consider linksexhibiting 2-fold symmetry and prove a rank inequality for a variant ofKhovanov homology.

Feb 21

04:20 pm

Exley Science Center Tower ESC 638

一道本不卡免费高清 Kyle Hayden, Boston College From algebraic curves to ribbon disks and back Abstract: There is a rich, symbiotic relationship betweenknot theory and the study of algebraic curves in complex spaces. In particular,intersecting an algebraic curve in C^2 with a three-sphere of constant radiusyields a knot or link that contains useful information about the algebraiccurve. We'll look at a thirty-year-old conjecture about the relationshipbetween different knots associated to the same algebraic curve. Using a simpleconstruction, we'll show that the conjecture is false and that counterexamplesare quite common.

Nov 29

04:20 pm

Exley Science Center Tower ESC 638

Patrick Devlin, Yale University Topological Methods in Combinatorics Abstract: It is sometimes remarked that combinatorics is not the study ofstructures or theorems, so much as the study of techniques. Several techniquesare well known and evidently quite fruitful (e.g., linear programming, theprobabilistic method, Fourier analysis, entropy, et cetera). But another toolthat should be in every discrete mathematician's backpocket is topology. Inthis talk, we will discuss some clever applications of topology tocombinatorics providing quick primers on any relevant topological (and combinatorial)concepts along the way. We will focus on work related to graph colorings andboolean function complexity and introduce several open problems and conjecturesin the area.

Oct 25

04:20 pm

Exley Science Center Tower ESC 638

Speaker: Arie Levit, Yale Title: Local rigidity of uniform lattices Abstract: Alattice is topologically locally rigid(t.l.r) if small deformations of it are isomorphic lattices. Uniform latticesin Lie groups were shown to be t.l.r by Weil [60']. We show that uniformlattices in any compactly generated topological group are t.l.r. Alattice is locally rigid(l.r) if small deformations arise from conjugation. It is a classical fact dueto Weil [62'] that lattices in semi-simple Lie groups are l.r. Relying on ourt.l.r results and on recent work by Caprace-Monod we prove l.r for uniformlattices in the isometry groups of certain CAT(0) spaces, with the exception ofSL_2(R), which occurs already in the classical case. Inthe talk I will explain the above notions and results, and present somegeometric ideas from the proofs. Thisis a joint work with Tsachik Gelander.

Oct 11

04:20 pm

一道本不卡免费高清Exley Science Center Tower ESC 638

一道本不卡免费高清 Speaker: Noelle Sawyer, Wes Title: The specification property and closed orbit measures Abstract: Given a compact metric space X, and a homeomorphism T on X, thedynamical system (X,T) has the specification property if we can approximatedistinct orbit segments with the orbit of a periodic point. I will present aresult by Sigmund showing that if (X,T) has the specification property, anyT-invariant measure on X can be approximated by a closed orbit measure.

Oct 4

04:20 pm

一道本不卡免费高清Exley Science Center Tower ESC 638

一道本不卡免费高清 Speaker: Shelly Harvey, Rice University Title: Braids, gropes, Whitney towers, and solvability oflinks Abstract: The n-solvable filtrations of the knot/linkconcordance groups were defined as a way of studying the structure of thegroups and in particular, the subgroup of algebraically slice knots/links. While the knot concordance group C^1 is knownto be an abelian group, when m is at least 2, the link concordance group C^m ofm-component (string) links is known to be non-abelian. In particular, it is well known that the purebraid group with m strings is a subgroup of C^m and hence when m is at least 3,this shows that C^m contains a non-abelian free subgroup. We study the relationship between the derivedsubgroups of the the pure braid group, n-solvable filtration of C^m, linksbounding symmetric Whitney towers, and links bounding gropes. This is joint with with Jung Hwan Park andArunima Ray.

Sep 27

04:20 pm

Exley Science Center Tower ESC 638

一道本不卡免费高清 Speaker: Samuel Lin, Dartmouth Title: Curvature FreeRigidity of Higher Rank Three- manifolds Abstract: Fixing K=-1, 0, or 1, a Riemannian manifold (M, g) is said to havehigher hyperbolic, spherical, or Euclidean rank if every geodesic in M admits anormal parallel field making curvature K with the geodesic. Rank rigidityresults, which usually involve a priori sectional curvature bounds,characterize locally symmetric spaces in terms of these geometric notions ofrank. Aftergiving a short survey of historical results, Ill discuss how rank rigidityholds in dimension three without a priori sectional curvature bounds.