\n| February 5, 2004<\/b> <\/th>\n | \nMary Ann Horn, Vanderbilt University <\/b><\/center>
\n
\nTheoretical challenges arising from
\nthe questions of controllability for elastic structures
\n<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nIn the context of control of elastic systems, the challenge of obtaining
\nrigorous theoretical results has given rise to the development of new
\nmathematical methods and expanded applications of known tools. This talk
\nwill give an overview of the questions of controllability and
\nstabilizability for plates, cylindrical shells and three-dimensional
\nelasticity, as well as the issues arising when single components are
\ncoupled into a more complex system. The need for and the utility of
\nhigh-powered mathematical tools such as microlocal analysis, Carleman
\nestimates and Riemannian geometry will be illustrated and examples of some
\nof the current challenges will be discussed. <\/p>\n Contact person<\/u>: Guoliang Yu<\/font><\/p>\n<\/td>\n<\/tr>\n\n| February 12, 2004<\/b> <\/th>\n | \nKim Ruane, Tufts University<\/b><\/center>
\n
\nGroups with
\nspecified boundary<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nThe result I will speak about is in the spirit of two well-known
\nresults. The first says if $G$ is a convergence group acting on the
\ncircle,
\nthen $G$ is virtually fuchsian (proved by Casson-Jungreis, Tukia-Gabai).
\nThe
\nsecond result says if $G$ is a one-ended word hyperbolic group with
\none-dimensional boundary, then that boundary is a circle, a Sierpinski
\ncarpet,
\nor a Menger curve (proved by Kapovich and Kleiner). If the boundary is
\ncircle,
\nthe first result applies to show $G$ is virtually fuchsian. If it’s a
\nSierpinski carpet, then they have a theorem about the structure of the
\ngroup.
\nIn this case, it is conjectured that $G$ is a geometrically finite
\nKleinian
\ngroup (obviously related to Cannon’s Conjecture concerning S^2 boundary).
\nThe
\nMenger curve boundary is the “generic” case for a word hyperbolic group
\nwith
\none-dimensional boundary and a characterization of these groups is far
\nfrom
\nknown. <\/p>\n\nI wish to consider the following related general question. Suppose $G$
\nacts
\ngeometrically on a $\\cat(0)$ space $X$ whose boundary is homeomorphic to
\nsome
\nspace $Y$. Given a particular space $Y$, what can you say about $X$ and
\n$G$?
\nFor instance, if $Y$ is a circle, then I will show that $X$ is either the
\nEuclidean plane and $G$ is a Bieberbach group or $X$ is the hyperbolic
\nplane in
\nwhich case the above result applies to say that $G$ is virtually fuchsian.
\nThe
\ncase where $Y$ is the circle is not difficult to prove, but the techniques
\nalready show something very interesting. Next, I consider $Y$ the
\nsuspension
\nof the Cantor set and show that $X$ is in fact “almost” isometric to the
\nmetric
\nproduct of a tree with the real line and $G$ is virtually the product of a
\nfree
\ngroup and $\\mathbb Z$. This case is already much more difficult than the
\ncircle and again, the techniques used should hopefully yield some powerful
\nresults. <\/p>\n Contact person<\/u>: Mike Mihalik<\/font><\/p>\n<\/td>\n<\/tr>\n\n| February 19, 2004<\/b> <\/th>\n | \nFrank Quinn, Virginia Polytechnic Institute and
\nState University<\/b><\/center>
\n
\nWhat is a
\nmanifold?<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nShort names such as “manifold” or “group” tend to be attached to
\ncentral objects in an area, as identified by tradeoffs between generality
\nand properties. More general objects with significantly fewer properties,
\nsuch as “homology manifolds” or “semigroup”, and more special objects with
\nslightly more properties, such as “real analytic manifold” or “algebraic
\ngroup” are thought of as perturbations on the central object. However what
\nwe see as the “central object” often changes as we learn more. In this
\nlecture I’ll trace changes in the meaning of “manifold” as it tracked
\ndevelopment of the subject over the last century. We may be on the verge
\nof
\nanother major change of viewpoint, though whether the word “manifold” will
\nfollow it this time remains to be seen.<\/p>\nContact person<\/u>: Bruce Hughes<\/font><\/p>\n<\/td>\n<\/tr>\n\n| February 25, 2004<\/b> <\/th>\n | \nMikhail Perepelitsa, Northwestern University<\/b><\/center>
\n
\nNote: Wednesday, 4:10 pm in SC 1308<\/strong><\/center>
\n
\nExistence of solutions of two
\ndimensional
\ncompressible Navier-Stokes equations with uniform in time
\npoint-wise bounds on density<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nWe consider the two dimensional Navier-Stokes equations that
\ndescribe
\nthe motion of compressible, viscous, barotropic flow. The
\nbulk viscosity coefficient is assumed to be a function of the
\ndensity
\nof the flow that grows a least as fast as the equilibrium pressure.
\nWe
\nprove that given periodic initial data in which the density is
\nbounded
\nand does not contain vacuum, there exists global in time weak
\nsolution
\nand the density is uniformly bounded and does not contain vacuum.<\/p>\nContact person<\/u>: Gieri Simonett<\/font><\/p>\n<\/td>\n<\/tr>\n\n| February 26, 2004<\/b> <\/th>\n | \nJennifer Pietenpol, School of Medicine, Vanderbilt
\nUniversity<\/b><\/center>
\n
\np53 and
\nMechanisms of Cell Cycle Checkpoints<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nAlthough most cells in an adult human are quiescent or in a
\nnon-proliferative state, specialized cells such as those of the
\nhematopoietic system, those that generate skin, or those that line the
\ngastrointestinal tract, maintain proliferation. On average, about 2
\ntrillion cell divisions occur in an adult human every 24 hours. It is
\ncritically important that various cell types divide at a rate sufficient
\nto produce the needed cells for growth and replacement. However, if any
\ngiven cell type divides more rapidly than is necessary, the normal
\norganization and functions of the organism will be disrupted as
\nspecialized tissues are invaded and interfered with by the rapidly
\ndividing cells. Such is the course of events in cancer. Over the past
\ntwo decades, unraveling the basic molecular events controlling eukaryotic
\ncell cycle transitions has been an area of intense research pursuit.
\nStudies in a variety of organisms have identified an evolutionarily
\nconserved signal transduction system for controling cell cycle transitions
\nthrough regulation of the activity of key enzymes called cyclin-dependent
\nkinases. Further, many investigations have focused on how the signaling
\npathways that mediate the cell cycle transitions are regulated and
\nmodified after cellular stresses. Human cells are continuously exposed to
\nexternal agents (e.g., reactive chemicals and UV light) as well as
\ninternal agents (e.g. byproducts of normal intracellular metabolism such
\nas reactive oxygen intermediates) that can induce cell stress. Eukaryotic
\ncells have evolved cell cycle machinery with a series of surveillance
\npathways termed cell cycle checkpoints to ensure that cells copy and
\ndivide their genomes with high fidelity during each replication cycle.
\nCell cycle arrest after DNA damage is critical for maintenance of genomic
\nintegrity and loss of normal cell cycle checkpoint signaling is a hallmark
\nof tumor cells. The ability to manipulate cell cycle checkpoint signaling
\nalso has important clinical implications, as modulation of the checkpoints
\nin human tumor cells may enhance cellular sensitivity to chemotherapeutic
\nregimens that induce DNA damage. This presentation will focus on the
\nmechanics of the cell cycle as well as checkpoint signaling pathways, with
\nparticular focus on the tumor suppressor p53, and how this knowledge may
\nlead to more efficient use of current anticancer therapies and the
\ndevelopment of novel agents. The hope is that from a detailed
\nunderstanding of these processes, more incisive approaches to cancer
\ntreatment will evolve that exploit the molecular defects in cancer cells.<\/p>\nContact person<\/u>: Guoliang Yu<\/font><\/p>\n<\/td>\n<\/tr>\n\n| March 4, 2004<\/b> <\/th>\n | \nRalph Mckenzie, Vanderbilt University
Matthew
\nValeriote, McMaster University
Pawel M. Idziak, Jagiellonian
\nUniversity<\/b><\/center>
\nGenerative
\ncomplexity in algebra<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nThe generative complexity of a class $K$ of algebras is the function $G_K$
\ndefined for positive integers $n$ by setting $G_K(n)$ equal to the number
\nof non-isomorphic $n$-generated algebras in $K$. We have studied $G_K$
\nmainly for $K$ a locally finite variety (equationally defined class of
\nalgebras). Besides making some easy observations about the ways in which
\nthe behaviour of $G_K$ imposes algebraic and structural constraints on
\n$K$, we shall outline the proof of a three-year-old result of P. Idziak,
\nR. McKenzie and M. Valeriote giving a precise determination of all the
\nlocally finite varieties $K$ for which $G_K(n)$ is bounded by some
\npolynomial function of $n$. In the category of varieties, the directly
\nindecomposable locally finite varieties with polynomially many models are
\nthe varieties of modules over finite rings of finite representation type,
\nand the finite matrix powers of varieties of $M$-sets with (possibly) some
\nconstants, where $M$ is any finite group. <\/p>\n Contact person<\/u>: Ralph Mckenzie<\/font><\/p>\n<\/td>\n<\/tr>\n\n| March 18, 2004<\/b> <\/th>\n | \nStefan Richtner, University of Tennessee,
\nKnoxiville<\/b><\/center>
\n
\nAnalytic contractions and
\nnontangential limits<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nLet f be a complex-valued holomorphic function in the open unit disc D of
\nthe complex plane. f is said to have nontangential limit L at z, |z|=1, if
\nthere is a fixed angle A inside D with vertex at z such that the limit of
\nf(z) from within A is L. A theorem of Fatou’s implies that every function
\nf in the Hardy space H2 has nontangential limits at a.e. point of the unit
\ncircle, and a theorem of Beurling’s exploits these boundary values to give
\nprecise information about the invariant subspace structure of that the
\nlinear operator Mz, (Mz)f(z) = zf(z) on H2. If H is a Hilbert space of
\nanalytic functions that properly contains H2, then there may be a set of
\npositive measure inside the unit circle such that all functions in H have
\nnontangential limits a.e. on this set.<\/p>\nIn this talk I will discuss efforts to describe conditions for the
\nexistence of such a set in terms of the norm on H and the relevance of
\nthis
\nfor the invariant subspace structure of Mz when Mz acts on H.<\/p>\n Contact person<\/u>: Dechao Zheng<\/font><\/p>\n<\/td>\n<\/tr>\n\n| March 25, 2004<\/b> <\/th>\n | \nRoger Smith, Texas A&M University<\/b><\/center>
\n
\nCohomology
\nof von Neumann Algebras<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nIn the 1940’s, Hochschild introduced cohomology groups for
\nalgebras, and these were adapted by Kadison and Ringrose
\nin the 1970’s to the functional analytic setting of von Neumann
\nalgebras, the weakly closed self-adjoint subalgebras of bounded
\noperators on a Hilbert space. These groups $H^n(M,X)$ are defined
\nin terms of a module $X$ over the algebra $M$ and can be used as
\nisomorphism invariants. When $X=M$, they also act as obstruction groups
\nwhose vanishing gives structural information about the algebras.
\nFor example, the statement that $H^1(M,M)=0$ is, in different language,
\na celebrated theorem of Kadison and Sakai that derivations of
\na von Neumann algebra are always implemented by elements of the algebra.
\nIn their original work, Kadison and Ringrose conjectured that
\n$H^n(M,M)$ should always vanish, and proved this in a number of cases.
\nFurther progress had to await the recently developed theory of completely
\nbounded maps. In this talk we will survey the current state of affairs and
\ndescribe some of our own work on this topic. The presentation will be
\naimed at a general audience with very little background assumed.<\/p>\nContact person<\/u>: Dietmar Bisch<\/font><\/p>\n<\/td>\n<\/tr>\n\n| April 1, 2004<\/b> <\/th>\n | \nBurt Ovrut, University of Pennsyvania<\/b>
\n
[Joint colloquium with Department of Physics]<\/center>
\n
\nNOTE: Thursday, 4:00 pm in SC
\n4327
Tea at 3:30 pm in SC 6333<\/strong><\/center>
\n
Brane
\nWorlds and Geometry<\/font><\/strong><\/center>
\n
\nAbstract<\/u>:
\nThe fundamental concepts underlying superstrings and M-theory will be
\nreviewed. The compactification of M-theory to the observed
\nfour-dimensional spacetime will be discussed, leading to the idea that our
\nuniverse is a “brane” floating in a higher dimensional space. To obtain
\nrealistic particle physics on the brane, one must have the appropriate
\ngeometric and vector bundle properties on the background compact manifold.
\nThese provide an important link between modern mathematics and high energy
\nphysics. <\/p>\n Contact person<\/u>: Tom Kephart<\/font><\/p>\n<\/td>\n<\/tr>\n<\/table>\n
\n
\nColloquium Chair (Spring 2004): Guoliang Yu<\/b><\/p>\n","protected":false},"excerpt":{"rendered":" Mathematics Colloquia, Spring 2004 Thursdays 4:10 pm in 1206 Stevenson Center, unless otherwise noted Tea at 3:30 pm in 1425 Stevenson Center February 5, 2004 Mary Ann Horn, Vanderbilt University Theoretical challenges arising from the questions of controllability for elastic structures Abstract: In the context of control of elastic systems, the challenge of obtaining rigorous…<\/p>\n","protected":false},"author":637,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-53","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/pages\/53","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/users\/637"}],"replies":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/comments?post=53"}],"version-history":[{"count":1,"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/pages\/53\/revisions"}],"predecessor-version":[{"id":54,"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/pages\/53\/revisions\/54"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/media?parent=53"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/wp-json\/wp\/v2\/tags?post=53"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}} | | | | | | | | |