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| Discrete Mathematics Seminar | ||
| Topic: | Learning a hidden matching with application to whole-genome sequencing | |
| Presenter: | Benny Sudakov, Princeton University and the Institute for Advanced Study | |
| Date: | Wednesday, March 26, 2003, Time: 2:15 p.m., Location: Fine Hall 224 | |
| Abstract: | Click here to see abstract | |
| Department Colloquium | ||
| Topic: | List decoding of error-correcting codes | |
| Presenter: | Madhu Sudan, MIT | |
| Date: | Wednesday, March 26, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | The task of dealing with errors (or correcting them) lies at the very heart of communication and computation. The mathematical foundations for this task were laid in two concurrent and interdependent works by Shannon and Hamming in the late 1940s. The two theories are strikingly powerful and distinct in their modelling of the error. Shannon's theory models errors as effected by a probabilistic/stochastic process, while Hamming envisions them as being introduced by an adversary. While the two theories share a lot in the underlying tools, the quantitative results are sharply diverging. Shannon's theory shows that a channel that corrupt (arbitrarily) close to 50% of the transmitted bits can still be used for transmission of information. Hamming's theory in contrast has often been interpreted to suggest it can handle at most 25% error on a binary channel. So what can we do if an adversary is given the power to introduce more than 25% errors? Can we protect information against this, or do we just have to give up? The notion of list-decoding addresses precisely this question, and shows that under a relaxed notion of "decoding" (or recovering from errors), the quantitative gaps between the Shannon and Hamming theories can be bridged. In this talk, we will describe this notion and some recent algorithmic developments. | |
| Ergodic Theory and Statistical Analysis Seminar | ||
| Topic: | Universality of discrete orthogonal polynomial ensemble | |
| Presenter: | Jinho Baik, Princeton University | |
| Date: | Thursday, March 27, 2003, Time: 2:00 p.m., Location: Fine Hall 214 | |
| Abstract: | In the random matrix theory, it is known that in the bulk scaling limit, the correlation functions of the scaled eigenvalues are universal (sine kernel) for a general class of unitary invariant measure on Hermitian matrices. The density function of the eigenvalues of unitary invariant measure is given by the Coulomb gas of beta=2 with certain external (continuous) potential. In this talk, we replace the potential by pure point measure. We prove the universality for a general class of pure point measures when we take continuum limit and bulk scaling limit simultaneously. An application of this result is the computation of the local correlation functions of random hexagon tiling. This is a joint work with Thomas Kriecherbauer, Ken McLaughlin and Peter Miller. | |
| Cohomology of Groups *** Please note NEW SEMINAR | ||
| Topic: | Finite dimensional G-spaces | |
| Presenter: | William Browder, Princeton University | |
| Date: | Thursday, March 27, 2003, Time: 3:00 p.m., Location: Fine Hall 801 | |
| Abstract: |
Borel in 1957 gave a construction which turned an arbitraryG-space into a free G-space, by multiplying by a free contractible G-space. When can one determine if a given free space X is the end product of such a construction (up to some kind of homotopy)? If G is a finite p-group and if X has the p homology type of a finite complex, and a condition on fundamental group, then X is the mod p type of a finite G-space. This relies on the Smith theorem for homotopy fixed points proved by Lannes-Zarati and by Dwyer-Wilkerson. This was inspired by and generalizes work of Grodal and Smith in the case where X is a sphere. |
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| Joint Institute for Advanced Study /Princeton University/ Rutgers University Non-Linear Analysis Seminar | ||
| Topic: | Topological Singularity in some Non-linear PDE Problems | |
| Presenter: | Fang-Hua Lin, Courant Institute, New York University | |
| Date: | Thursday, March 27, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: |
Many
interesting natural phenomena contain some sort of singular behavior and are
often manifested through energy concentrations. Singularities of
solutions of Partial Differential Equations which describe these phenomena
are, therefore, an important part of facets. One can divide these
singularities into two basic categories: topological and
non-topological. There are many examples of non-topological
singularities such as spikes in the reaction-diffusion systems, concentrated
vorticities in the Euler or the Navier-Stokes equations. Singularities
in these examples may or may not carry quantified amounts of energy. On
the other hand, the topological singularities often not only carry a definite
topological information but also a quantified amount of energy. Because
of this, they are often more stable energetically and dynamically. The
purpose of this lecture is to describe some recent works on analysis of
topological singularity in some variational and evolution problems.
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| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | On the class number one problem for some special real quadratic fields | |
| Presenter: | Andras Biro, Budapest | |
| Date: | Thursday, March 27, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
| Topology Seminar | ||
| Topic: | Hyperbolic Manifolds with Convex Boundary | |
| Presenter: | Jean-Marc Schlenker, Université Paul Sabatier | |
| Date: | Thursday, March 27, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: |
Let
M be a compact 3-manifold with boundary, which admits a convex co-compact
hyperbolic metric. One can describe the hyperbolic metrics on M for which
the boundary is smooth and strictly convex.
Theorem A: the induced metrics have curvature K>-1, and each is obtained for a unique hyperbolic metric on M. Theorem B: the third fundamental forms of the boundary have curvature K<1, and their closed geodesics which are contractible in M have length L>2\pi. Each is obtained for a unique hyperbolic metric on M. Theorem B has analogs when the boundary is supposed to look locally like an ideal or a hyperideal polyhedron. As a consequence, we find an extension of the Koebe circle packing theorem when the sphere is replaced by the boundary of M. |
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| Geometric Analysis Seminar ***CANCELLED *** | ||
| Topic: | TBA | |
| Presenter: | Jie Qing, UC at Santa Cruz | |
| Date: | Friday, March 28, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
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| Analysis Seminar | ||
| Topic: | Quasi-Periodic Solutions for Non-Linear Random Schrodinger Equation | |
| Presenter: | Wei-Min Wang, Institute for Advanced Study | |
| Date: | Monday, March 31, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| Abstract: | I start the talk by giving an overview of the problem and related issues. I then sketch the construction of time quasi-periodic solutions for discrete non-linear Schrodinger equation, using a Newton scheme and Lyapunov- Schmidt P and Q decompositions. The main new dificulty is the concurrence of small divisors from the original linear equation and that from the non-linearity. This is joint work with J. Bourgain. | |
| PACM Colloquium | ||
| Topic: | Direct Simulations of Suspensions of Long Slender Elastic Filaments | |
| Presenter: | Anna-Karin Tornberg, Courant Institute, New York University | |
| Date: | Monday, March 31, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: | The dynamics of long slender
filaments or fibers suspended in fluids are fundamental to understanding many
flows arising in physics, biology and engineering. Such filaments often have
aspect ratios of length to radius ranging from a few hundred to several
thousand. Full discretizations of such thin objects in a 3D domain is very
costly. Slender body theory yields an integral equation along the filament
centerline, relating the force exerted on the body to the filament velocity.
The equation is asymptotically accurate to $O(\varepsilon^2 \log \varepsilon)$,
where the slenderness parameter $\varepsilon$ is the aspect ratio of the
filament. The equation is extended to the case of multiple interacting
filaments.
We consider filaments that are inextensible and elastic. Replacing the force in the integral equation by an explicit expression using Euler-Bernoulli elasticity, yields a time-dependent integral equation for the motion of the filament centerline, coupled with an auxiliary integro-differential equation for the filament tension. Our numerical method is based on a regularized version of these slender body equations that is asymptotically equivalent to the original formulation. The filament centerline is parameterized by arclength, and discretized uniformly. The numerical algorithm is based on a combination of finite differences and special quadrature methods. We present three dimensional simulations of single as well as interacting filaments in a shear flow, in parameter ranges where the filaments develop rather large curvatures, and discuss some interesting features of these simulations. |
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| Analysis Seminar *** Please note special date | ||
| Topic: | Linability and spaceability of some nonlinear sets in Function Spaces | |
| Presenter: | Vladimir Gurariy, Kent State University | |
| Date: | Tuesday, April 1, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| Abstract: | The set M in Vector space X is said to be n-linable ( linable ) in X if M contains a linear manifold Y such that dimY=n ( corr. dimY=infinity ),(if X is Topological vector space and Y is closed infinitedimensional then M is said to be spaceable). In last years were discovered surprisingly many " very nonlinear " sets in Function Spaces, which are linable or even spaceable. For example, the set of nowhere differentiable functions on [0,1] is spaceable in C[0,1]( V.P.Fonf,V.I.Gurariy, M.I.Kadec, 1991). We present some new results in this direction, including following result of author together with Per Enflo: " The set of functions in C with infinitely many zeroes on [0,1] is spaceable any infinitedimensional subspace X of C". In particular this gives positive answer on old question on existence such nontrivial function in X. | |
| Algebraic Geometry Seminar | ||
| Topic: | Theta divisors, resolutions and moduli of curves | |
| Presenter: | Gavril Farkas, University of Michigan, Ann Arbor | |
| Date: | Tuesday, April 1, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Abstract: | One of the defining problems in the theory of algebraic curves in the last two decades has been Green's Conjecture predicting that one can read the intrinsic geometry of each curve from the equations of its canonical embedding. I will describe how the moduli space of curves can be used in a rather surprising way to prove two statements intimately related to Green's Conjecture: the Minimal Resolution Conjecture linking the geometry of a canonical curve to the resolution of general subsets of its points and a conjecture of Lazarsfeld about the theta divisors of powers of the normal bundle of a curve embedded in its Jacobian. This is joint work with M. Mustata and M. Popa. | |
| Mathematical Physics Seminar | ||
| Topic: | Lifshits tails in magnetic fields | |
| Presenter: | Simone Warzel, Univ. Erlangen-Nuernberg | |
| Date: | Tuesday, April 1, 2003, Time: 4:30 p.m., Location: Jadwin A06 | |
| Geometric Analysis Seminar *** Please note special date and location | ||
| Topic: | Regularity of biharmonic maps into Riemannian manifolds | |
| Presenter: | Changyou Wang, University of Kentucky | |
| Date: | Wednesday, April 2, 2003, Time: 3:00 p.m., Location: Fine Hall 322 | |
| Abstract: | In this talk, I will consider both intrinsic and extrinsic biharmonic maps into general Riemannian manifolds. I will sketch the ideas to prove smoothness of biharmonic maps from domains of dimension four and partial regularity for stationary biharmonic maps from domains of dimensions five or above. The same theorems were previously proved by Chang-Wang-Yang when the target manifold is the standard sphere. | |
| Department Colloquium | ||
| Topic: | Stochastic Loewner Evolutions | |
| Presenter: | Stanislav Smirnov, Royal Institute of Technology, Stockholm | |
| Date: | Wednesday, April 2, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | We will talk about Loewner Evolutions driven by stochastic processes, starting with Scramm-Loewner Evolution. We will discuss fractal properties of their trajectories and their relation to scaling limits of lattice models. | |
| Ergodic Theory and Statistical Analysis Seminar | ||
| Topic: | Ergodic properties of boundary actions | |
| Presenter: | Tatiana Nagnibeda, Royal Institute of Technology, Stockholm | |
| Date: | Thursday, April 3, 2003, Time: 2:00 p.m., Location: Fine Hall 214 | |
| Abstract: | We shall discuss ergodic properties of the action of a subgroup H of a free group F on the Poisson boundary of the simple random walk on F. The action is ergodic if and only if the quotient F/H admit no non-constant bounded harmonic function. Methods from combinatorial group theory allow us to identify the conservative and the dissipative part of the action. We also present necessary and sufficient conditions of conservativity of the action in terms of geometry of the quotient. This is a joint work with R. Grigorhcuk and V. Kaimanovich. | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Zeros of families of elliptic curve L-functions | |
| Presenter: | Matthew Young, Rutgers University | |
| Date: | Thursday, April 3, 2003, Time: 4:15 p.m., Location: Hill Center 425 (Rutgers University) | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Non-Linear Analysis Seminar | ||
| Joseph D'Atri Memorial Lecture | ||
| Topic: | On the Ricci Flow | |
| Presenter: | Richard Hamilton, Columbia University | |
| Date: | Thursday, April 3, 2003, Time: 4:30 p.m., Location: Hill Center 705 (Rutgers University) | |
| Topology Seminar | ||
| Topic: | One parameter families of Calabi-Yau threefolds | |
| Presenter: | John Morgan, Columbia University | |
| Date: | Thursday, April 3, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | There are lots of examples of one-parameter families of Calabi-Yau threefolds occurring as hypersurfaces or complete intersections in toric varieties. We study the resulting variations of Hodge structure from these families and compare the results to all possible variations and to various conjectures arising out of mirror symmetry conjectures. | |
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| PACM Colloquium | ||
| Topic: |
Interval analysis and set-membership techniques in estimation |
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| Presenter: | Isabelle Braems, MAE, Princeton University | |
| Date: | Monday, April 7, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: | Interval analysis has been developed more than four decades ago to control numerical round-off errors in computers, in a rigorous way. It has then reached many other fields (assisted proof demonstrations, numerical simulation, estimation…) and applications (biology, chemical engineering, economics, computer vision, robotics…) where guaranteed computations are essential. In this talk we shall focus on parameter and state estimation problem. We will emphasize how interval analysis permits to estimate in a guaranteed way a reliable enclosure of all the global minima in optimization problems, or of all the acceptable solutions in the bounded-error context. This talk will first briefly present (or recall) the bases of interval analysis. Several applications -including non-identifiable kinetic parameteridentification, reliable characterization of a thermal set-up, and robot localization- will illustrate the performance of this approach. | |
| Algebraic Geometry Seminar | ||
| Topic: | Threefold divisorial contractions contracting an irreducible divisor onto a curve | |
| Presenter: | Nikos Tziolas, Max Planck Institute | |
| Date: | Tuesday, April 8, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Abstract: | Divisorial contractions is one of the elementary maps that appear in the minimal model program, and their understanding is essential for the study of the birational geometry of threefolds. Given a curve C in a Gorenstein terminal threefold X, I will give conditions depending on the singularities of X and the equations of C, for the existence of a terminal divisorial contraction Y---->X that contracts an irreducible divisor E onto C. I will classify all such contractions and describe their singularities. | |
| Mathematical Physics Seminar | ||
| Topic: | Quantum chaos: universal versus system-specific fluctuations | |
| Presenter: | Oriol Bohigas, Laboratoire de Physique Theorique et Modeles Statistiques (LPTMS), Orsay, France | |
| Date: | Tuesday, April 8, 2003, Time: 4:30 p.m., Location: Jadwin A06 | |
| Abstract: | Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework several properties will be discussed. Results will be illustrated with two very different systems: atomic nuclei and the Riemann zeta function. | |
| Department Colloquium | ||
| Topic: | Universality for mathematical and physical systems | |
| Presenter: | Percy Deift, New York University | |
| Date: | Wednesday, April 9, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | All physical systems in equilibrium
obey the laws of thermodynamics. In other words, whatever the precise nature
of the interaction between the atoms and molecules at the microscopic level,
at the macroscopic level, physical systems exhibit universal behavior in the
sense that they are all governed by the same laws and formulae of
thermodynamics. The speaker will recount some recent history of universality ideas in physics starting with Wigner's model for the scattering of neutrons off large nuclei and show how these ideas have led mathematicians to investigate universal behavior for a variety of mathematical systems. This is true not only for systems which have a physical origin, but also for systems which arise in a purely mathematical context such as the Riemann hypothesis, and a version of the card game solitaire called patience sorting. |
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| Geometric Analysis Seminar | ||
| Topic: | A Bernstein problem for special Lagrangian equations | |
| Presenter: | Yu Yuan, University of Washington | |
| Date: | Friday, April 11, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
| Abstract: | In this talk, we derive a Bernstein type result for the special Lagrangian equation, namely, any global convex solution must be quadratic. In terms of minimal surfaces, the result says that any global minimal Lagrangian graph with convex potential must be a hyper-plane. | |
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| PACM Colloquium | ||
| Topic: | Elastic strain in epitaxial thin films | |
| Presenter: | Russel Caflisch, University of California at Los Angeles | |
| Date: | Monday, April 14, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: | In an epitaxial thin films the lattice properties of the film are determined by those of the underlying substrate. A mismatch between the lattice spacing of the substrate and film will introduce a strain into the film, which can significantly influence the material structure and properties. This talk will describe analysis and computation for strain in an epitaxial film with harmonic interatomic potentials and intrinsic surface stress. The resulting force field at a step and the interactions between steps will be described. Generalizations to epitaxial wires and particles will be presented. | |
| Ergodic Theory and Statistical Analysis Seminar | ||
| Topic: | A spectral gap property for measures;applications to the Anderson model | |
| Presenter: | Carol Shubin, California State University Northridge | |
| Date: | Thursday, April 17, 2003, Time: 2:00 p.m., Location: Fine Hall 214 | |
| Abstract: | We discuss products of random matrices as they arise from studying the discrete Anderson model on the strip. We obtain a quantitative bound of the largest Lyapunov exponent. This was joint work with T. Wolff and R. Vakilian. We discuss extensions of this work by T. Wolff, first to $PSL(2,\R)$ and then more generally to noncompact semi-simple Lie groups. | |
| Topology Seminar | ||
| Topic: | TBA | |
| Presenter: | Alejandro Adem, University of Wisconsen | |
| Date: | Thursday, April 17, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Geometric Analysis Seminar | ||
| Topic: | TBA | |
| Presenter: | Aobing Li, Rutgers University | |
| Date: | Friday, April 18, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
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| Analysis Seminar | ||
| Topic: | From Hilbert's variational principle to Einstein's equations as a well posed initial value problem | |
| Presenter: | James York, Cornell University | |
| Date: | Monday, April 21, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| PACM Colloquium | ||
| Topic: | TBA | |
| Presenter: | Carlos Castillo-Chavez, Cornell University | |
| Date: | Monday, April 21, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Algebraic Geometry Seminar | ||
| Topic: | TBA | |
| Presenter: | Jason Starr, MIT | |
| Date: | Tuesday, April 22, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Department Colloquium | ||
| Topic: | Stationary Determinantal Processes (Fermionic Lattice Gases) | |
| Presenter: | Russell Lyons, Indiana University | |
| Date: | Wednesday, April 23, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract | Eigenvalues of random matrices arise in various areas of physics and mathematics. The most-studied such probability measures have a determinantal form. Several people have studied other specific determinantal processes, as well as a general theory. We shall discuss the general theory of stationary random fields on integer lattices that are defined via minors of multi-dimensional Toeplitz matrices. Explicit examples include combinatorial models, finitely dependent processes, and renewal processes in one dimension. Among the interesting properties of these processes, we focus mainly on whether they have a phase transition analogous to that which occurs in statistical mechanics. We describe necessary and sufficient conditions for the existence of such a phase transition and give several examples to illustrate the theorem. This is joint work with Jeff Steif. | |
| Ergodic Theory and Statistical Analysis Seminar | ||
| Topic: | Diffusive and Coalescing Flows | |
| Presenter: | Yves Le-jan, Université Paris-Sud | |
| Date: | Thursday, April 24, 2003, Time: 2:00 p.m., Location: Fine Hall 214 | |
| Abstract | Coalescence and stickyness are introduced in a simple exemple. Then the compressible Kraichnan model for turbulent advection motivates new developments in the theory of flows driven by sochastic differential equations. It appears that some of these flows cannot be generated by a gaussian noise. | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Non-Linear Analysis Seminar | ||
| Topic: | On the time evolution and steady states for inelastic Boltzmann equations | |
| Presenter: | Irene Gamba, University of Texas at Austin | |
| Date: | Thursday, April 24, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Are motivic L-functions rational? | |
| Presenter: | M. Larson, Indiana | |
| Date: | Thursday, April 24, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
| Geometric Analysis Seminar | ||
| Topic: | TBA | |
| Presenter: | Xiaodong Wang, MIT | |
| Date: | Friday, April 25, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
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| PACM Colloquium | ||
| Topic: | On the time evolution and steady states for inelastic Boltzmann equations | |
| Presenter: | Irene Gamba, University of Texas at Austin | |
| Date: | Monday, April 28, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Algebraic Geometry Seminar | ||
| Topic: | TBA | |
| Presenter: | Tomohide Terasoma, Institute for Advanced Study | |
| Date: | Tuesday, April 29, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Department Colloquium | ||
| Topic: | TBA | |
| Presenter: | S.R.Srinivasa Varadhan, New York University | |
| Date: | Wednesday, April 30, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Counting number fields of bounded discrminant | |
| Presenter: | Jordan Ellenberg, Princeton University | |
| Date: | Thursday, May 1, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
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| Department Colloquium | ||
| Topic: | The lost proof of Loewner's theorem | |
| Presenter: | Barry Simon, Caltech | |
| Date: | Wednesday, May 7, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract | A real-valued function, F, on an interval (a,b) is called matrix monotone if F(A) < F(B) whenever A and B are finite matrices of the same order with eigenvalues in (a,b) and A < B. In 1934, Loewner proved the remarkable theorem that F is matrix monotone if and only if F is real analytic with continuations to the upper and lower half planes so that Im F > 0 in the upper half plane. This deep theorem has evoked enormous interest over the years and a number of alternate proofs. There is a lovely 1954 proof that seems to have been "lost" in that the proof is not mentioned in various books and review article presentations of the subject, and I have found no references to the proof since 1960. The proof uses continued fractions. I'll provide background on the subject and then discuss the lost proof and a variant of that proof which I've found, which avoids the need for estimates, and proves a stronger theorem. | |
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| Algebraic Geometry Seminar | ||
| Topic: | TBA | |
| Presenter: | B. Guralnick | |
| Date: | Tuesday, May 13, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |