Weekly Calendar

November 5-9, 2001

Monday Tuesday Wednesday Thursday Friday

Seminars Announcements Conferences Calendar Archive

Items for inclusion in the Weekly Calendar should be submitted via e-mail to Hilda Britt. Deadline for inclusion in the Weekly Calendar is 5 p.m. Thursdays. Speakers are encouraged to provide abstracts.

Orange & Blue Bar

MONDAY, NOVEMBER 5

  
RAP ``Etale cohomology'',  159 Altgeld Hall,  10:00 a.m.
  
David Gepner (Graduate Student, UIUC)
Constructible sheaves

  
CAS LEBURTON PRESENTATION/Center for Advanced Study,  Levis Faculty Center,  12:00 p.m.
  
Jean-Pierre Leburton (Department of Electrical & Computer Engineering, Associate at the Center for Advanced Study, 1999-2000)
Artificial Atoms and Molecules for Quantum Computing
NOTE: Location of talk 2nd Floor, Music Room, Levis Faculty Center, 919 West Illinois Street, Urbana. All Center for Advanced Study events are free and open to the public. For more information call 333-6729. Web information at http://www.cas.uiuc.edu.

  
Math 400 - Introduction to Graduate Mathematics,  245 Altgeld Hall,  4:00 p.m.
  
Robert Bauer (Assistant Professor, UIUC)
Random walk, Brownian motion, and the heat equation

  
VIGRE: Math 500,  243 Altgeld Hall,  4:00 p.m.
  
Lia Petracovici (Graduate Student, UIUC)
Non-accessible critical points of certain rational functions with Cremer points
  
Abstract: Let R be a rational function with a completely invariant (super)attracting Fatou component. We show that R has a non-accessible critical point in its Julia set, provided that R has a Cremer fixed point with the small cycles property. This extends Kiwi's result which states that the same is true for polynomials with Cremer fixed points.


TUESDAY, NOVEMBER 6

  
Symplectic and Contact Geometry RAP,  143 Henry Bldg,  10:00 a.m.
Speaker and Title to be Announced

  
Max Newman Topology,  345 Altgeld Hall,  11:00 a.m.
See listing on Thursday at 11:00 a.m.

  
RAP ``Spaces of non-positive curvature'',  243 Altgeld Hall,  11:00 a.m.
  
Peter Brinkmann (Doob Postdoc, UIUC)
Some topological applications of CAT(0) geometry

  
Probability and Statistics Seminar,  2 Illini Hall,  11:00 a.m.
Please see Joint Mathematics & Statistics Colloquium listed on Thursday at 4:00 p.m.

  
Several Complex Variables Seminar,  243 Altgeld Hall,  12:00 p.m.
  
Alexander Tumanov (Associate Professor,UIUC)
Complex curves in real manifolds

  
Quantum Information Science Seminar,  280 Materials Research Laboratory,  12:00 p.m.
  
Tony Leggett (Professor, UIUC, Dept. of Physics)
Flux states in rf SQUIDs as possible qubits
  
Abstract: A single-junction (``rf'') superconducting interference device (``SQUID'') threaded by a half-quantum of magnetic flux has two degenerate states which are macroscopically distinct (in the sense that e.g. the difference in magnetic moment is of the order of 1010 Bohr magnetons); quantum tunnelling splits the degeneracy, and the rate of such tunnelling can be controlled by external manipulation of the SQUID parameters. At first sight these two states are an implausible candidate for the basis of a qubit, since in view of their macroscopic distinctness one might think that any superosition would be decohered very rapidly by the environment; indeed, for many years there was considerable scepticism in the quantum measurement community that such a superposition (the original search for which was motivated by foundational rather than quantum-computing considerations) would ever be observable at all. However, two recent experiments have given strong evidence for the existence of the superposition state, albeit with a degree of decoherence (believed to arise principally from the external instrumentation needed to perform measurements on the system) which would need to be substantially reduced to make the system a practical qubit. If such a reduction can be attained, the macroscopic nature of the physical system (and the macroscopic difference of the two basis states) is expected to give substantial advantages in the context of practical quantum computation. References:

J.R.Friedman et al., Nature 406, 43 (2000) (evidence for superposition of SQUID states

C.H.van der Wal et al., Science 290, 773 (2000) ( " )

J.E.Mooij et al., Science 285, 1036 (application as qubit)

C.H.van der Wal, thesis, Delft 2001, ch.4 (borrowable for xeroxing from A.J.L.) (realistic consideration of possibility of reduction of decoherence).

  
Analytic and Elementary Number Theory,  243 Altgeld Hall,  1:00 p.m.
  
Alexandru Zaharescu (Assistant Professor, UIUC)
Heilbronn's Problem
  
Abstract: Heilbronn showed in 1948 that, given any real number a and any e > 0, there exist infinitely many integers n with ||an2|| £ n-1/2+e, where ||x || denotes the distance of x to the nearest integer. It is conjectured that the exponent 1/2 can be improved to 1, but it was only recently that the square root barrier had been broken. In this talk, we explain the ideas behind the work, present the history of the problem, and discuss some related problems.

  
Differential Geometry Seminar,  347 Altgeld Hall,  1:00 p.m.
No meeting this week

  
Logic Seminar,  241 Altgeld Hall,  1:00 p.m.
  
Carl Jockusch (Professor, UIUC)
Ramsey's Theorem and the Arithmetical Hierarchy
  
Abstract: Let [X]n denote the set of all n-element subsets of the set X . A form of Ramsey's Theorem asserts that for any infinite set X and any function f from [X]n to {0,1} there is an infinite subset Y of X which is ``homogeneous'' in the sense that f is constant on [Y]n. Effective versions of this result concern the case where X is the set of all natural numbers and the function f is computable. I will discuss where Y can be chosen to lie in the arithmetical hierarchy, with emphasis on the strong form where the infinite homogeneous set Y must be independent of the computable function f , modulo finite sets. This is recent joint work with Tamara Lakins and answers some questions we raised (for the case n > 2) and also (blush) refutes a previously published result of ours (for the case n = 2). These results shed some light on the extent to which the proof of Ramsey's Theorem can be made effective.

  
Geometric Potpourri Seminar,  243 Altgeld Hall,  2:00 p.m.
  
Richard L. Bishop (Emertius Professor, Department of Mathematics, UIUC)
Lipschitz approximations to K-convex functions
  
Abstract: A convex function on a geodesic metric space is one that is convex along every geodesic, as a function of arclength. A K-convex function is a generalization, for which the line supporting the graph from below at each point is replaced by the graph of a solution of the differential equation f¢¢+ Kf = 0, i.e., a sinusoid (if K > 0) or a hyperbolic function (if K < 0). If a K-convex function is Lipschitz continuous, then it has a well-defined differential at each point, but otherwise the directional derivative may depend on not only the direction but also on the geodesic chosen to represent the direction. Thus it becomes important in some applications to approximate a K-convex function by Lipschitz convex functions. We give examples of K-convex functions defined in terms of the distance function on a CAT(K) space. These examples generalize some known types of convex functions on CAT(0) spaces, e.g., the distance from a convex set and a Busemann function. The dual construction corresponding to the concavity of distance from the boundary of a space of nonnegative curvature is also considered.

The main theorem is that a K-convex function on a CAT(K) space (with some natural conditions when K > 0) is the limit of Lipschitz K-convex functions. The approximations stem from a convex set construction that is interesting even in the case of domains in Euclidean, hyperbolic, and spherical spaces.

This reports joint work with Stephanie B. Alexander.

  
Motivic Cohomology Seminar,  159 Altgeld Hall,  2:00 p.m.
  
Sung Myung (Graduate Student, UIUC)
The regulator map for motivic cohomology using the dilogarithm function

  
Stochastic and Nonlinear Analysis,  347 Altgeld Hall,  2:00 p.m.
  
Manual Portilheiro (University of Wisconsin, Madison)
Weak solutions for contractive equations and relaxation limits
  
Abstract: The notion of viscosity solution for Hamilton-Jacobi equations and fully nonlinear elliptic equations, and that of entropy solution for conservation laws can be related through a suitable abstraction. This generalization of ``entropy inequality'' can be used to push the method of ``perturbed test functions'' from Hamilton-Jacobi equations to conservation laws. This is very useful in studying certain relaxation limits.

  
RAP on Geometric Representation Theory,  345 Altgeld Hall,  2:30 p.m.
  
William Haboush, (Professor, UIUC)
Chapter 2 of Chriss and Ginzburg (cont.)

  
Commutative Ring Theory Seminar,  243 Altgeld Hall,  3:00 p.m.
No meeting today

  
Graph Theory and Combinatorics,  241 Altgeld Hall,  3:00 p.m.
  
Nikolai Kuzjurin (Inst. for System Programming, Russian Acad. Sci., Moscow)
Explicit constructions and derandomization techniques
  
Abstract: When we have a proof by the probabilistic method that some combinatorial structure exists, we can be interested in finding such a structure efficiently, that is, by a deterministic polynomial time algorithm. Intensive study in recent years led to the development of different techniques for derandomizing probabilistic existence proofs. In my talk I intend to give brief survey of these techniques and describe explicit construction of asymptotically good packings. The existence of such packings was proved by Rodl (1985) by the probabilistic method.

  
Study Seminar on Harmonic Analysis,  347 Altgeld Hall,  3:00 p.m.
  
Dr. Jorge Rivera-Noriega (Doob Postdoc, UIUC)
Harmonic analysis in locally flat domains, cont.
  
Abstract: We are studying the paper of C. Kenig and T. Toro on harmonic analysis in locally flat domains

  
RAP - Descriptive set theory and Rosenthal compacta,  241 Altgeld Hall,  4:00 p.m.
  
Dominika Polkowska (Graduate Student, UIUC)
The structure of Baire class 1 functions (cont.)


WEDNESDAY, NOVEMBER 7

  
RAP ``Etale cohomology",  159 Altgeld Hall,  10:00 a.m.
  
David Gepner (Graduate Student, UIUC)
Constructible sheaves (cont.)

  
RAP on Quantum Cohomology,  160 English Bldg,  3:00 p.m.
  
Xinyun Zhu (Graduate Student, UIUC)
Continuing Chapter 5 and beginning Chapter 6

  
Nonstandard Analysis Seminar,  243 Altgeld Hall,  4:00 p.m.
  
Yevgeniy Gordon (Professor, Eastern Illinois University)
On approximations of locally compact groups by finite quasigroups, V

  
RAP - Conformal invariance, intersection exponents and critical percolation,  145 Altgeld Hall,  4:00 p.m.
  
Robert Bauer (Assistant Professor, UIUC)
Universality for conformally invariant intersection exponents I

  
Information Protection Seminar,  114 Coordinated Science Lab,  4:30 p.m.
  
Jonathan Webster (Graduate Student, UIUC)
Efficient Linear Algebra
  
Abstract: We will discuss various methods of solving the linear system of equations Ax = b, where A is a large non-symmetric sparse matrix over a finite field. Such matrices arise in sub-exponential algorithms for integer factorization and discrete logarithm problems. A comparison will be made between traditional methods and improvements made for this particular problem.


THURSDAY, NOVEMBER 8

  
Max Newman Topology,  345 Altgeld Hall,  11:00 a.m.
  
Amnon Neeman (Professor, Australian National University, Canberra, Australia)
The non-commutative analog of lifting a vector bundle from an open subscheme

  
Math - Physics (BCDE) Lunch Seminar,  6-110 Engineering Science Bldg,  12:05 p.m.
  
Albion Lawrence (SLAC)
D-Branes on Calabi-Yau Threefolds and Derived Categories
  
Abstract: String theory models with minimal supersymmetry are useful both because they are models for supersymmetric phenomenology and because `stringy' geometry comes into its own in such backgrounds. We will discuss the construction of such models using D-brane defects in Calabi-Yau backgrounds, highlighting their description as objects in the derived category of coherent sheaves. We will discuss how string theory generalizes geometry in these examples.

  
Several Complex Variables Seminar,  243 Altgeld Hall,  12:00 p.m.
  
Bernhard Lamel (Doob Postdoc, UIUC)
Compactness for the d-bar Neumann Problem

  
Analytic and Elementary Number Theory,  243 Altgeld Hall,  1:00 p.m.
  
Kevin O'Bryant (Graduate Student, UIUC)
Algebraic Properties of a Combinatorial Object from the Analytic Theory of Diophantine Approximation
  
Abstract: For each irrational a and positive integer n, there is a unique permutation p such that 0 < { p(1) a} < { p(2) a} < ¼ < { p(n) a} < 1. This permutation is a combinatorial object: there is no apparent reason to multiply two of these permutations. Nevertheless, I will show that these permutations do have an algebraic structure which is important in the study of low-complexity 0-1 sequences. This motivates many conjectures and even a few results concerning the sign and order of the permutation as a function of a and n.

  
Group Theory,  347 Altgeld Hall,  1:00 p.m.
  
Ilya Kapovich (Assistant Professor, UIUC)
Foldings and graphs of groups, II
  
Abstract: We will describe a geometric algorithm for obtaining induced subgroup splittings and solving the membership problem for amalgamated free products, HNN-extensions and fundamental groups of general graphs of groups. Other applications include proving generalizations of Grushko's theorem and obtaining some coherence results.

  
RAP on Noncommutative Lp spaces,  345 Altgeld Hall,  1:00 p.m. (cont. at 3:00 p.m.)
  
Michael Marsalli (Professor, Illinois State University)
The Dual of Noncommutative H1
  
Abstract: Let \Cal M be a von Neumann algebra with a faithful normal trace t, and let H¥ be a finite subdiagonal subalgebra of \Cal M. We define a Hilbert transform relative to H¥, and we show that this transform is bounded on Lp(\Cal M) for 1 < p < ¥. Let H1 be the closure of H¥ in Lp(\Cal M). By analyzing the Hilbert transform on L1(\Cal M), we can identify the dual space of H1 as a concrete space of operators.

  
Algebraic Geometry Seminar,  347 Altgeld Hall,  2:00 p.m.
  
Michael Thaddeus (Columbia University and the Institute for Advanced Study)
The Higgs bundles and mirror symmetry
  
Algebraic Number Theory,  241 Altgeld Hall,  2:00 p.m.
  
Leon McCulloh (Professor, UIUC)
Galois module structure of abelian extensions}
  
Abstract: I describe the main ingedients needed to determine the realizable Galois module classes of rings of integers in extensions of a number field with abelian Galois group G: Kumer theory of G-extensions, resolvends, Stickelberger map, class group Cl(OKG)$ "Rag" map.

  
Analysis Seminar,  243 Altgeld Hall,  2:00 p.m.
  
Alexander Kisilev (University of Chicago)
Scattering for Schrödinger operators with long-range potentials
  
Abstract: We prove WKB-type asymptotics of solutions and existence of modified wave operators for one-dimensional Schrödinger operators with potential in Lp(reals), p < 2. If in addition the potential is conditionally integrable, then the usual Möller wave operators exist. All previous results in this class required strong additional assumptions on the potential. The results are close to optimal in a sense that there are examples of potentials in Çp > 2 Lp for which the spectrum is purely singular and hence no wave operators can exist. The methods involve application of Fourier analysis to study asymptotic behavior of eigenfunctions. In particular we prove new results on almost everywhere convergence of certain oscillatory multilinear operators. The p = 2 case remains open and appears to be linked to a nontrivial generalization of Carleson's a.e. convergence theorem.

  
Knot Theory RAP,  345 Altgeld Hall,  2:00 p.m.
  
George Francis (Professor, UIUC)
The Anatomy of the Figure-8 Knot Complement
  
Abstract: I will describe visually intuitive ways of looking at knot-complements, their hyperbolic structure (when they have one), their foliation by Seifert surfaces and their monodromy. The figure-eight knot is our protagonist in this topological opera. Though most of the ideas are Thurston's, their pictures are most revealing.

  
Special Seminar,  347 Altgeld Hall,  2:00 p.m.
  
Michael Thaddeus (Columbia University and the Institute for Advanced Study)
The Higgs bundles and mirror symmetry
  
Commutative Ring Theory Seminar,  243 Altgeld Hall,  3:00 p.m.
  
Hans-Bjorn Foxby (Professor, University of Copenhagen, Denmark)
Depth and amplitude of complexes
  
Abstract: The depth of a finitely generated module M over a local ring (R,m,k) can be calculated by several methods: in terms of length of M-regular sequences in m, vanishing of Ext(k,M), vanishing of local cohomology Hm(M), or vanishing of H(M tensor K) for a Koszul complex K for a set of generators for m. The last three methods yield also the depth of non-finite modules - or even complexes with bounded homology. The talk discusses these methods for complexes with non-bounded homology, amplitude inequalities for such complexes, and an application concerning flat dimensions of modules. This is joint work with stralian National University, Canberra, ACT 0200, Australia Srikanth Iyengar.

  
RAP on Research Problems in Coloring Theory and Extremal Combinatorics,  241 Altgeld Hall,  3:00 p.m.
Research Problems in Combinatorics

  
Joint Mathematics & Statistics Colloquium,  245 Altgeld Hall,  4:00 p.m.
  
Walter Philipp (Professor Emeritus, Departments of Mathematics and Statistics, UIUC)
Spooky action at a distance, time correlated hidden parameters and the theorem of Bell
  
Abstract: This is joint work with Karl Hess, Beckman Institute, UIUC. In a 1935 paper Einstein, Podolsky and Rosen put forward a Gedanken experiment challenging the completeness of quantum theory and suggesting the existence of hidden parameters. In 1964 John Bell proved his famous inequalities derived from a mathematical model that show that such hidden parameters cannot exist. We analyze the assumptions of this model and show that possible time dependencies have not been handled satisfactorily. We find that the introduction of time-like correlated random parameters permits the construction of a more general mathematical model which, in contrast to Bell's inequality, does not contradict the result for the spin pair correlation predicted by quantum theory. The construction uses basic facts from the theory of B-splines and from weak convergence of probability measures.
Refreshments at 3:15 p.m. in Room 321 Altgeld Hall


FRIDAY, NOVEMBER 9

  
RAP ``Etale cohomology",  159 Altgeld Hall,  10:00 a.m.
  
David Gepner (Graduate Student, UIUC)
Constructible sheaves (cont.)

  
RAP - Conformal invariance, intersection exponents and critical percolation,  145 Altgeld Hall,  4:00 p.m.
  
Robert Bauer (Assistant Professor, UIUC)
Universality for conformally invariant intersection exponents

  
Model Theory Seminar,  141 Altgeld Hall,  4:00 p.m.
  
James Tyne (Graduate Student, UIUC)
Valuation and Residue Properties for power bounded theories
  
Abstract: Suppose that R is a model of some extension of RCF, and that Ráañ is an elementary extension of R, and that these models are equipped with valuations, v,w. The Valuation Property asserts that if the value groups are different, then there is r in R such that w(a-r) is not in the value froup of R. The Residue Property asserts that if the residue fields are different, then there are c,d in R such that ca-d witnesses this difference. I will define these terms, state these properties more precisely, and show that these properties hold for o-minimal power bounded theories.

File translated from TEX by TTH, version 2.01.
On 2 Nov 2001, 14:30.