Weekly Calendar

October 15-19, 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, OCTOBER 15

  
RAP ``Etale cohomology'',  159 Altgeld Hall,  10:00 a.m.
  
David Gepner (Graduate Student, UIUC)
Cech cohomology for Grothendieck topologies

  
Math 400 - Introduction to Graduate Mathematics,  245 Altgeld Hall,  4:00 p.m.
  
Bob Jerrard (Associate Professor, UIUC)
How to Solve Nonlinear Partial Differential Equations

  
Special Applied Math Seminar,  241 Altgeld Hall,  4:00 p.m.
  
N.G. Hatcher, L.S. Yafremava (R. Gillette lab, Department of Molecular and Integrative Physiology, Program in Biophysics and Computational Biology)
Modeling the dynamics of intracellular processes: diffusion, enzyme kinetics and neuromodulation
  
Abstract: Neurons encode information in the nervous system through rapidly changing electrical potentials that propagate across the cell membranes. These voltage potentials are determined by channel proteins within the membrane that open and close like gates regulating ionic currents. We model the action of an ion channel that gates a Na+ current when bound to the intracellular signal molecule, cyclic Adenosine Monophosphate (cAMP). In this model, cAMP released from a point source in the center of the cell diffuses to the membrane while being degraded by the enzyme phosphodiesterase. To describe kinetics of this process, we solve conventional diffusion equation in spherical coordinates. The results of this model allow the determination of cAMP concentration at the membrane, the kinetics of phosphodiesterase, and the kinetics of the cAMP gated current in vivo.


TUESDAY, OCTOBER 16

  
Symplectic and Contact Geometry RAP,  143 Henry Bldg,  10:00 a.m.
  
Susan Tolman (Associate Professor, UIUC)
Maslov index for dummies, II

  
Max Newman Topology,  345 Altgeld Hall,  11:00 a.m.
  
Vahagn Minasian (Graduate Student, UIUC)
Thesis preview on functional equations and operads

  
RAP ``Spaces of non-positive curvature'',  243 Altgeld Hall,  11:00 a.m.
  
Brad Edge (Graduate Student, UIUC)
Classification of isometries of CAT(0) spaces (cont.)
  
Abstract: We will present the classification of isometries of CAT(0) spaces as either elliptic, parabolic or hyperbolic. Specific geometric and algebraic properties of hyperbolic isometries will be discussed.

  
Probability and Statistics Seminar,  2 Illini Hall,  11:00 a.m.
See listing on Thursday at 11:00 a.m.

  
Several Complex Variables Seminar,  243 Altgeld Hall,  12:00 p.m.
  
John D'Angelo (Professor, UIUC)
Commutative Algebra and the Cauchy-Riemann Equations

  
Quantum Information Science Seminar,  280 Materials Research Laboratory,  12:00 p.m.
No meeting this week

  
Analytic and Elementary Number Theory,  243 Altgeld Hall,  1:00 p.m.
  
Professor Harold Diamond (UIUC)
A survey of elementary methods in prime number theory
  
Abstract: One of the major milestones in the history of number theory is the elementary proof of the Prime Number Theorem (PNT) obtained by Selberg and Erdos in the late 1940s. Before then, it had been generally believed that the PNT could not be proved without using analytic tools, for among other reasons, the nonvanishing of the Riemann zeta function at all points 1+it in the complex plane is in some sense equivalent to the PNT. The methods of Selberg and Erdos have since been refined to give elementary proofs of other versions of the PNT (error terms, primes in arithmetic progressions, etc). These results, however, are still considerably weaker than what can be proved using analytic tools. Also, other elementary approaches to the PNT have been found, though none is really easy! In this talk we discuss the ideas underlying these methods, and survey some of the progress that has occurred in the past 50 years.

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

  
Logic Seminar,  241 Altgeld Hall,  1:00 p.m.
  
Slawomir Solecki (Associate Professor, UIUC)
Embedding E1 in the coset equivalence relation (cont.)
  
Abstract: Let G be a Polish group and let H be its analytic subgroup. I will talk about the relationship between the complexity (in the sense of Borel reducibility) of the coset equivalence relation G/H and the existence of a Polish group topology on H preserving the Borel structure of H. In the first talk, I will present the context of the problem and some background material. Later on I plan to present a general theorem on embedding the equivalence relation E1 into G/H including some details of its proof.

  
Geometric Potpourri Seminar,  243 Altgeld Hall,  2:00 p.m.
  
Professor Vince Matsko (Quincy University)
Teaching a Course on Polyhedra
  
Abstract: Developing a three-dimensional intuition is important in many disciplines. Chemists, architects, computer engineers, physicists, and mathematicians, to name a few, rely on three-dimensional geometry. However, many students choosing majors in college are ill-prepared in this regard. In many cases, their exposure to three-dimensional geometry has been minimal. When they have had modules in geometry, often the teacher was just one step ahead of them.

To address the needs of such students, a course was developed five years ago at Quincy University. This course, _Higher Geometry_, was designed to give students a solid introduction to the geometry of polyhedra. The only prerequisite for the course is a working knowledge of plane trigonometry. With this background, basic concepts in spherical trigonometry are introduced. Dihedral angles of polyhedra are calculated, as are data for constructing geodesic models.

Essential to the success of the course is having students build three-dimensional models. With each topic, one lecture presentation is supplemented with one hands-on laboratory class. Students benefit greatly from such a course design.

Here, an outline of the course and teaching methodologies will be presented. Sample problems and construction projects will be described. Suggestions for instructors interested in developing such a course will be provided.

  
Stochastic and Nonlinear Analysis,  347 Altgeld Hall,  2:00 p.m.
  
A. Wilkinson (Northwestern University)
Exponents, entropy, and partial hyperbolicity

  
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.
  
Sandra Spiroff (Graduate Student, UIUC)
Limiting Behavior on Restriction of Divisor Classes to Hypersurfaces

  
Graph Theory and Combinatorics,  241 Altgeld Hall,  3:00 p.m.
  
Nikolai Kuzjurin (Institute for System Programming Russian Academy of Sciences, Moscow)
On the number of partial Steiner systems
  
Abstract: A partial Steiner system is a family F of k-subsets of an n-element set such that each l-subset of the n-set is contained in at most one k-subset belonging to F. Let N(l,k,n) be the number of such partial Steiner systems. We give a short probabilistic proof of the following result: If l and k are fixed, with l < k, then N(l,k,n) = n(1-o(1))(k-l)nl/(k)l, where n tends to infinity and (k)l = k(k-1)...(k-l+1).


  
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)
Borel and Baire class 1 functions


Mathematics Colloquium,  245 Altgeld Hall,  4:00 p.m.
  
Professor Yu.G. Reshetnyak (Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences)
On the conformal representation of alexandrov surfaces
  
Abstract: We consider two-dimensional manifolds of bounded curvature. The theory of two-dimensional manifolds of bounded curvature can be viewed as general Alexandrov's surface theory. A metric space (M,r) is called a two-dimensional manifold of bounded curvature if (M,r) is homeomorphic to a two-dimensional manifold; the metric r is intrinsic: for every pair of points X,Y Î M, the distance r(X,Y) is the greatest lower bound of lengths of curves joining X to Y and, for every point P Î M, there is a sequence of Riemannian metrics (rn)n Î \bold N which are defined in a neighborhood U of the point P and such that the functions rn converge uniformly to rU = r|U on the set U×U and the sequence (|wn|(U))n Î \bold N is bounded, where |wn|(U) = \iintUKnd Sn, here Kn is the Gaussian curvature of the Riemannian metric rn and dSn is the area element. In particular, metrics of bounded curvature include polyhedral metrics. The main result states

Let M be a two-dimensional manifold of bounded curvature. Then every point X Î M has a neighborhood U such that the metric of the manifold in this neighborhood can be given by a linear element of the form

ds2 = l( x,y) ( dx2+dy2)
where the function logl(x,y) is the difference of two subharmonic functions. The converse is also true: if, locally, the metric r on a two-dimensional manifold M is given by ds2 = l(x,y) (dx2+dy2), and logl(x,y) is the difference of two subharmonic functions, then M is a two-dimensional manifold of bounded curvature.

The coordinates in which the linear element is given by ds2 = l(dx2+dy2) are called isothermal. We intend to give some applications of general isothermal coordinates in geometry and complex analysis.

Refreshments at 3:15 p.m. in Room 321 Altgeld Hall
WEDNESDAY, OCTOBER 17

  
RAP ``Etale cohomology",  159 Altgeld Hall,  10:00 a.m.
  
David Gepner (Graduate Student, UIUC)
Comparing Cech and etale cohomology

  
RAP on Quantum Cohomology,  160 English Bldg,  3:00 p.m.
  
Yong Fu (Graduate Student, UIUC)
``Notes on stable maps and quantum cohomology'' by Fulton and Pandharipande, Chapters 2-4

  
RAP - Conformal invariance, intersection exponents and critical percolation,  145 Altgeld Hall,  4:00 p.m.
  
Robert Bauer (Assistant Professor, UIUC)
Symmetries and ``cascade'' relations for Brownian intersection exponents I

  
Information Protection Seminar,  114 CSL,  4:30 p.m.
  
Jonathan Sorenson (Butler University)
Algorithms for Computing the Greatest Common Divisor
  
Abstract: The problem of computing the greatest common divisor (GCD) of two integers has been of great interest to number theorists since ancient times. Today, we use GCD algorithms in applications such as integer factoring, primality testing, symbolic computation, and cryptography. In this talk I will review what is known about computing integer GCDs, and give an in-depth presentation of the k-ary GCD algorithm, a generalization of the binary algorithm which was published about ten years ago. I will also discuss some empirical timing results comparing several practical GCD algorithms, and finish with an overview of recent results, work in progress, and open problems.

  
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, III



THURSDAY, OCTOBER 18

  
Probability and Statistics Seminar,  2 Illini Hall,  11:00 a.m.
  
Professor Zongwu Cai (Department of Mathematics, University of North Carolina, Charlotte, North Carolina)
Flexible Seasonal Financial Time Series Models
  
Abstract: In this study, we propose a new class of flexible seasonal time series models that consists of a common trend function over the periods and additive individual trend (seasonal effect) functions that are specific to each season with the periods. Those individual trend functions can be either fixed or random. We also extend the models to functional-coefficient seasonal time series models to include the exogenous variables. Local linear techniques are used to estimate the trend and seasonal effect functions and a new bandwidth selector based on a combination of generalized cross-validation and empirical bias method is used. The consistency of the proposed estimators is obtained without any specification of the error distribution, the asymptotic normality of the proposed estimators is established under the strong mixing conditions, and a consistent estimator of the asymptotic variance is provided. The proposed methodologies are illustrated by three economic and financial time series, which exhibit extreme nonlinear and non-stationary behavior. This is joint work with Rong Chen, Department of Information and Decision Sciences, College of Business Administration, The University of Illinois at Chicago, Chicago, Illinois.

  
Math - Physics (BCDE) Lunch Seminar,  6-110 Engineering Science Bldg,  12:05 p.m.
  
Eric Zaslow (Assistant Professor, Northwestern University)
A Mirror "Theorem" for Open-String Gromov-Witten Invariants
  
Abstract: The mirror correspondence between a Lagrangian submanifold a its dual holomorphic submanifold leads to predictions of Gromov-Witten invariants involving holmorphic maps from discs, where the boundary gets mapped to the Lagrangian. Localization calculations describe these open-string Gromov-Witten invariants in terms of related closed-string (ordinary) equivariant Gromov-Witten invariants, where an equivariant mirror theorem exists. We show, then, that the physical predictions hold. At higher genera, no physical predictions apply, though calculations verify a strict integrality check of the open-string invariants.

  
Several Complex Variables Seminar,  243 Altgeld Hall,  12:00 p.m.
  
John D'Angelo (Professor, UIUC)
Commutative Algebra and the Cauchy-Riemann Equations, II

  
Analytic and Elementary Number Theory,  243 Altgeld Hall,  1:00 p.m.
  
Professor Heini Halberstam (Emeritus Professor, UIUC)
The Erdos-Fuchs theorem (expository talk)
  
Abstract: It is well-known that the number Q(N) = |{(m,n): m2+n2 £ N}| of lattice points in a circular disk centered at the origin and of radius N1/2 is appproximated by pN. G.H. Hardy showed in 1915 that there is a limit to this approximation: there exist arbitrarily large values of N for which the difference |Q(N)-pN| is of order at least (N log N)1/4. His proof was difficult and depended heavily on arithmetical properties of the sequence of squares. It came as a surprise when, in 1956, Erdös and Fuchs demonstrated that Hardy's result is essentially a special case of a general law of the following nature: If {an} is any sequence of nonnegative integers such that, for some c > 0, A(N) = |{(am,an): am+an £ N}| is approximated by cN, then A(N)-cN = o(N1/4(logN)-1/2) cannot hold. Moreover, their proof was elegant and transparent.

  
Group Theory,  347 Altgeld Hall,  1:00 p.m.
  
Ilya Kapovitch Assistant Professor, UIUC)
Foldings and graphs of groups
  
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.)
No meeting this week

  
Algebraic Geometry Seminar,  159 Altgeld Hall,  2:00 p.m.
  
Ezra Getzler (Professor, Northwestern University)
The Equivariant Toda Conjecture
  
Abstract: We state and prove a conjecture (found in joint work with R. Pandharipande, and generalizing a conjecture of Eguchi and Yang) for the S1-equivariant Gromov-Witten invariants of CP1 in genus 0. We discuss possible generalizations to higher genera.

  
Algebraic Number Theory,  241 Altgeld Hall,  2:00 p.m.
  
Leon McCulloh (Professor, UIUC)
Relative module structure of rings of integers I
  
Abstract: The first of two lectures on the module structure of rings of integers related to questions about the existence of relative integral or normal integral bases in bases in finite extensions of number fields.

  
Analysis Seminar,  243 Altgeld Hall,  2:00 p.m.
  
Richard S. Laugesen (Associate Professor, UIUC)
A new characterization of wavelets
  
Abstract: A wavelet is a square-integrable function whose system of translates and dilates is an orthonormal basis for L2. There are two issues here: the orthonormality of the system, and its completeness. I will show with the aid of almost periodic functions that if one assumes orthonormality, then completeness of the system is equivalent to a simple ``Calderon condition'' on the Fourier transform of the wavelet.

  
Knot Theory RAP,  345 Altgeld Hall,  2:00 p.m.
  
Elizabeth Denne (Graduate Student, UIUC)
Torus knots, II
  
Abstract: This talk will discuss presentations of knot groups, beginning with Rolfsen's approach to the fundamental group of the complement of a torus knot and ending with Wirtinger presentations.

  
Commutative Ring Theory Seminar,  243 Altgeld Hall,  3:00 p.m.
  
Sandra Spiroff (Graduate Student, UIUC)
Limiting Behavior on Restriction of Divisor Classes to Hypersurfaces, (cont.)

  
Decision, Control and Optimization Seminar,  B02 CSL,  3:00 p.m.
  
Prof. Ioannis Kontoyiannis (Brown University, Division of Applied Mathematics and Department of Computer Science, Providence, RI)
On the Role of Memory in Data Compression
  
Abstract: We consider the problem of lossy data compression and examine the role played by memory: For data generated by a memoryless source, we ask in what way (if any) the absence of memory in the data can be used to simplify the task of compression. First we briefly review three classical problems of data compression in this light: Shannon's rate-distortion problem, Marton's error-exponents question, and the Neuhoff-Gilbert rate-distortion problem for zero-delay codes. Then we turn to our main question of interest, that of characterizing the best achievable error-exponents performance of *zero-delay* codes with finite memory. In a number of different scenarios (fixed-rate, fixed-distortion, and fixed-slope), we show that optimal performance can be achieved by time-sharing (at most two) entropy-coded scalar quantizers. We also give single-letter expressions for the best achievable error exponents.

This is joint work with Neri Merhav, Technion, Israel.

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

  


FRIDAY, OCTOBER 19

  
RAP ``Etale cohomology",  159 Altgeld Hall,  10:00 a.m.
  
Bin Wang (Graduate Student, UIUC)
Comparing cohomology on different sites

  
RAP - Conformal invariance, intersection exponents and critical percolation,  145 Altgeld Hall,  4:00 p.m.
  
Robert Bauer (Assistant Professor, UIUC)
Symmetries and ``cascade'' relations for Brownian intersection exponents II

  
Model Theory Seminar,  141 Altgeld Hall,  4:00 p.m.
  
James Tyne (Graduate Student, UIUC)
titleValuation and Residue Properties for power bounded theories
  
Abstract: Suppose that R is a model of some extension of RCF, and that R < a > 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 Î 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 Î 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 power bounded theories.

Special Analysis and Probaility seminar,  345 Altgeld Hall,  4:00 p.m.
Conformal invariance of critical percolation
  
Stanislav Smirnov (KTH & KVA, Stockholm)
  
Abstract: Percolation is perhaps the simplest model in statistical mechanics, which exhibits an interesting phase transition. For a lattice one colors vertices or edges independently black with probability p and white with probability (1-p), and then studies properties of ''clusters" - connected black subgraphs. It is known that there is a (lattice-dependent) parameter pc such that there exists a ''fat infinite cluster" if p > pc and there are ''only small clusters" if p < pc. Critical percolation (i.e. when p: = pc) is especially interesting, e.g. it is conjectured to be conformally invariant in the scaling limit (as mesh of the lattice tends to zero), which allowed physicists to predict many of its properties. We will discuss recent progress in mathematical understanding of critical percolation and related processes.

File translated from TEX by TTH, version 2.01.
On 12 Oct 2001, 15:49.