TUESDAY, JANUARY 30
- 345 Altgeld Hall, 11:00 a.m.
- MAX NEWMAN TOPOLOGY
- Tony Bedenikovic
- Two-Complexes as Graph Complement Cone Complexes
- Abstract: We define a graph complement cone complex (i.e., a gccc) to be a
3-complex which is the union of a graph complement in a cube with handles
and the cone over the boundary of the cube with handles. We
show that every finite 2-complex 3-deforms to a gccc and list some
consequences of this fact.
- 2 Illini Hall, 11:00 a.m.
- PROBABILITY AND STATISTICS SEMINAR
- Chengcheng Hu, Department of Biostatistics, University of Washington
- Cox Regression with Mismeasured or Missing Covariates
- Abstract: This talk deals with the estimation of the Cox proportional hazards model when covariates are measured with error or missing. For the measurement error problem, the classical additive measurement error model is considered, as well as a more general model which represents the mismeasured version of the covariate as an arbitrary linear function of the true covariates plus a random noise. No distributional form is imposed on the covariates or the error. Assuming that the covariates are measured precisely for a validation set, we develop consistent and asymptotically normal estimators for the regression parameters and the cumulative baseline hazard function. Simulation studies indicate that the proposed estimators work well for practical sample sizes, and a real example is provided. The method is also adapted to the situation when only replicate measurements are available for the covariates, instead of a validation set. A similar approach is taken to study the Cox model with missing covariates. Imputed covariates are used and a class of modified partial likelihood score functions are proposed to correct the bias in the ordinary imputation approach. The resulting estimators are shown to be consistent and asymptotically normal.
Note: If you are interested in meeting Chengcheng Hu on Monday, January 29 and Tuesday (morning only), January 30, please contact Usha Dhar at u-dhar.edu or call 244-7192 to set up a time.
- 243 Altgeld Hall, 12:00 p.m.
- SEVERAL COMPLEX VARIABLES SEMINAR
- Professor Sanghyun Cho, Sogang University, visiting UIUC
- Sobolev Estimates for d-bar
- 241 Altgeld Hall, 1:00 p.m.
- ANALYTIC NUMBER THEORY SEMINAR
- Mike Bennett, UIUC
- to be announced
- 243 Altgeld Hall, 1:00 p.m.
- LOGIC SEMINAR
- Anand Pillay, Department of Mathematics, UIUC
- A Compact Complex Manifold with the DOP
- Abstract:I point out that a certain (three-dimensional) compact complex manifold X, produced some years ago by Lieberman and studied further by Campana, has certain "bad" model-theoretic properties when viewed naturally as a first order structure. Specifically the theory of X has Morley rank 3 but U-rank 2, and also has the DOP (Shelah's dimensional order property). X is a certain family of abelian varieties and I also point out that the "generic fibre" is not Kahler (in a sense that can be made precise).
- 345 Altgeld Hall, 2:00 p.m.
- SPACES ON NON-POSITIVE CURVATURE RAP
- Professor Richard Bishop
- Organizational meeting
- 159 Altgeld Hall, 3:00 p.m.
- COMMUTATIVE RING THEORY RAP
- Professor Sean Sather-Wagstaff, Department of Mathematics, UIUC
- The Homological Conjectures, cont.
- 241 Altgeld Hall, 3:00 p.m.
- GEOMETRIC POTPOURRI SEMINAR
- Dr. Marcin Mazur, Department of Mathematics, UIUC
- Circular triples
- Abstract: In the geometry of a triangle an important topic is an investigation of distinguished triples of points, each on a
different side of a triangle, e.g. midpoints of sides, feet of altitudes, ... . I will introduce a new such triple, called
circular, which can be characterized by the following property:
points P, Q, R on sides AB, BC, CA form a circular triple
iff the quadrilaterals APQR, BQRP, CRPQ are circumscribed. I will explain how I discovered such triples, sketch a proof (not
quite elementary) that every triangle possesses exactly one circular triple, and provide some nice properties of circular triples.
- 345 Altgeld Hall, 3:00 p.m.
- GRAPH THEORY AND COMBINATORICS
- Jeong-Hyun Kang
- Packing and covering triangles in graphs
- Abstract: Let n(G) be the maximum size of a set of pairwise
edge-disjoint triangles
of G, and let t(G) be the minimum size of an edge-covering of the
triangles of G. We want to bound t(G) in terms of n(G).
Trivially, n(G) £ t(G) £ 3n(G).
The graphs K4 and K5 show that t(G) can be as large as 2n(G).
In 1981, Tuza conjectured that 2n(G) is an upper bound for t(G).
He proved conjecture for planar graphs, K5-free chordal graphs, and graphs
with n vertices and at least 7n2/16 edges. Krivelevich proved that graphs
without subdivisions of K3,3 satisfy the conjecture, improving on planar
graphs. Tuza also showed that t(G) £ 7n(G)/3 when G is tripartite,
and Haxell and Kohayakawa improved this bound to t(G) £ (2-e)n(G)
for a small positive constant e.
In this seminar, we will show that t(G) < (3-e)n(G) for an
e that is at least 3/23. Thus t(G) < 2.8696n(G). This is the
first nontrivial upper bound for general graphs, shown by Haxell in 1999.
- 141 CSRL, 3:30 p.m.
- TOPICS IN SYSTEMS SEMINAR
- Professor Karl J. Åstöm, Department of Automatic
Control, Lund Institute of Technology, Lund, Sweden
- Modeling of Physical Systems
- Abstract: Modeling and simulation have experienced an amazing development since its beginning in the 1920s. At that time, the technology was available only at
a handful of university groups. Today it is available on the desks of all
engineers. The talk presents the current status of modeling and simulation.
It draws on the historical perspective to explain how the field has
developed. Particular emphasis is given to shifts in technology and
paradigms. Even if the technology of modeling has advanced considerably the
standard tools used today are very similar to the ones used 40 years ago.
Recently there has been several attempts to develop methodologies that are
much more appropriate for modeling of complex technical systems. These
methodologies draw from object oriented methodology in computer science,
differential algebraic equations in numerical mathematics, and control
theory. The tools Dymola, Omola, Omsim and Modelica which all have their
origins in Lund are discussed. An example of modeling of a thermal boiler
is used for illustration.
- 245 Altgeld Hall, 4:00 p.m.
- SPECIAL SEMINAR
- Moxun Tang, University of Minnesota
- Turing patterns in the CIMAS reaction diffusion system
- Abstract: In one of the most important papers in theoretical biology
of last century, Turing predicted in 1952 that chemicals
can react and diffuse in such a way as to
destabilize a homogeneous stationary state, and result in
inhomogeneous spatial patterns. He suggested that this mechanism
could play a major role in biological pattern formation.
In spite of significant efforts devoted to studies of
his theory, the first experimental evidence for Turing structures
was only observed in 1990 by De Kepper and coworkers in the
chlorite-iodide-malonic acid-starch (CIMAS) reaction.
In this talk I will describe some fundamental properties
of Turing patterns, through our mathematical analysis for
the Lengyel-Epstein model, a two-variable reaction diffusion
system which captures the crucial feature of the CIMAS reaction.
Several analytic results concerning the global dynamics of this
system, especially our theorem showing existence of
various Turing patterns observed in the laboratory and in
computer simulations, will also be presented.
Refreshments at 3:15 pm in Room 321 Altgeld Hall.
WEDNESDAY, JANUARY 31
- B02 CSRL, 3:00 p.m.
- DECISION, CONTROL AND OPTIMIZATION SEMINAR
- Jerawan Chudoung, Department of General Engineering, UIUC
- Robust Control for Nonlinear Switched Systems
- Abstract: In this talk we discuss results in robust control theory for
nonlinear switched systems. By a switched system, we mean a dynamical system where
the system dynamic changes abruptly in response to a control command,
usually with an associated cost. Such a system exhibits a ``hybrid" feature
involving both continuous and discrete aspects. Many real world problems
can be formulated as switched control systems, for example traffic control,
satellite control and a manual transmission system on a car. When one
applies the ``standard" robust control theory to a switched system,
typically the result is a control law presenting a ``chattering" phenomena.
To avoid this phenomena, we formulate a robust control problem for a
general nonlinear system with finitely many admissible controls and with
positive cost assigned to switching of controls. We formulate the problem
both in an L2-gain/kissipative system framework and in a game-theoretic
framework. We show that the control strategy achieving the dissipative
inequality is obtained by solving the system of quaivariational
inequalities in the viscosity sense; in fact this solution is also used to
address stability analysis of the switched system.
NOTE: Coffee and cookies at 2:40 p.m. before the seminar in Room 154 CSRL.
- 114 CSRL, 4:30 p.m.
- INFORMATION PROTECTION SEMINAR
- Professor Nigel Boston, Department of Mathematics, UIUC
- A mathematical foundation for watermarking.
- Abstract: Digital watermarking for copyright protection has attained
great importance recently but many of the methods used are ad hoc.
Moulin has shown in work with O'Sullivan that the information-theoretic
notion of capacity carries over nicely from coding theory. In this talk
mathematical axioms for a theory of watermarking are developed in
analogy to algebraic coding theory.
- 245 Altgeld Hall, 4:00 p.m.
- SPECIAL SEMINAR
- Ilia Binder, Harvard University
- Harmonic measure and polynomial Julia sets
- Abstract: We discuss the multifractal analysis of planar harmonic measure. We
are especially concerned with sharp bounds for the local dimension of
harmonic measure-so called universal spectra. The theory is well
established for simply connected domains, since in this case the
technique of conformal mappings can be applied.
It is conjectured that the universal spectra for the non simply
connected domains are the same as for the simply connected ones. We
will discuss the proof of the conjecture for a particular class of
planar domains, the basins of attraction to infinity of polynomials. The proof uses holomorphic motion in the dynamical Teichmüller space.
Refreshments at 3:15 pm in Room 321 Altgeld Hall.
THURSDAY, FEBRUARY 1
- ESB 6.110, 12:00 p.m.
- MATH - PHYSICS (BCDE) LUNCH SEMINAR
- Professor Matthew Ando, Department of Mathematics, UIUC
- The Witten genus and equivariant elliptic cohomology
- 241 Altgeld Hall, 1:00 p.m.
- ANALYTIC NUMBER THEORY SEMINAR
- Professor Walter Philipp, UIUC
- Metric Theorems for Distribution Measures of Pseudorandom Sequences
- 347 Altgeld Hall, 1:00 p.m.
- GROUP THEORY SEMINAR
- Professor Ilya Kapovitch, Department of Mathematics, UIUC
- Boundaries of Hyperbolic Groups, continued
- 243 Altgeld Hall, 2:00 p.m.
- ALGEBRAIC NUMBER THEORY
- Mr. Soroosh Yazdani
- Nevanlinna theory and the abc-conjecture
- 347 Altgeld Hall, 2:00 p.m.
- ANALYSIS SEMINAR
- Professor Robert Kaufman, Department of Mathematics, UIUC
- Dimension, Hölder Classes, and a Stochastic Process
- Abstract: An elementary stochastic process is used to solve an
extremal problem on Hausdorff dimension.
- 145 Altgeld Hall, 3:00 p.m.
- COLORING THEORY RESEARCH GROUP
- Discussion of open problems
- 243 Altgeld Hall, 3:00 p.m.
- COMMUTATIVE RING THEORY RAP
- Sean Sather-Wagstaff, Department of Mathematics, UIUC
- The Homological Conjectures, cont.
- 347 Altgeld Hall, 3:00 p.m.
- GALOIS MODULES
- Professor Marcin Mazur, Department of Mathematics, UIUC
- Application of trees and Euler systems to the lifted root number
conjecture (continuation)
- 245 Altgeld Hall, 4:00 p.m.
- SPECIAL SEMINAR
- Xiuxiong Chen, Princeton University
- Extremal Kaehler metrics and Kaehler Ricci flow
- Abstract:In this talk, I will first give a brief survey of important issues
in Kaehler geometry, especially the problem of existence and uniqueness
of the extremal Kaehler metric (includes the constant scalar curvature
metric, Kaehler Einstein metric). I will also explain how my own work fit
into this big picture. In the second half of the talk, I will concentrate
on my recent work with G. Tian on Kaehler Ricci flow, where we show that
the Kahler ricci flow in Kaehler-Einstein manifolds converges to a unique
Kaehler-Einstein metric if the initial metric has positive bisectional
curvature.
Refreshments at 3:15 pm in Room 321 Altgeld Hall.
FRIDAY, FEBRUARY 2
- 243 Altgeld Hall, 4:00 p.m.
- MODEL THEORY SEMINAR
- Matthias Aschenbrenner
- Expansions of algebraically closed fields in o-minimal structures
- Abstract: We will continue to study the paper of Peterzil and Starchenko
with the same title, on the subject of developing one-variable complex
analysis in an o-minimal context.
- 314 Altgeld Hall, 4:00 p.m.
- SPECIAL SEMINAR
- Van Ha Vu, Microsoft Research
- Title and abstract to be announced
Refreshments at 3:15 pm in Room 321 Altgeld Hall.
