THURSDAY, APRIL 26
- ESB 6.110, 12:00 p.m.
- MATH - PHYSICS (BCDE) LUNCH SEMINAR
- Professor Daniel Grayson, Department of Mathematics, UIUC
- Intersection numbers in certain noncommutative algebras, cont.
- 241 Altgeld Hall, 1:00 p.m.
- ANALYTIC NUMBER THEORY
- John Steinig, University of Geneva
- The least common multiple of integers of the form an-bn
- 347 Altgeld Hall, 1:00 p.m.
- GROUP THEORY SEMINAR
- Professor Yevgenii Gordon
- Quantum Computation and Problems in Group theory II
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- 241 Altgeld Hall, 2:00 p.m.
- ALGEBRAIC GROUPS AND THEIR REPRESENTATIONS
- Frobenius Splitting of Sehubert Cells
- 243 Altgeld Hall, 2:00 p.m.
- ALGEBRAIC NUMBER THEORY
- to be announced
- 347 Altgeld Hall, 2:00 p.m.
- ANALYSIS SEMINAR
- Marc Rieger, Max-Planck-Institute for Mathematics in the Sciences, Leipzig
- Nonconvex Dynamical Problems
- Abstract: Many problems in continuum mechanics, especially in the
theory of elastic materials, lead to nonlinear partial differential
equations. The nonconvexity of their underlying energy potential is a
challenge for mathematical analysis, since convexity plays an
important role in the classical theories of existence and
regularity. In the last years one main point of interest was to
develop techniques to circumvent these difficulties. One approach was
to use different notions of convexity like quasi- or polyconvexity,
but most of the work was done only for static (time independent)
equations. In this talk we summarize results concerning existence and
regularity of nonconvex dynamical problems.
In the first part we give an introduction where we sketch some of the
applications (mainly from physics) for nonconvex dynamical problems and
collect some of the mathematical tools used in this field, in particular
the concept of Young measures. In the second part we present different
notions of existence to handle various nonconvex dynamical problems.
Here a focal point are elastodynamical equations, due to their interesting
applications in the material science. We prove existence of so-called
Young measure solutions for these equations. Finally we discuss
regularity questions for parabolic equations. We present a surprising
example (obtained in joint work with S. Müller and V. Sverák)
about existence of wildly oscillatory solutions for nonconvex, but
strictly quasiconvex parabolic equations.
- 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
- Per Jensen
- Projective Schemes, cont.
- 347 Altgeld Hall, 3:00 p.m.
- GALOIS MODULES
- Marcin Mazur, Department of Mathematics, UIUC
- The lifted root number conjecture, continued
- 245 Altgeld Hall, 4:00 p.m.
- MATHEMATICS COLLOQUIUM
- Almut Burchard, Department of Mathematics, University of Virginia, Charlottesville
- Rearrangement Inequalities for Multiple Integrals
- Abstract: Among all sets of a given volume, the ball has the smallest possible
surface area. Balls have many other extremal properties; for instance,
a particle performing Brownian motion will ``on average'' take more
time to leave a ball than it would take to leave any other set of the
same volume. In this talk, I will discuss a useful tool for proving
such statements: a comparison principle for multiple integrals that
was established by Brascamp, Lieb, and Luttinger (BLL) in 1977. I
would like to explain why it is true, and how it relates to
isoperimetric inequalities. Certain aspects of the BLL inequality are
not well understood, including its cases of equality and possible
extensions to curved spaces. I will conclude with some recent results
in that direction.
Refreshments at 3:15 p.m. in Room 321 Altgeld Hall
FRIDAY, APRIL 27
- 1 Illini Hall, 3:00 p.m.
- PROBABILITY AND STATISTICS SEMINAR
- Professor Karin Rosenblatt, Department of Community Health
- Cancer in Shanghai Textile Workers - Relationship With Reproductive and Contraceptive Factors
- Abstract: This seminar will describe the relationship between
reproductive and contraceptive actors and cancer in a cohort study of
267,551 female workers employed at the Shanghai Textile Industry
Bureau. Reproductive and contraceptive practices in the cohort
(eg. large use of IUDs, high frequency of induced abortions) and how
they differ from those observed in the United States will be
discussed. Relationships between these practices and all and specific
types of cancer were evaluated using Cox Proportional Hazards models.
For most associations with cancer, adjustments were made for age,
using linear splines, and number of live births. Methodologic issues
concerning epidemiologic concepts of adjustment for confounding
variables and multiple comparisons will be discussed by focusing on
relationships with colon cancer.
- 243 Altgeld Hall, 4:00 p.m.
- MODEL THEORY SEMINAR
- Rahim Moosa, UIUC
- A nonstandard Riemann existence theorem and "counter-examples
- 314 Altgeld Hall, 5:30 p.m.
- SPECIAL SEMINAR
- John Sullivan, Department of Mathematics, UIUC
- Soap-Bubble Singularities and Deltahedra
- Abstract: Over 100 years ago, Plateau observed the geometric structure of soap froths: at any corner where bubbles meet there are exactly four bubbles in a tetrahedral pattern. Plateau¹s rule was not proved until about 20 years ago; the proof relies on ruling out seven other possibilities. For instance, when we dip a wire frame cube into soapy water, the resulting soap film has four Plateau corners instead of one corner of a new type. We will examine how the eight candidates for possible corner patterns arise from the eight polyhedra with equilateral-triangle faces (these include Platonic solids as well as less familiar ones). We will also see how similar ideas can be developed in higher dimensions, where there are more possibilities for singularities (types of corners) in soap films. This talk is intended for a general audience including high school students.
