Alumni Conference

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9:00 - 9:30: Coffee and breakfast in 511 Lake Hall.

9:30 - 10:20: Pablo Pelaez:
Title: The Atiyah-Hirzebruch Spectral Sequence in Algebraic Geometry.

Abstract: In algebraic topology the skeletal filtration gives rise to the Atiyah-Hirzebruch spectral sequence, for complex K-theory we then get a spectral sequence with E2-term given by the singular cohomology of a space with coefficients in the K-theory of a point and converging to the K-theory of the given space.  The analogue in algebraic geometry for complex K-theory is given by Quillen's higher algebraic K-theory, the goal of the lecture is to discuss some of the endeavors to construct in algebraic geometry a cohomology theory and a spectral sequence which resemble singular cohomology and the Atiyah-Hirzebruch spectral sequence in algebraic topology.

10:30 - 11:20: Ahmet Seven:
Title: Mutation classes of skew-symmetrizable matrices

Abstract: Mutation of skew-symmetrizable matrices is a fundamental operation that first arised in Fomin-Zelevinsky's theory of cluster algebras; it also appears naturally in many different areas of mathematics. In this talk, we will discuss mutation classes of skew-symmetrizable  matrices and their graphs. In particular, we will discuss some invariants associated with these mutation classes.

11:30 - 12:00: Hanai Sadaka:
TItle: Robust Stability and Stability Radius for Linear Time Delay Systems with Multi-Structure Perturbations

Abstract: We consider the problems of robust stability and stability radius pertaining to delay systems with multi-structure perturbations. The connection between recently published results on stability robustness in the domain of time delays and robust stability with respect to structured perturbation of system matrices is investigated. We present computable stability radius formula for multi-delay systems using Rekasius substitution. Using the concepts of kernel and offspring curves, which describe the complete portrait of possible imaginary characteristic roots, the fundamental stability region is defined among a set of disjoint stability regions for two time-delay systems. This enables us to provide a necessary and sufficient condition for stability robustness of two time-delay systems with structured uncertainties in terms of two distinct linear matrix inequalities. We also report an explicit formula for stability radius of a special class of time-delay systems. Illustrative examples are included to capture the stability radius surfaces with respect to two time-delays in an arbitrary stability region.

12:30 - 2:00: Lunch in 511 Lake Hall.

2:00 - 2:30: Christopher Beasley.

2:40 - 3:10: Alexandru Suciu:
Title: Betti numbers of abelian covers

Abstract: I will discuss methods for computing the Betti numbers of abelian Galois covers of spaces.

3:20 - 3:50: Egon Schulte.
Title: Polytopes, Symmetry and Groups

Abstract: Symmetric polytopes and tessellations have been with us since before recorded history, and a strong strain of mathematics since classical times has centered on them. The modern abstract theory of polytopes and symmetry started more than 30 years ago, and since than has taken on a vigorous life. We discuss some important developments in this area.

4:00 - 4:30: Question and Answer period.