Mathematics
http://illinois.edu/calendar/list/3024
Events hosted by the Department of Mathematics at the University of Illinois at Urbana-ChampaignMathematics in Science and Society: Olaf Sporns (Indiana University)
http://illinois.edu/calendar/detail/3024/31776181
colloquiahttp://illinois.edu/calendar/detail/3024/31776181Mon, 21 Apr 2014 14:00:00 CDTOlaf Sporns (Indiana University) will present "Computational Connectomics: Mapping and Modeling Human Brain Networks". Abstract: Recent advances in network science have greatly increased our understanding of the structure and function of many networked systems, ranging from transportation networks, to social networks, the internet, ecosystems, and biochemical and gene transcription pathways. Network approaches are also increasingly applied to the brain, at several levels of scale from cells to entire nervous systems. Early studies in this emerging field of brain connectomics have focused on mapping brain network topology and identifying some of its characteristic features, including small world attributes, modularity and hubs. More recently, the emphasis has shifted towards linking brain network topology to brain dynamics, the patterns of functional interactions that emerge from spontaneous and evoked neuronal activity. I will give an overview of recent work characterizing the structure of complex brain networks, with particular emphasis on studies demonstrating how the network topology of the connectome constrains and shapes its capacity to process and integrate information.
2:00 p.m., 1005 Beckman Institute, Monday, April 21, 2014Coble Memorial Lectures, Ian Agol (University of California, Berkeley)
http://illinois.edu/calendar/detail/3024/31776176
colloquiahttp://illinois.edu/calendar/detail/3024/31776176Mon, 05 May 2014 16:00:00 CDTThe Coble Memorial Lectures will be presented May 5-7 by Ian Agol (University of California, Berkeley). Abstract: Waldhausen conjectured in 1968 that every aspherical 3-manifold has a finite-sheeted cover which is Haken (contains an embedded essential surface). Thurston conjectured that hyperbolic 3-manifolds have a finite-sheeted cover which fibers over the circle. The first lecture will be an overview of 3-manifold topology in order to explain the meaning of Waldhausen's virtual Haken conjecture and Thurston's virtual fibering conjecture, and how they relate to other problems in 3-manifold theory. The second lecture will give some background on geometric group theory, including the topics of hyperbolic groups and CAT(0) cube complexes after Gromov, and explain how the above conjectures may be reduced to a conjecture of Dani Wise in geometric group theory. The third lecture will discuss the proof of Wise's conjecture, that cubulated hyperbolic groups are virtually special, and some discussion of a new proof of Wise's Malnormal Special Quotient Theorem. Part of these results are joint work with Daniel Groves and Jason Manning.Coble Memorial Lectures, Ian Agol (University of California, Berkeley)
http://illinois.edu/calendar/detail/3024/31776177
colloquiahttp://illinois.edu/calendar/detail/3024/31776177Tue, 06 May 2014 16:00:00 CDTThe Coble Memorial Lectures will be presented May 5-7 by Ian Agol (University of California, Berkeley). Abstract: Waldhausen conjectured in 1968 that every aspherical 3-manifold has a finite-sheeted cover which is Haken (contains an embedded essential surface). Thurston conjectured that hyperbolic 3-manifolds have a finite-sheeted cover which fibers over the circle. The first lecture will be an overview of 3-manifold topology in order to explain the meaning of Waldhausen's virtual Haken conjecture and Thurston's virtual fibering conjecture, and how they relate to other problems in 3-manifold theory. The second lecture will give some background on geometric group theory, including the topics of hyperbolic groups and CAT(0) cube complexes after Gromov, and explain how the above conjectures may be reduced to a conjecture of Dani Wise in geometric group theory. The third lecture will discuss the proof of Wise's conjecture, that cubulated hyperbolic groups are virtually special, and some discussion of a new proof of Wise's Malnormal Special Quotient Theorem. Part of these results are joint work with Daniel Groves and Jason Manning.Coble Memorial Lectures, Ian Agol (University of California, Berkeley)
http://illinois.edu/calendar/detail/3024/31776178
colloquiahttp://illinois.edu/calendar/detail/3024/31776178Wed, 07 May 2014 16:00:00 CDTThe Coble Memorial Lectures will be presented May 5-7 by Ian Agol (University of California, Berkeley). Abstract: Waldhausen conjectured in 1968 that every aspherical 3-manifold has a finite-sheeted cover which is Haken (contains an embedded essential surface). Thurston conjectured that hyperbolic 3-manifolds have a finite-sheeted cover which fibers over the circle. The first lecture will be an overview of 3-manifold topology in order to explain the meaning of Waldhausen's virtual Haken conjecture and Thurston's virtual fibering conjecture, and how they relate to other problems in 3-manifold theory. The second lecture will give some background on geometric group theory, including the topics of hyperbolic groups and CAT(0) cube complexes after Gromov, and explain how the above conjectures may be reduced to a conjecture of Dani Wise in geometric group theory. The third lecture will discuss the proof of Wise's conjecture, that cubulated hyperbolic groups are virtually special, and some discussion of a new proof of Wise's Malnormal Special Quotient Theorem. Part of these results are joint work with Daniel Groves and Jason Manning.