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DTSTART;TZID=America/New_York:20260116T160000
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DTSTAMP:20260113T201232Z
CREATED:20260113T201229Z
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SUMMARY:ANTCoG seminar: Talia Fernós
DESCRIPTION:Talia Fernós\, Visiting Professor at Vanderbilt University and Professor in the Department of Mathematics at University of North Carolina\, Greensboro (on leave) \n\n\n\n \n\n\n\nTitle: The semi-simple theory of acylindricity in higher-rank \n\n\n\nAbstract:  \n\n\n\nAcylindricity may be viewed as a generalization of being a uniform lattice in a locally compact second countable group. The recent surge of results concerning acylindrical actions on hyperbolic spaces demonstrates the utility of the property. Trees are of course examples of hyperbolic spaces\, and by considering products\, we start to see new and interesting behaviors that are not present in rank-1\, such as the simple Burger-Mozes-Wise lattices\, or Bestvina-Brady kernels.  \n\n\n\nIn a joint worth with S. Balasubramanya we introduce a new class of nonpositively curved groups. Viewing the theory of S-arithmetic semi-simple lattices as inspiration\, we extend the theory of acylindricity to higher rank and consider finite products of delta-hyperbolic spaces. The category is closed under products\, subgroups\, and finite index over-groups. Weakening acylindricity to AU-acylindricity (i.e. acylindricity of Ambiguous Uniformity) the theory captures all S-arithmetic semi-simple lattices with rank-1 factors\, acylindrically hyperbolic groups\, colorable HHGs\, and many others.  \n\n\n\nIn this talk\, we will discuss the Tits’ alternative and deduce that a group G that admits an (unbounded) AU-acylindrical action on such a product is “semi-simple” from the point of Out(G)\, thereby giving a partial resolution to a recent conjecture by Sela.
URL:https://mathstats.uncg.edu/event/antcog-seminar-talia-fernos/
CATEGORIES:Colloquia
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DTSTART;TZID=America/New_York:20260128T160000
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DTSTAMP:20260324T190520Z
CREATED:20260113T192339Z
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SUMMARY:Helen Barton Lecture: "Optimal Transport and Topological Data Analysis for single-cell biology"
DESCRIPTION:Professor Zixuan Cang\, North Carolina State University \n\n\n\nTitle: “Optimal Transport and Topological Data Analysis for single-cell biology” \n\n\n\nAbstract: Single-cell and spatial transcriptomics data examines high-throughput gene expression profiles at fine resolutions providing an unprecedented opportunity to elucidate the underlying complex biological processes. Optimal transport and Topological Data Analysis has proven to be an effective tool for exploiting complex structures in high-dimensional data. In this talk\, we will discuss several optimal transport variants motivated by the biological applications\, where there are detailed application-specific constraints\, multiple distribution species\, and multiple embedding spaces of the same system. We will illustrate the applications of these tools for addressing multi-compatible molecular species in cell-cell communication analysis and devising coherent trajectories of the same biological system from multi-omics datasets. We will also discuss some applications of topological data analysis to single-cell data analysis.
URL:https://mathstats.uncg.edu/event/10051/
LOCATION:Petty Science Building Room 150\, 317 College Ave\, Greensboro\, North Carolina\, 27412
CATEGORIES:Helen Barton Lecture Series
ATTACH;FMTTYPE=image/png:https://mathstats.uncg.edu/wp-content/uploads/2026/01/Zixuan-Cang.png
ORGANIZER;CN="UNCG Mathematics & Statistics Department":MAILTO:mathstats@uncg.edu
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