Invited Speakers
Titles and Abstracts
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Elizabeth Gross
University of Hawai`i at Mānoa, USA 
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Computational algebraic geometry for evolutionary biologyAbstract: Abstract: A main goal of phylogenomics is to understand the evolutionary history of a set of species. These histories are represented by directed graphs where the leaves represent living species and the interior nodes represent extinct species. While it is common to assume the evolutionary history is a tree, when events such as hybridization are present, networks are more realistic. However, allowing for networks, rather than simply trees, complicates the process of inference. One recent approach to phylogenetic network inference is rooted in computational algebraic geometry. In this talk, we discuss the role computational algebraic geometry and symbolic computation has played in the statistical problems related to network inference with a focus on problems related to identifiability and model selection. |
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Erich L. Kaltofen
North Carolina State University and Duke University, USA 
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Encounters in Symbolic Computation: Ideas for the AgesAbstract: I will describe my encounters with several people and research problems during my career. I will give some new twists to known results and resulting open problems in symbolic computation, whose solution I have attempted and which I would like to see solved. |
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Daniel Roche
United States Naval Academy, USA 
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Corrigimus, verificamus, vincimus: Ensuring algorithmic accuracy in an age of uncertaintyAbstract: For nearly as long as it has been developing fast heuristic, approximate, and randomized algorithms, the computer algebra community has also been keen to produce methods by which we can verify accuracy and even correct a small number of errors. These routines are much more efficient than trivially recomputing the result, but are often themselves randomized and can be wrong with controllably small probability. Nonetheless, provable probabilistic correctness is useful when running code on unreliable or cloud-based hardware, or when the original computation relies on unproven heuristics. The latter case may be increasingly relevant in the coming years as the code produced by generative AI models continues to improve in quality and inevitably makes its way into production. We will examine a few recent methods for interactive verification and error correction for some basic problems in linear algebra, pointing out connections and differences to related work from the coding theory and applied cryptography communities. |