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DTSTART;TZID=America/Chicago:20250404T140000
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DTSTAMP:20260419T011951
CREATED:20250325T233420Z
LAST-MODIFIED:20250325T233420Z
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SUMMARY:Colloquium: Dr. Suzanne Boyd
DESCRIPTION:Polynomial-time Computability of the Julia Set for Polynomial Skew Products of Two Complex Variables\nDr. Suzanne Boyd\nAssociate Professor\nUniversity of Wisconsin-Milwaukee \nIngrained in the modern study of dynamical systems is the use of computer experiments for revelation and illustration. In this talk\, I will explain a polynomial-time computer algorithm for approximating the Julia set of a polynomial skew product of two complex variables. I will begin by defining the involved terms\, including computability\, Julia set\, and polynomial skew product. This work is joint with Christian Wolf. It relies on some my previous work on designing and implementing rigorous computer algorithms to confirm results of the experimental observations on the dynamics of polynomial maps of two complex variables\, including polynomial skew products. These algorithms are designed to locate a neighborhood of the chain recurrent set\, build a model of the dynamics of the map on this set\, and attempt to determine hyperbolicity (or Axiom A) of the map on its chain recurrent set.
URL:/math/event/drsuzanneboyd/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
X-TRIBE-STATUS:
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DTSTART;TZID=America/Chicago:20250417T130000
DTEND;TZID=America/Chicago:20250417T140000
DTSTAMP:20260419T011951
CREATED:20250114T155559Z
LAST-MODIFIED:20250312T210355Z
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SUMMARY:Marden Colloquium: Dr. Trachette Jackson
DESCRIPTION:Agent-based Modeling of Dysregulated Cell Signaling and the Tumor-Immune Landscape Predicts New Possibilities for Combination Therapy\nDr. Trachette Jackson\nProfessor of Mathematics and Associate Vice President for Research – Strategic Partnerships and Inclusive Excellence\nUniversity of Michigan \nMathematical models\, specifically agent-based models (ABMs)\, have shown recent successes in uncovering the multiscale dynamics that shape the trajectory of cancer. They have enabled the optimization of treatment methods and the identification of novel therapeutic strategies. To assess the combined effects on tumor growth and the immune response of monoclonal antibodies that boost the immune system (immunotherapy) and small molecule inhibitors (SMI) that counteract the effect of driver mutations\, we build and analyze an ABM that captures key facets of tumor heterogeneity and immune cell dynamics\, their spatial interactions\, and their response to therapeutic pressures. Our model predicts that under certain conditions\, immunotherapy alone is optimal; in others\, immunotherapy followed by mutation-targeted therapy is best. These results suggest that optimal treatment depends on the strength of cellular signaling pathways and highlight the need to quantify mutation-dependent cell signaling and the fitness advantage conferred on cancer cells harboring these mutations.
URL:/math/event/marden-colloquium-dr-trachette-jackson/
LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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DTSTAMP:20260419T011951
CREATED:20250113T161237Z
LAST-MODIFIED:20250421T135206Z
UID:10016200-1745589600-1745593200@uwm.edu
SUMMARY:Colloquium: Prof. Caroline Terry
DESCRIPTION:Measuring Combinatorial Complexity via Regularity Lemmas\nProf. Caroline Terry\nAssociate Professor\nUniversity of Illinois-Chicago \nMany tools have been developed in combinatorics to study global structure in finite graphs. One such tool is called Szemerédi’s regularity lemma\, which gives a structural decomposition for any large finite graph. Beginning with work of Alon-Fischer-Newman\, Lovász-Szegedy\, and Malliaris-Shelah\, it has been shown over the last 15 years that regularity lemmas can be used to detect structural dichotomies in graphs\, and that these dichotomies have deep connections to model theory. One striking example is a dichotomy in the size of regular partitions\, first observed by Alon-Fox-Zhao. Specifically\, if a hereditary graph property H has finite VC-dimension\, then results of Alon-Fischer-Newman and Lovász-Szegedy imply all graphs in H have regular partitions of size polynomial is 1/ε. On the other hand\, if H has infinite VC-dimension\, then results of Gowers and Fox-Lovász show there are graphs in H whose smallest 1/ε-regular partition has size at least an exponential tower of height polynomial in 1/ε. In this talk\, I present several analogous dichotomies in the setting of hereditary properties of 3-uniform hypergraphs.
URL:/math/event/colloquium-caroline-terry/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
X-TRIBE-STATUS:canceled
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