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DTSTAMP:20260615T203650
CREATED:20240411T201711Z
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SUMMARY:Colloquium: Prof. Roger Howe
DESCRIPTION:Mathematics around the Heisenberg Group\nProf. Roger Howe\nProfessor Emeritus\nYale University \nIn the mid 1920s\, Werner Heisenberg formulated the CCR – canonical commutation relations – describing the relationship between the operations of measuring position and of measuring momentum of a particle in quantum mechanics. These have been fundamental to the later\, dramatically successful development of subatomic physics. Shortly after Heisenberg’s work\, Hermann Weyl pointed out that the CCR defined the relations of a Lie algebra\, whose associated group is a two-step nilpotent group with one dimensional center. Today\, this group (and its increasingly large set of cousins) is known as the “Heisenberg group”. Over the remainder of the 20th century\, appreciation grew of the fundamental role of the Heisenberg group in disparate mathematical topics\, including harmonic analysis\, partial differential equations\, invariant theory and representation theory\, in both finite and infinite dimensions. This talk will review and attempt to summarize some of the manifold connections between these topics that are mediated by the Heisenberg group
URL:https://uwm.edu/math/event/colloquium-prof-roger-howe/
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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DTSTART;TZID=America/Chicago:20240426T100000
DTEND;TZID=America/Chicago:20240426T120000
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SUMMARY:PhD Dissertation Defense: Mr. William Braubach
DESCRIPTION:Coarse Homotopy Extension Property and its Applications\nMr. William Braubach\nUniversity of Wisconsin-Milwaukee \nA pair (X\, A) has the homotopy extension property if any homotopy of A can be extended to a homotopy of X. The main goal of this dissertation is to define a coarse analog of the homotopy extension property for coarse homotopies and prove coarse versions of results from algebraic topology involving this property.\nFirst\, we define a notion of a coarse adjunction metric for constructing coarse adjunction spaces. We use this to redefine coarse CW complexes and to construct a coarse version of the mapping cylinder. We then prove various pairs of spaces have the coarse homotopy extension property. In particular\, pairs of coarse CW complexes. We then prove results involving the coarse homotopy extension property\, leading to the result that a coarse map f from X into Y is a coarse homotopy equivalence if and only if the coarse mapping cylinder coarse deformation retracts onto its copy of X. We use this to prove our main result\, a coarse version of Whitehead’s Theorem: If a cellular coarse map f between coarse CW complexes induces isomorphisms between coarse homotopy groups\, then f is a coarse homotopy equivalence. \nAdvisor: Prof. Boris Okun \nCommittee Members:\nProfs. Boris Okun\, Craig Guilbault\, Jeb Willenbring\, Jonah Gaster\, and Chris Hruska
URL:https://uwm.edu/math/event/phd-dissertation-defense-mr-william-braubach/
LOCATION:EMS Building\, Room E425\, E425; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Defenses
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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DTSTART;TZID=America/Chicago:20240426T123000
DTEND;TZID=America/Chicago:20240426T133000
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CREATED:20240422T160442Z
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SUMMARY:Graduate Student Colloquium: Alex Moon
DESCRIPTION:Counting Orbits of Defective Parking Functions\nAlex Moon\nPhD Student\nUniversity of Wisconsin-Milwaukee \nParking functions are well-studied objects in combinatorics and representation theory which constitute tuples of preferred parking spots for cars under a linear parking scheme. This talk will generalize to defective parking functions. I will enumerate the orbits of defective parking functions under the action of the symmetric group by characterizing them as nondecreasing tuples and sketching a bijection to standard nondecreasing parking functions. I will also introduce the concept of the conjugate of a nondecreasing parking function in order to simplify the case where the number of cars and spots differ. \nThis is a joint with Pamela E. Harris\, Aaron Ortiz\, Lauren J. Quesada\, Cynthia Marie Rivera Sánchez\, and Dwight A. Williams II.
URL:https://uwm.edu/math/event/graduate-student-colloquium-alex-moon/
LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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DTSTART;TZID=America/Chicago:20240426T140000
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SUMMARY:Colloquium: Fredric Ancel
DESCRIPTION:
URL:https://uwm.edu/math/event/colloquium-fredric-ancel/
LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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