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DTSTART;TZID=America/Chicago:20250227T100000
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DTSTAMP:20260614T103758
CREATED:20250226T135546Z
LAST-MODIFIED:20250226T135546Z
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SUMMARY:PhD Dissertation Defense: Kimberly Harry
DESCRIPTION:Kostant’s Formula and Parking Functions: Combinatorial Explorations\nKimberly Harry\nUniversity of Wisconsin-Milwaukee \nWe let L(λ) denote the irreducible highest weight representation of the classical simple Lie algebra g with highest weight λ. Kostant’s weight multiplicity formula gives a way to compute the multiplicity of a weight µ in L(λ)\, denoted m(λ\, µ)\, via an alternating sum over the Weyl group whose terms involve the Kostant partition function. The Weyl alternation set A(λ\, µ) is the set of Weyl group elements that contribute nontrivially to the multiplicity m(λ\, µ). We prove that Weyl alternation sets are order ideals in the weak Bruhat order of the Weyl group. Specializing to the Lie algebra of type A\, we prove that the Weyl alternation sets A(˜α\, µ)\, where ˜α is the highest root of sl_{r+1}(C) and µ is a positive root is a product of Fibonacci numbers. Using this result\, we show that the q-multiplicity of the positive root in the representation L(˜α) is precisely a power of q. We give a complete characterization of the Weyl alternation sets A(˜α\, µ)\, where µ is now a negative root of sl_{r+1}(C). We also show that the cardinality of these Weyl alternation sets satisfies a two-term recurrence relation involving Fibonacci numbers. Time permitting I will present further results related to collaborative projects I have contributed to during my years at UWM. \nAdvisor: Pamela E. Harris \nCommittee Members:\nProfs. Jeb Willenbring\, Kevin McLeod\, Gabriella Pinter\, and Jonah Gaster
URL:https://uwm.edu/math/event/phd-dissertation-defense-kimberly-harry/
LOCATION:EMS Building\, Room W434\, W434; 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:20250228T123000
DTEND;TZID=America/Chicago:20250228T133000
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CREATED:20250226T142543Z
LAST-MODIFIED:20250226T142543Z
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SUMMARY:Graduate Student Colloquium: Matt McClinton
DESCRIPTION:Fractal Geometry and Non-Integer Dimensions\nMatt McClinton\nPhD Graduate Student\nUniversity of Wisconsin-Milwaukee \nPopularized in the 1980s\, fractals have become something of a household name. These fractal sets often demonstrate peculiar topological properties. One such property is the notion of a fractal dimension. Sets such as the Cantor set\, Sierpinski Gasket (SG)\, and the von Koch curve are traditionally visualized in 2D images. However\, these sets actually exist in-between dimensions 1 and 2! \nCertain fractals can be built using what is known as an Iterated Function System (IFS)\, and there is a powerful theorem stating that having an IFS representation of a fractal provides a simple means of determining the fractal dimension. I will begin by stating the IFS that generates the Sierpinski Gasket. There are two transformations on the Gasket to which creates the Level-n Stretched Sierpinski Gasket (SSG^n). I will demonstrate how one constructs the IFS for SSG^n\, as well as provide the highlights to a theorem in which I prove the fractal dimension of SSG^n.
URL:https://uwm.edu/math/event/graduate-student-colloquium-matt-mcclinton-2/
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:20250228T140000
DTEND;TZID=America/Chicago:20250228T150000
DTSTAMP:20260614T103758
CREATED:20250114T154837Z
LAST-MODIFIED:20250210T190030Z
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SUMMARY:Colloquium: Prof. Alastair Fletcher
DESCRIPTION:Infinitesimal Spaces of Quasiregular Mappings\nProf. Alastair Fletcher\nProfessor of Mathematical Sciences and Director of Undergraduate Studies\nNorthern Illinois University \nHow can we differentiate functions which are not differentiable? In the context of quasiregular mappings\, a generalization of holomorphic functions where now infinitesimal circles are mapped to infinitesimal ellipses\, there is a satisfactory answer to this question given by infinitesimal spaces. In this talk\, we will survey these objects and discuss some ongoing work with relevance to the Decomposition Problem for bi-Lipschitz maps.
URL:https://uwm.edu/math/event/alastair-fletcher/
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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