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DTSTART;TZID=America/Chicago:20250611T143000
DTEND;TZID=America/Chicago:20250611T163000
DTSTAMP:20260606T130048
CREATED:20250604T182125Z
LAST-MODIFIED:20250604T182125Z
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SUMMARY:PhD Dissertation Defense: Mr. Steffen Domke
DESCRIPTION:Convergence Of A Numerical Scheme For Optimal Stopping Of A Diffusion Over A Finite Time-Horizon\nMr. Steffen Domke\nGraduate Student\nUniversity of Wisconsin-Milwaukee \nThis dissertation establishes an approximation scheme for finite time-horizon\nstopping problems involving a singular stochastic process on a compact state\nspace\, characterized by a singular martingale problem. The stopping problem\nis converted to a linear program (LP) with infinitely many constraints and\nvariables having infinite degrees of freedom. \nTo obtain a numerical solution\, the infinite-dimensional LP is converted\ninto a finite LP. The original LP is approximated by a sequence of finite LPs\,\nlimiting to both a finite set of constraints and a finite-dimensional solution\nspace. The value of an optimal approximate solution is shown to be arbitrarily\nclose to the optimal value of original LP\, and hence of the stopping probem\,\nwith increasing refinement of the approximation. Feasibility of the approximate\nsolutions is guaranteed due weak convergence of measures\, but only in the limit.\nThe problem of pricing an American floating strike lookback call option can be\nreformulated to fit the models covered by this dissertation. The price and the\nstopping boundary can therefore be approximated using this scheme. \nAdvisor:\nRichard Stockbridge \nCommittee Members:\nDavid Spade\, Lei Wang\, Jeb Willenbring\, and Chao Zhu
URL:https://uwm.edu/math/event/phd-dissertation-defense-mr-steffen-domke/
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:20250415T153000
DTEND;TZID=America/Chicago:20250415T170000
DTSTAMP:20260606T130048
CREATED:20250324T183250Z
LAST-MODIFIED:20250421T130347Z
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SUMMARY:MS Thesis Defense: Mr. Gregor Grote
DESCRIPTION:Homomesy: Theory\, Applications\, and Explorations\nGregor Grote\nGraduate Student\nUniversity of Wisconsin-Milwaukee \nHomomesy is a phenomenon that occurs in combinatorial structures when the average value of a statistic over each orbit is the same. This talk explores the theory of homomesy for arbitrary sets\, functions\, and statistics. I provide general results about homomesy and show how these can be used to solve problems in combinatorics more efficiently. \nAdvisor:\nPamela E. Harris \nCommittee Members:\nSuzanne L. Boyd\nDavid Spade
URL:https://uwm.edu/math/event/ms-thesis-defense-mr-gregor-grote/
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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BEGIN:VEVENT
DTSTART;TZID=America/Chicago:20250227T100000
DTEND;TZID=America/Chicago:20250227T120000
DTSTAMP:20260606T130048
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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