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DTSTART;TZID=America/Chicago:20241101T123000
DTEND;TZID=America/Chicago:20241101T133000
DTSTAMP:20260420T153654
CREATED:20241022T141444Z
LAST-MODIFIED:20241022T144645Z
UID:10016189-1730464200-1730467800@uwm.edu
SUMMARY:Graduate Student Colloquium: Kim Harry
DESCRIPTION:A q-analog of Kostant’s Weight Multiplicity Formula and a Product of Fibonacci Numbers\nKim Harry\nPhD Graduate Student\nUniversity of Wisconsin-Milwaukee \nUsing Kostant’s weight multiplicity formula\, we describe and enumerate the terms contributing a nonzero value to the multiplicity of a positive root µ in the adjoint representation of sl_{r+1}(C)\, which we denote L(˜α)\, where ˜α is the highest root of sl_{r+1}(C). We prove that the number of terms contributing a nonzero value to the multiplicity of the positive root µ = α_i + α_i+1 + · · · + α_j with 1 ≤ i ≤ j ≤ r in L(˜α) is given by the product F_i · F_(r−j+1)\, where F_n is the nth Fibonacci number. Using this result\, we show that the q-multiplicity of the positive root µ = α_i + α_i+1 + · · · + α_j with 1 ≤ i ≤ j ≤ r in the representation L(˜α) is precisely q^{r−h(µ)}\, where h(µ) = j − i + 1 is the height of the positive root µ. Setting q = 1 recovers the known result that the multiplicity of a positive root in the adjoint representation of sl_{r+1}(C).
URL:/math/event/graduate-student-colloquium-kim-harry/
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
X-TRIBE-STATUS:
GEO:43.0758771;-87.8858312
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Chicago:20241101T140000
DTEND;TZID=America/Chicago:20241101T153000
DTSTAMP:20260420T153654
CREATED:20240826T192228Z
LAST-MODIFIED:20241025T170950Z
UID:10016170-1730469600-1730475000@uwm.edu
SUMMARY:Colloquium: aBa Mbirika & Morgan Fiebig
DESCRIPTION:A graphical approach to the Fibonacci sequence (Fn) n≥0 modulo m extended to the Lucas sequences (Un(p\,q))n≥0 and (Vn(P\,q))n≥0\naBa Mbirika & Morgan Fiebig\nUniversity of Wisconsin – Eau Claire \nThe goal of this talk is twofold: (1) extend theory on statistics in the Fibonacci and Lucas sequences modulo m to the Lucas sequences U :=(Un(p\,q))n≥0 and V :=(Vn(p\,q)n 0\, and (2) apply this theory to a novel graphical approach of U and V modulo m. The statistics we explore are the period π(m)\, entry point e(m)\, and order ω(m) := pi(m)/e(m). We generalize a wealth of known Fibonacci and Lucas statistical results to the U and V setting. Based on ω(m)\, we describe behaviors shared by infinite families of nondegenerate U and V sequences with parameters q = ± 1. In our graphical approach we place the cycle of repeating terms of the periods of U and V in a circle\, and patterns which would otherwise be overlooked emerge. In particular\, we exhibit some tantalizing examples in the following three sequence pairs: Fibonacci and Lucas\, Pell and associated Pell\, and\, balancing and Lucas-balancing. Our proofs utilize results from primary sources ranging from the ground-breaking papers of Lucas in 1878 and Carmichael in 1913\, to the seminal works of Wall in 1960 and Vinson in 1963\, amongst others.
URL:/math/event/colloquium-aba-mbirika/
CATEGORIES:Colloquia
X-TRIBE-STATUS:
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Chicago:20241115T123000
DTEND;TZID=America/Chicago:20241115T133000
DTSTAMP:20260420T153654
CREATED:20241113T152405Z
LAST-MODIFIED:20241113T164702Z
UID:10016191-1731673800-1731677400@uwm.edu
SUMMARY:Graduate Student Colloquium: Eric Redmon
DESCRIPTION:Finite State Machines and Bounded Permutations\nEric Redmon\nGraduate Student\nMarquette University \nWe define a k-bounded permutation π of length n to be a permutation such that for each pair of adjacent entries $\pi$ and $\pi(i + 1)$ for $i = 1\, 2\, 3\, . . . \, n − 1$ we have $|\pi(i) − \pi(i + 1)| \leq k$. Previous work has shown that the generating function for this family of permutations is rational\, and has computed generating functions for small values of $k$. In this talk\, we will discuss the nature of finite state machines and how we can leverage the insertion encoding devised by Albert\, Linton\, and Ruškuc to build a finite state machine that we can use to find generating functions for larger values of $k$.
URL:/math/event/graduate-student-colloquium-eric-redmon/
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
X-TRIBE-STATUS:
GEO:43.0758771;-87.8858312
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Chicago:20241115T140000
DTEND;TZID=America/Chicago:20241115T153000
DTSTAMP:20260420T153654
CREATED:20240826T192945Z
LAST-MODIFIED:20241029T133524Z
UID:10016171-1731679200-1731684600@uwm.edu
SUMMARY:Colloquium: Dr. Lei Hua
DESCRIPTION:Unified Tail Dependence Measures and Its Applications in High-Frequency Financial Data\nDr. Lei Hua\nAssociate Professor\, Director of Statistical Consulting Service\nNorthern Illinois University \nIn this presentation\, I will first motivate the necessity for a unified tail dependence measure\, followed by an examination of the theoretical framework for developing such measures utilizing random variables characterized by regularly varying tails. Specific instances that result in unified tail dependence measures applicable in practical scenarios will be demonstrated. Ultimately\, I will explore the application of the unified tail dependence measure in the analysis of high-frequency financial market data and discuss novel empirical insights from financial markets.
URL:/math/event/colloquium-nick-mayers/
CATEGORIES:Colloquia
X-TRIBE-STATUS:
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Chicago:20241122T123000
DTEND;TZID=America/Chicago:20241122T133000
DTSTAMP:20260420T153654
CREATED:20241030T170149Z
LAST-MODIFIED:20241119T221438Z
UID:10016190-1732278600-1732282200@uwm.edu
SUMMARY:Colloquium: Nick Mayers
DESCRIPTION:  \nWell-Behaved Kohnert Posets\nDr. Nicholas Mayers\nPostdoctoral Research Scholar\nNorth Carolina State University \nKohnert polynomials form a family of polynomials indexed by diagrams that consist of unit cells arranged in the first quadrant. Many families of well-known polynomials have been shown to be examples of Kohnert polynomials\, including key\, Schur\, and Schubert polynomials. Given a diagram D\, the monomials occurring in the corresponding Kohnert polynomial encode diagrams formed from D by applying sequences of certain moves\, called “Kohnert moves\,” each of which alters the position of at most one cell. In this talk\, we focus on the underlying sets of diagrams which generate the monomials of Kohnert polynomials. With each such collection of diagrams\, one can associate a poset structure which is known to not\, in general\, be well-behaved. In particular\, the corresponding “Kohnert posets” generally do not have a unique minimal element\, are not ranked\, and are not lattices. Here\, we will focus on recent attempts to find conditions under which Kohnert posets are well-behaved in the sense that they have a unique minimal element\, are ranked\, or are EL-Shellable. No background knowledge concerning posets is assumed.
URL:/math/event/colloquium-nick-mayers-2/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
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